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【音频测试基础知识】加权滤波器
发表于 2008-4-26 16:46:54
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.

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【音频测试基础知识】PMPO音乐功率真相
发表于 2008-4-26 16:14:36
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.

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