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发表于 2008/4/26 16:46:54

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【音频测试基础知识】加权滤波器

A-weighting in detail

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A, B, C and D weighting


The A-weighting curve is one of a set of four, defined in various standards relating to sound level measurement as A, B, C, and D. Curves A, B and C are for low, medium and high loudness sounds. D is specifically for measuring very loud aircraft noise.

The A-weighing curve is based on the 40-phon equal-loudness contour for typical human hearing, being a rough approximation of that curve after inversion to indicate gain rather than level. Although our absolute threshold of hearing is around 0 Phons, this is a very quiet level indeed, and only realised in specially isolated conditions. 40 phon is the sort of level likely to exist in a normal quiet environment.

While early experimenters had to approximate roughly in order that the A-weighing curve could be realised economically in a filter that did not need too many components, today we could easily realise the true curve. This has not been done, but a revision is arguably overdue, especially as the A-weighting curve is not defined above 20kHz and fails to reflect the steep cut-off in our hearing above 15kHz which is also not made clear by the equal loudness contours, which aim to quantify only our in-band response. Unless the A-weighting filter is used in conjunction with a band-limiting filter cutting off above 20kHz, it cannot be used with any validity for loudness measurement, since ultrasonic noise from many sources can affect the measurement – a fact that is usually overlooked. More damning though, is the fact that equal loudness contours are now known to be invalid for noise measurement, even though this what sound level meters incorporating A-weighting are mostly used for! The later ITU-R weighting curve should therefore be considered for all noise measurement purposes, though this is currently only used in broadcasting and professional audio, and is not usually incorporated into sound level meters.

2 Equal-loudness contours

In 1933 Fletcher and Munson (1933) investigated the variation in apparent loudness of sounds with frequency and found that they needed to plot a set of 'equal loudness' contours, because the ear’s frequency response varied with loudness level. They presented volunteer subjects with pure tones at various frequencies, and asked them to adjust the level until they judged each tone to sound equal in loudness to a 1kHz reference tone. Then they repeated the experiment with different levels of reference tone. This revealed that our ears are much less sensitive to low frequency sounds, especially at low levels. Robinson and Dadson repeated the experiment in 1956, and obtained somewhat different results, which were considered to be more accurate, and became the basis for the ISO standard, ISO226 until modern experiments began to cast doubt on their validity, resulting in a survey by the International Standards Organisation. This led to the release, in 2003, of a new standard: ISO 226:2003, which was derived from the reported results of various experimenters. The graphs shown here compare first the Fletcher-Munson and then the Robinson-Dadson results with the modern curves, and it can be seen that while the former appear to be badly out at high levels in the low-frequency region they are in quite good agreement at low levels. The Robinson-Dadson curves, which until 2003 formed the basis for ISO226, differ significantly, showing around 12dB greater sensitivity in the region around 150Hz. The recent ISO survey report commented that it was fortunate that the 40-phon contour of Fletcher and Munson, on which the A-weighting filter was based, does agree quite well with the new ISO226 standard.

3 Possible errors

The reasons for these discrepancies appear not to have been investigated, but several factors make the experiment very difficult. Firstly, loudness is only a subjective quality, and it is quite hard to say when two tones at different frequencies sound equally loud. This is especially true at frequencies below 100Hz where we sense the sound less as a tone and more as a feeling.

Then there is the difficulty of providing an undistorted sound source of known level. Even today, most loudspeakers have at least one percent of harmonic distortion at most frequencies, and very few indeed would be able to achieve even this at 20Hz and 100dB SPL. Fletcher and Munson used headphones, but in 1933 most headphones had poor low-frequency response, and it seems likely that what their subjects were hearing below 100Hz consisted mostly of higher harmonics, which would explain their apparently superior sensitivity at high levels. The steep slope of the curves at low frequencies means of course that we are very sensitive to harmonics, and it is now well known that our brains even have the special ability to ‘postulate’ a missing fundamental, so that we think we hear the fundamental even when it is not there, a phenomenon that makes small loudspeakers sound more acceptable than they otherwise would!

Robinson and Dadson used loudspeakers for their experiment, and one can only wonder at how they managed to generate a flat distortion-free level of 125dB SPL at 20Hz in 1956 (if they did)! Their results show an almost level response from 1kHz down to 200Hz compared to a 10dB loss of sensitivity on the modern ISO 226 curve, in a region that poses no special difficulties for loudspeaders. It is possible that a room resonance or reinforcing reflection off the floor caused the apparent increase in sensitivity around 150Hz, because today a large room surrounded by absorbent wedges on all sides, together with a false floor supporting the listener, would be necessary to avoid such effects. However, one would expect them to have been fully aware of these problems, which would also be expected to cause anomalies at lower frequencies.

To confuse matters, my own tests using headphones, carefully calibrated using an in-ear microphone, on my own ears, show no fall in sensitivity at 200Hz! Were Robinson and Dadson right after all, and if so why the discrepancy in the new ISO 226 curve? One explanation I can suggest is that the ear’s low frequency response depends on the tautness of the eardrum, which is governed by the stapedius and tensor timpani muscles, which tense under loud conditions, and remain tensed for hours and even days. Several modern studies were by Japanese researchers. Could it be that their subjects were adapted to noisy city life, and not kept in quiet conditions for several days prior to and during testing?

Another problem that arises when trying to generate very high levels at low frequencies for these experiments is the need for an extremely low level of amplifier noise, because any hiss is not masked by the tone, and so must be kept 125dB or more below the tone if it is to be inaudible. This is just about impossible today, and inconceivable in the days of valves (vacuum tubes), though a possible way round the problem is to use an acoustic filter during the low-frequency tests (such as a quilt hung in front of the loudspeaker!).

4 Frontal versus side presentation

A complicating factor in the derivation of equal-loudness contours is the fact that our ears have a different frequency response in every direction. This becomes increasingly true above about 2kHz, and does not affect low frequencies, being caused by head-masking and the complicated shape of the outer ear, or pinna.

Very low frequencies pass around the head and are sensed equally by each ear purely as pressure variation, but as the wavelength of a sound becomes comparable with the dimensions of our head (1kHz equates to 320mm or roughly 1 foot) this starts to get in the way so that each ear becomes progressively less sensitive to sound from its opposite side as frequency increases. At still higher frequencies the outer ear begins to focus the sound, forming a cavity with various resonances that are excited to varying degrees by sounds from different directions, in both the horizontal and vertical planes. These two mechanisms, both involving difference in loudness between the ears are used by the brain to enable us to locate the direction of sounds in both the horizontal and vertical planes, along with another mechanism which uses the different time-of arrival at each ear, or phase difference, to determine direction. The latter mechanism takes over in the lower 100Hz to 2kHz region, and is made use of in stereo reproduction, though it cannot give us information about sounds originating above or behind us where the pinna comes into effect.

Head masking and pinna effects have been quantified in terms of another set of contours referred to as ‘Head-related transfer functions’, which also vary considerably between individuals at high frequencies. They are relevant to the determination of equal-loudness contours because we are considerably more sensitive to high frequency sound coming directly from each side, as in headphone listening, than to sound from a single loudspeaker at centre-front, with stereo presentation from two speakers at 60 degrees separation coming somewhere in between. Modern equal-loudness contours are for frontal presentation, but although Fletcher and Munson used headphones, the ISO survey lists their experiment as using ‘compensated headphones’. Most modern headphones intended for listening to stereo are in fact designed with a severe dip in their response around 3-10kHz, without which they would sound too bright; a fact that is not commonly recognised.

5 Towards a better noise-weighting standard

A modern version of A-weighting might be expected to take the form of the inverse 40-phon ISO 226 curve, as shown here compared to both the traditional A-weighting curve and the later ITU-R 468 weighting. This is not necessarily the best shape for it though, because above 2kHz each ISO curve is the result of averaging results from many individuals, some of whom have dips where others have peaks. A more sensible approach would therefore be to plot the results for many individuals and then draw a smooth curve through the maxima, since for noise measurement purposes we are more interested in what someone might hear than in what one person does not hear. We might then choose to err on the high side (by perhaps 6dB) around 6kHz, because it is now known that we are most sensitive to random noise in this region, as reflected in the ITU-R 468 weighting curve, and in practice environmental noise tends to be part tonal (music and some machinery) and part random (wind noise, traffic, and machinery).

Sound level meters currently use rms detection, which would be reasonable if our perception of loudness was related to power, but it in not. A series of clicks or tone-bursts sound almost as loud as the continuous sound, provided that the gaps between them are not too long, showing that our perception of loudness has more to do with peak level than average or rms. As the duration of a tone-burst is reduced below about 50ms, however, is starts to sound progressively quieter, showing that our ears take time to respond in each frequency band. To be perceptually valid therefore, sound level and noise level measurements must use some form of ‘quasi-peak’ detector with carefully devised integration times, as is the case with the ITU-R 468 standard. The traditional sound-level meter with traditional A-weighting is therefore starting to look rather irrelevant for all practical purposes.

6 Computed noise-measurement

Better still would be a system that aimed to model our hearing characteristics using a bank of overlapping narrow-band filters, with varying bandwidths, spaced across the audible spectrum. Their outputs would be combined using an algorithm that also incorporated quasi-peak detection and non-linearity to produce a result that remained reasonably valid for all types of sound at all levels. This need not be too difficult using modern digital processing, and would be relevant for all applications, from environmental and aircraft noise measurement to measurements on audio systems and telephone networks.

o-o-o-o-o-o-o-o-o-o-o-o-o-o

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发表于 2008/4/26 16:14:36

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【音频测试基础知识】PMPO音乐功率真相

True vs 'PMPO' Power

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1 Introduction

The term '''audio power''' is used in the specification or measurement of audio amplifiers or loudspeakers. A meaningful and reliable measure of the power output of an audio amplifier, or the power handling of a loudspeaker is ''continuous sine wave power'', or more strictly 'continuous average sine wave power'. Such a figure will often be found in advertising literature referred to as "true RMS power", but this is quite incorrect. Although there is such a thing as RMS (root mean square) power, it is neither useful as a measurement nor what is intended by those who use the term. The sine wave power is found by averaging the instantaneous power output over a long period of time (or one complete cycle), so it is actually the ''average power'' or ''mean power''. The term RMS is used mistakenly due to the fact that the mean power is calculated from the RMS voltage and current (or one of them and the impedance); power being proportional to the square of voltage or current.


2 ‘Music Power' - the Real Issues

The term ''"Music Power"'' has been used in relation to both amplifiers and loudspeakers with some validity. When live music is recorded without amplitude compression or limiting, the resulting signal contains brief peaks of very much higher amplitude (20 dB or more) than the mean, and since power is proportional to the square of signal voltage their reproduction would require an amplifier capable of providing brief peaks of power around a hundred times greater than the average level. Thus the ideal 100-watt audio system would be capable of handling brief peaks of 10,000 watts in order to avoid clipping (see Programme levels). Most loudspeakers are in fact capable of handling peaks of several times their continuous rating (though not a hundred times!), since thermal inertia prevents the voice coils from burning out on short bursts. It is therefore acceptable, and desirable, to drive a loudspeaker from a power amplifier with a higher continuous rating several times that of the speaker, but only if care is taken not to overheat it, which is difficult, especially on modern recordings which tend to be heavily compressed and so can be played at high levels without the obvious distortion that would result from a 'real' recording when the amplifier started clipping.

Music power is a less valid term when applied to most amplifiers. Most power amplifiers can give more output on brief bursts than their continuous rated output, but not usually to an extent that is relevant in the context of the above. There are three reasons for the enhanced short-burst power.

Most amplifiers do not have regulated power supplies but rely on a full-wave rectifier and large smoothing capacitor to provide a reasonably steady supply voltage. This charges to its peak voltage on quiet passages where little current is being drawn, but 'sags' to around 10% less under heavy current demand. Since 10% voltage drop corresponds to 20% power drop, the steady-state power output of the amplifier, which has to be quoted is always some 20% lower than the brief power capability. A 100-watt amplifier is therefore likely to handle brief peaks of up to 120 W without clipping. This might sound good in a specification, but it should be noted that it is only 1 dB, which is a change in level not usually even detectable by the human hearing system! It is also usually only available for some 10 milliseconds, which is too short to be of much benefit in real programme material. The term peak music power, in this context, is of no real significance.

It is possible to take a cost-effective approach to power amp design by reducing the size of the heat sinks on the output devices below that needed to avoid overheating on continuous sine wave drive at maximum output. Such an approach was once valid, as it recognised that fact that on 'real' recordings there is no need to provide for continuous full output as the gross distortion caused by clipping on brief peaks will result in the user turning down the volume before damage is done. On modern amplifiers it is possible to take such an approach without risk of damage, using integrated amplifier chips, which tend to incorporate 'thermal protection'. However, the trend towards heavy compression and limiting on commercial recordings in recent years means that people expect to play these at high volume without clipping, and so the validity of the 'peak music power' approach to amplifier design has mostly been removed.

While the above is true for most 'domestic' amplifiers, it need not be so, especially in relation to monitoring, and uncompressed reproduction. Some professional amplifiers, and 'active' speakers, incorporate sophisticated electronic thermal protection circuits which integrate the power delivered to the speaker and take account of its thermal capacity properly. This enables them to handle peak power levels safely while limiting the continuous power that can be applied in a way that makes sense.


3 Power Handling in 'Active' Speakers

Active speakers often use two or three power amplifiers, each handling only part of the audio frequency spectrum. The main benefit of this approach is that it enables complicated crossover filters to be used on the low level signal, and eliminates the bulky and awkward inductors and capacitors normally used in crossover networks. There is, however, another big advantage that is not usually recognised. When two tones are reproduced simultaneously, a single amplifier normally has to handle the peak power that results when both are at their crest. Because of the square-law relationship, this means that two tones each generating 10 watts result in a power handling requirement of 40 watts. With multiple amplifiers, the two tones can be handles separately, by 10 watt amps. Thus a 'bi-amped' system can handle peaks of up to twice the combined rating of its amplifiers, and a 'tri-amped' system, on three tones, gains even more! This is of course because the signal has a high 'crest factor'. In practice, music peaks often consist of percussion riding on top of bass notes, and so the benefit is very real, as these are each always handled separately. This is a benefit that would cost a lot to realise if the single amplifier approach were taken, making 'bi-amping' a very cost-effective approach.


4 US Market Regulations

In the US on May 3, 1974, the Amplifier Rule CFR 16 Part 432 (39 FR 15387) was instated by the Federal Trade Commission (FTC) requiring audio power and distortion ratings for home entertainment equipment to be measured in a defined manner with power stated in RMS terms. This rule was amended in 1998 to cover self-powered speakers such as are commonly used with personal computers (see examples below). This regulation did not cover automobile entertainment systems, which consequently still suffer from power ratings confusion. However, a new regulation called CEA 2006 includes car electronics, and is being phased into the market as slowly as possible by many manufacturers.

Unfortunately there are no similar laws in much of the rest of the world.

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发表于 2008/4/26 16:13:17

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【音频测试基础知识】信噪比与动态范围

Signal-Noise and Dynamic Range

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Introduction

Hi-fi equipment specifications tend to include the terms ‘signal to noise ratio’ and ‘dynamic range’, both of which are confusing and best avoided. Noise has to be measured with reference to something, but the only sensible reference point is ‘alignment level’ (see article on this). Signal to noise ratio has no real meaning as audio signals are constantly changing so there is no such thing as ‘signal level’. Dynamic range is an ambiguous term that is commonly used in three different ways. To audio professionals it refers to the ratio of maximum to minimum levels in a recording or programme. It can also mean the difference between maximum permitted level (clipping level or full-scale digital) and noise level, but maximum level is often hard to define, for example on analog tape recordings, and the term has become corrupted by a tendency to refer to the dynamic range of CD players as meaning the noise level on a blank recording with no dither, in other words just the analog noise content at the output. This is not particularly useful; especially since many CD players incorporate automatic muting in the absence of signal to make them appear even quieter!

Subjectively Valid Noise Measurement

Professionals measure noise in dB below alignment level, which is a reference point above which ‘headroom’ exists up to maximum permitted level. Professionals often allow 18dB of headroom, as recommended by the EBU (European Broadcasting Union), so a noise level of –60dB ITU-R 468 would represent a dynamic range of 78dB, which if measured A-weighted might come out 11dB better at 89dB. A noise level of -60dB AL would be considered reasonably good by professionals, with –68dB representing the best attainable from 16-bit digital audio (noise shaped), and more than good enough for most purposes (see article 'Analysing Programme Levels').

The 96dB Myth

Audiophiles may talk in terms of 96 to 120dB dynamic range, but they often fail to refer to any measurement standard, making the figures meaningless. Attempts to calculate the dynamic range of digital audio on the basis that 16 bits represents a ratio of 65000:1 or 96dB are invalidated by the fact that the full digital count represents the peak possible level, rather than the rms equivalent of the maximum possible sinewave, while the minimum count of one has little to do with the noise level, which depends on the type of dither (or noise-shaping) used. They also fail to take any account of weighting for subjective validity.

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发表于 2008/4/26 16:12:10

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【音频测试基础知识】噪音测量

Noise Measurement

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Introduction to noise measurement

Noise in general refers to unwanted sound, often loud, but in audio systems it is the low-level hiss or buzz that intrudes on quiet passages that is of most interest. All recordings will contain some background noise that was picked up by microphones, such as the rumble of air conditioning, or the shuffling of an audience, but in addition to this every piece of equipment which the recorded signal subsequently passes through will add a certain amount of electronic noise, which ideally should be so low as to contribute insignificantly to what is heard.

Microphones, amplifers and recording systems all add some electronic noise to the signals passing through them, generally described as hum, buzz or hiss. All buildings have low-level magnetic and electrostatic fields in and around them emanating from mains supply wiring, and these can induce hum, commonly at 50 or 100Hz into signal paths. Screened cables help to prevent this, and on professional equipment, where longer interconnections are common, balanced signal connections (most often with XLR connectors) are usually employed. Hiss is the result of random signals, often arising from the random motion of electrons in transistors and other electronic components, or the random distribution of oxide particles on analog magnetic tape. It is predominantly heard at high frequencies, sounding like steam or compressed air.

Attempts to measure noise in audio equipment as rms voltage, using a simple level meter or voltmeter, do not produce useful results; a special noise-measuring instrument is required. This is because noise contains energy spread over a wide range of frequencies and levels, and different sources of noise have different spectral content. For measurements to to allow fair comparison of different systems they must be made using a measuring instrument that responds in a way that corresponds to how we hear sounds. From this, three requirements follow. Firstly, it is important that frequencies above or below those that can be heard by even the best ears are filtered out and ignored; by bandwidth limiting (usually 22Hz to 22kHz). Secondly, the measuring instrument should give varying emphasis to different frequency components of the noise, in the same way that our ears do; a process referred to as ‘weighting’. Thirdly, the rectifier, or detector, which is used to convert the varying alternating noise signal into a steady positive representation of level should take time to respond fully to brief peaks to the same extent that our ears do; it should have the correct ‘dynamics’.

The proper measurement of noise therefore requires the use of a specified method, with defined measurement bandwidth and weighting curve, and rectifier dynamics, and two main methods defined by standards are currently in common use: A-weighing, and ITU-R 468, formerly known as CCIR weighting.

A-weighting

A-weighting uses a weighting curve based on ‘equal loudness contours’ that describe our hearing sensitivity to pure tones, but it turns out that the assumption that such contours would be valid for noise components was wrong. While the A-weighting curve peaks by about 2dB around 2kHz, it turns out that our sensitivity to noise peaks by some 12dB at 6kHz. Another weakness of A-weighting is that it is usually combined with an rms (root mean square) rectifier, which measures mean power, with no attempt made to account for proper hearing dynamics.

ITU-R 468 weighting

When measurements started to be used in reviews of consumer equipment in the late 1960’s it became apparent that they did not always correlate with what was heard. In particular, the introduction of Dolby B noise-reduction on cassette recorders was found to make them sound a full 10dB less noisy, yet they did not measure 10d better. Various new methods were then devised, including one which used a harsher weighting filter and a quasi-peak rectifier, defined as part of the German DIN45 500 ‘Hi Fi’ standard. This standard, no longer in use, attempted to lay down minimum performance requirements in all areas for ‘High Fidelity’ reproduction.

The introduction of FM radio, which also generates predominantly high-frequency hiss, also showed up the unsatisfactory nature of A-weighting, and the BBC Research Department undertook a research project to determine which of several weighting filter and rectifier characteristics gave results that were most in line with the judgment of panel of listeners, using a wide variety of different types of noise. BBC Research Department Report EL-17 formed the basis of what became known as CCIR recommendation 468, which specified both a new weighting curve and a quasi-peak rectifier. This became the standard of choice for broadcasters worldwide, and it was also adopted by Dolby, for measurements on its noise-reduction systems which were rapidly becoming the standard in cinema sound, as well as in recording studios and the home.

Though they represent what we truly hear, CCIR weighted noise figures are typically some 11dB worse than A-weighted, a fact that brought resistance from marketing departments reluctant to put worse specifications on their equipment than the public had been used to. Dolby tried to get round this by introducing a version of their own called CCIR-Dolby which incorporated a 6dB shift into the result (and a cheaper average reading rectifier), but this only confused matters, and was very much disapproved of by the CCIR.

With the demise of the CCIR, the 468 standard is now maintained as ITU-R 468, by the International Telecommunications Union, and forms part of many national and international standards, in particular by the IEC (International Electrotechnical commission), and the BSI (British Standards Institute). It is by far the best way to measure noise, and the only way that allows fair comparisons; and yet the flawed A-weighting has made a comeback in the consumer field recently, for the simple reason that it gives the lower figures that are considered more impressive by marketing departments.

Signal to noise ratio and Dynamic range

Hi-fi equipment specifications tend to include the terms ‘signal to noise ratio’ and ‘dynamic range’, both of which are confusing and best avoided. Noise has to be measured with reference to something, but this should be ‘alignment level’. Signal to noise ratio has no real meaning as audio signals are constantly changing so there is no such thing as ‘signal level’. Dynamic range used to mean the difference between maximum level and noise level, but maximum level is often hard to define, for example on analog tape recordings, and the term has become corrupted by a tendency to refer to the dynamic range of CD players as meaning the noise level on a blank recording with no dither, in other words just the analog noise content at the output. This is not particularly useful; especially since many CD players incorporate automatic muting in the absence of signal to make them appear even quieter!

Professionals measure noise in dB below alignment level, which is a reference point above which ‘headroom’ exists up to maximum permitted level. Professionals often allow 18dB of headroom, as recommended by the EBU (European Broadcasting Union), so a noise level of –60dB ITU-R 468 would represent a dynamic range of 78dB, which if measured A-weighted might come out 11dB better at 89dB. A noise level of -60dB AL would be considered reasonably good by professionals, with –68dB representing the best attainable from 16-bit digital audio (noise shaped), and more than good enough for most purposes.

Audiophiles may talk in terms of 96 to 120dB dynamic range, but they often fail to refer to any measurement standard, making the figures meaningless. Attempts to calculate the dynamic range of digital audio on the basis that 16 bits represents a ratio of 65000:1 or 96dB are invalidated by the fact that the full digital count represents the peak possible level, rather than the rms equivalent of the maximum possible sinewave, while the minimum count of one has little to do with the noise level, which depends on the type of dither (or noise-shaping) used. They also fail to take any account of weighting for subjective validity.

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发表于 2008/4/26 16:09:09

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【音频测试基础知识】失真测量

Distortion Measurement

 


1 Introduction


Distortion, in audio systems, is usually understood as meaning ‘non-linear distortion’, which is heard as a roughness and confusion of the sound. Non-linearity often refers to a lack of proper correspondence between instantaneous input signal voltage and instantaneous output signal voltage. In a linear system, one with a linear transfer function that is, twice the input voltage produces twice the output voltage, but in practical systems this may not be the case.

2 THD (total harmonic distortion)

Plotting output versus input to determine the transfer function is not a useful method for determining distortion in audio systems though, for two reasons. Firstly, they usually respond only to changing signals (not DC), in the audio frequency range. Secondly they may suffer varying time delays (phase shift) at different frequencies. Both of these effects would produce a non-linear response to, say, a voltage ramp, even in a system free from non-linear distortion. Testing with a sine-wave input conveniently avoids these problems, while allowing the distortion to be quantified in terms of ‘harmonics’ (new components appearing at the output with frequencies that are multiples of the input sine wave frequency). The term ‘Total Harmonic Distortion’ refers to the sum of all these components, measured rms (root mean square) as a percentage of the total (rms) output.

THD is commonly measured by using a notch filter to remove the input frequency from the output, allowing what is left to be measured, and in this case the measurment should strictly be referred to as THD+noise, since it includes any random noise on the output.

3 Crossover Distortion – how THD fails as a measure of audibility

In the early days of audio, one form of non-linearity dominated in all systems. Valves (tubes), tape recordings and transformers all tended to produce less output at high levels of input, in a symetrical manner (affecting positive and negative sides of the signal equally). This ‘soft limiting’ squashes the peaks of the sine-wave, producing a form of distortion known as ‘odd-order’ which contains only odd harmonics of the input (3rd, 5th etc). Processes that cause asymetric distortion generate only even harmonics (2nd, 4th etc) and are rarer. Odd order distortion products are sometimes considered more objectionable than even order, since they are not musically related in the way that even order products are (by octave intervals).

With the introduction of transistor amplifier though, a new form of distortion arose, known as ‘crossover distortion’ and caused by a kink in the transfer characteristic as the sine-wave crosses zero. This is a form of ‘high order’ distortion, and produces odd harmonics (3rd, 5th, 7th, 9th etc) which extend right up the frequency range, with little reduction in amplitude, and because the ear analyses sounds in terms of frequency components, and is most sensitive to frequencies in the 2kHz-8kHz region, it turns out that we are particularly sensitive to even small amounts of crossover distortion, when compared to the ‘low-order’ distortion of valves and tape, which generate mostly 3rd harmonic.

While early experiments had determined that 0.1% THD (-40dB) was the very minimum that could be heard, it soon became apparent that this was not the case for transistor power amplifiers, where 0.01% or less could be heard as harshness on the sound. Nevertheless, THD measurements continued to be quoted, and audio measurement itself got a bad reputation among the ‘hi-fi’ fraternity, who turned to listening tests as the only way to assess audio equipment.

4 Attempts at Weighted Distortion measurement

What was really need was a subjectively valid method of measurement. To simply assume that measurements of noise, distortion or anything else are meaningful in themselves is to miss the point. Audio measurement, if it is to give useful results, should never be about quantifying a system in purely engineering terms. It must be about using methods that have already been shown to correspond to subjective effect, and such methods must rely in the first instance on listening tests. So why not just listen? There are many good reasons for measuring, rather than listening. Our ears vary greatly, between individuals and from day to day (depending on what levels of sound we have been exposed to) so they are not reliable tools. They also have dificulty distinguishing one form of corruption (such as distortion) in the presence of another (such as noise, or flutter, or the reverberation of the listening room). Then there is the problem of the long signal chain, in which recordings pass through numerous items, for example from microphone to mixer to tape recorder to transmitter to broadcast receiver to loudspeaker. If we are to guarantee that what we hear will be indistinguishable from the original, then each part of the chain must contribute a lower level of distortion or noise than our ears could possibly detect, if their sum total is to be inaudible.

Many researchers have tried over the years to devise schemes for measuring distortion that gave subjectively valid results, yet they mostly seem to have got it wrong! A commonly quoted method, for example, involves multiplying the level of each harmonic according to its number and yet such schemes are clearly flawed as they take no account of the fact that our hearing responds less and less to frequencies above 10kHz and hardly at all to 15 or 20kHz, above which few people hear anything at all. They are further flawed by their continued use of rms measurement, which greatly underestimates crossover distortion (and digital distortions) as will be explained.

5 Distortion Residue – a meaningful measurement at last

There is in fact a relatively simple way to weight distortion, which works remarkably well across all devices from tape to power amps and digital systems, and has been incorporated into a standard (IEC ). Lindos Electronics recommends this, and has chosen to call the result ‘Distortion Residue’ for easy identification as distinct from THD. It involves nulling out the fundamental of a 1kHz test tone, and then measuring what remains just as if it were noise, using the ITU-R 468 weighted measurement method (which Lindos Electronics refer to as simply 468-weighted). This emphasises high-order harmonics around 6kHz by 12dB but attenuates those above 10Khz, and ignores those above 20kHz. Because it uses a Quasi-Peak rectifier, the method also gives proper temporal weighting to brief bursts that would be largely ignored by the averaging inherent in rms measurement.

6 Why the Distortion Residue method works

When we listen to speech and music, the content is mostly in the 300Hz to 3kHz region. Because real sounds are complex and constantly changing, any low order distortion products from this region will appear more as random noise than as individual harmonics tones, but predominantly in the 900Hz to 9kHz part of the spectrum (3rd harmonic predominantly). If they were tones, we could fairly assess them using the A-weighting curve, derived from equal-loudness contours for our hearing process, but for noise such weighting is not valid. Rather than being most sensitive in the 2kHz region, as the A-weighting curve would suggest, our ears are much more sensitive in the 6kHz region, for reasons to do with spectral density that are explained elsewhere. This is why the 468-weighting curve, which was designed to reflect our sensitivity to noise rather than tones, should be used, with its 12.2dB of emphasis at 6.3kHz.

If we now consider speech or music subject to crossover distortion in a power amplifier, another very important consideration arises. Typical speech and music waveforms do not cross zero very often. There may be violins or cymbals contributing significant high frequencies to the waveform, but most of the time these will be riding on top of bass notes such that zero-crossings are much less frequent than they would be for a pure tone. Where a relatively pure tone does arise from a violin note, it will not have many audible harmonics, whatever the distortion mechanism, because the 3rd harmonic of a 3kHz tone is at 9kHz, and the 5th is at 15kHz which will not be heard by most listeners. Most people are surprised to find that they can tell absolutely no difference between a 6kHz square wave and a 6kHz sine wave, but of course the 3rd harmonic is at 18kHz, and even listeners who can hear to 18kHz will usually have greatly reduced sensitivity at this frequency.

The distortion residue from a typical speech or music signal passed through a power amplifier is therefore better imagined as a series of ‘clicks’ occurring every time the waveform passes through zero. Their total contribution to a Fourier Analysis over a period of seconds, as shown on a spectrum analyser, is very low, hence the low THD figures traditionally obtained from ‘bad’ amplifiers, but our ears do not analyse over seconds. Each hair-cell in the cochlea responds as a narrow band filter over a period of milliseconds (the higher the frequency the shorter the response time) and so it can give a brief comparatively high level response, heard as a click, to each crossover event. Whether we hear a given even depends on this short-term response, not some average over a relatively long period, as is implicit in any rms (root mean square) measurement.

The Quasi-Peak rectifier used for 468-weighted measurement, was based on listening tests in which subjects were asked to rate the loudness of various clicks, tone bursts, and other sounds of various duration, and with various repetition rates, against a reference tone. It therefore reflects pretty well the temporal aspects of hearing, and does not diminish the effect of each click by averaging, though it gives less weight to very short bursts, which our ears do not have time to respond to fully, or to bursts with a low repetition rate which our brains give less importance to.

7 Distortion Residue Measurement in practice

Distortion Residue measurement works, and its use is to be encouraged (hence its adoption as the sole method of distortion measurement in the Lindos MS10). It will always give a result higher than the corresponding THD measurement, but this is an advantage, making for easier measurement. On tape machines for example, where distortion is mostly 3rd-harmonic it will give a result some 8dB worse than a corresponding THD measurement, and if significant modulation noise is present, as on compact cassette, then this too will be properly emphasised leading to an even higher figure. On power amplifiers, the result may be 10 or 20dB worse than a corresponding THD measurement, depending on the harshness (order) of the crossover characteristic, giving quite a reliable indication of audible performance. Where once it used to be said that 0.1% THD (-60dB) represented the threshold of audibility for distortion, except for power amplifiers, it is probably now fair to say that 0.3% Distortion Residue (-50dB) represents the threshold of audibility regardless of what equipment is being measured. Digital systems normally produce distortion that is more like noise than harmonics, and faulty digital convertors are likely to produce repeating ‘clicks’ rather than tones, in much the same way as crossover distortion does, so the method is very well suited to digital measurements.

It should be noted that attempting to measure distortion residue at frequencies other than 1kHz would not be useful. At low frequencies (100Hz) the effect of the weighting filter would be to severely attenuate all the low order harmonics. Whilst weighted measurement of low frequency distortion might be a useful concept, emphasising the enhanced audibility of harmonics over their fundamental, the weighting curve would have to be normalised to a low frequency (such as 100Hz) rather than 1kHz, and should probably be closer to A-weighting, since low frequency distortion is commonly noticed on sustained bass notes.

8 Other Types of Distortion Measurement

Intermodulation distortion measurement is a valid way of measuring the interaction between components of different frequencies, and three main methods have been used, as explained elsewhere. The quoting of figures for intermodulation distortion never seems to have caught on though, possibly because the results from tape machines for example are atrociously high. This, coupled with the fact that tape recordings can sound very good, lends weight to the assertion that intermodulation distortion is not in itself as significant as some would have us believe.

The same is true of ‘Transient distortion measurement’, a topic that gained popularity for a while in audiophile circles. Provided that recordings are limited to 20kHz, as they should be, all that is needed is for every part of the signal path to be able to handle 20kHz at maximum level, a statement that again gains support from the fact that some of the best recordings were made on analog tape recorders, which struggle to manage this, and certainly cannot record square waves!

This is a complex topic, but Lindos recommends that distortion residue measurement is probably all that is generally required to indicate whether a signal path is likely to give audible distortion on programme material.

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发表于 2008/4/26 16:04:48

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理解dB

最近接了一个项目：音频测试。开始收集有关资料，全部整理在这里

Understanding Decibels (dB)

 


Understanding decibels (dB)

The decibel is widely used as a measure of the loudness of sound, but it is actually only a convenient way of specifying the ratio between two quantities, so a 6' 7" man could be said to be 1dB taller than a 6' man! An engineer might use it for such things in jest, but in general the dB is commonly used to express a wide variety of measurements in acoustics and electronics, where it helps in giving a manageable view of things that can cover huge range of values, where only geometric increase or decrease is important. It is especially useful in audio because our ears follow a roughly logarithmic law, referred to by psychologists as Weber's law. The smallest change in loudness that we can detect is about 1dB, or a ten percent change, regardless of whether the sound is very quiet or very loud, in other words we hear loudness 'geometrically' rather than 'arithmetically'.

The decibel is a dimensionless unit like percent and only has meaning when levels are specified relative to a reference level. In audio, the reference level is often specified with a suffix after the dB notation and a brief summary of the most commonly used standards follows:

dBm

dBm specifies a power level on a line, referenced to 1mW. In the early days of audio signals were passed along 'matched' transmission lines, meaning that both the source impedance and the load impedance were the same as the 'characteristic impedance' of the line, usually 600 ohms. This ensured that all energy sent down the line ended up in the load resistance, with non reflected back to cause frequency response anomalies or echoes.

dBu

dBu specifies that the voltage amplitude of an audio signal is referenced to 0.775 volts rms. This is the same voltage as would be needed to dissipate 1mW into a 600 ohm resistor, and is kept for historical reasons, though 600 ohm matched transmission is rarely used today. The standard for studio interconnection today uses low source impedance (<50 ohms) and high input impedance (10 or 20k ohm). The use of a 'solid' drive ensures more accurate levels, and reflections are not a problem over short paths (say <50m). The u is thought to stand for 'universal' or maybe 'unloaded'. 0dBu is the universal 'Alignment level' within many broadcast organisations and recording studios, with signal levels allowed into the 'headroom' region which may be 24dB, 18dB (EBU recommendation for programme interchange) or 8dB (EBU standard for radio and TV broadcasts and paths).
dBV

dBV specifies that the reference amplitude is 1V. This is sometimes used for consumer levels, but dBu are to be preferred because most audio instruments are calibrated in dBu.


dB SPL

This is a measure of sound pressure level, relative to 20 micropascals (µPa = 1×10^-6 Pa), an arbitrary figure chosen as being about the quietest sound a human can hear. This is roughly the sound of a mosquito flying 3 metres away!

dB FS

This means relative to full-scale or the point at which clipping occurs in a system. It is frequently used in referring to digital signal levels which do not in themselves correspond to any particular voltage, until they are converted using a D-A convertor.

dB AL (Recommended by Lindos)

This means dB relative to Alignment Level, which is a reference level or anchor point against which all else in an audio system is measured. Alignment level may correspond to different voltage levels in various part of the system or signal path (though commonly it will be 0dBu), and in a digital recording it may correspond with varying digital values, though commonly it will be -18dB FS (or -24 or -12) as defined in EBU recommendations. Importantly it is the reference at any point in a system above which Headroom is defined and relative to which noise is measured.

The great merit of this system is that a noise measurement made relative to Alignment Level will always be a reasonable guide to the true intrusiveness of the noise onto typical material, regardless of the headroom. Where less headroom is available for transmission, compression or limiting will usually be used to reduce brief peaks, but this has little effect on overall perceived loudness. A recording may start life with 24dB of headroom, and end up with only 9dB of headroom at the listener’s radio or television. Its ‘dynamic range’ has indeed been reduced, but it will not sound any noisier, assuming that it is the peaks that have been limited. Instead it will have lost ‘sparkle’ and impact. Specifying noise and headroom separately reflects these different qualities properly.

Decibels in Audio Recording and Reproduction

The dynamic range of the human ear is phenomenal, through a complex gain adjustment system a range of around 140dB is covered. Accurately capturing and reproducing the quietest and loudest sounds audible by humans is a formidable task.

The diagram below shows the range of levels handled by various stages in a typical audio chain, from live sound to loudspeaker. Note how most devices cannot cope with the full range without the use of compression or limiting.

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Useful Conversion Tables

It is useful to remember that 6dB is approximately a factor of 2.0, 10dB a factor of 3, and 20 dB exactly 10 times, when referring to voltage levels. When levels are multiplied, dB are added. Thus 26dB represents 20 times.

Power levels, being proportional to the square of the voltage, have different ratios, so that 3dB is twice the power, 6dB is 4 times the power, and 10dB is ten times the power. Usually, these days, it is voltage ratios that are relevant, and the following table will be found useful to commit to memory:


0dB x 1
+1dB x 1.1
0dB x 1
+1dB x 1.1
+3dB x 1.414 (root 2)
+6dB x 2
+10dB x 3
+20dB x 10
+30dB x 30
+40dB x 100
+50dB x 300
+60dB x 1000 etc

and:

-1dB x 0.9
-3dB x 0.707
-6dB x 0.5
-10dB x 0.3
-20dB x 0.10
-40dB x 0.01
-60dB x 0.001 etc
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