By Julian Hirsch
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FFT Loudspeaker Measurements
IN our loudspeaker lab-test re ports, we usually refer to FFT frequency-response measurements, without further elaboration, as a part of our regular test procedures. Since many readers may not fully understand the reference, I will try to explain it.
The frequency response of any device is normally measured by driving its input with a sine-wave (single-frequency) signal and measuring its output as the frequency is varied through the region of interest, usually from 20 to 20,000 Hz or some part of that range. Ideally, most audio components should have a uniform ("flat") frequency response, and some of them-notably amplifiers and CD players-do achieve that goal. Loudspeakers, however, which are probably the most critical components of a reproducing system, have many problems that keep them from attaining perfection, or even approaching it.
The typically irregular frequency response of loudspeakers produces some of the more obvious aberrations in the sound we finally hear.
Reduced to the simplest terms, loudspeaker frequency response is measured much like that of other components, except that a loud speaker's output is acoustic and must be converted to electrical form by a microphone before being measured. The microphone is an inverse analog of the speaker, but it is much closer to the ideal: a good laboratory microphone has a response that is flat within 1 dB from a few hertz out to 40,000 Hz. Loudspeaker measurements are complicated, however, by the speaker's interaction with the room in the form of resonances that create acoustic standing waves, which cause large pressure variations in different parts of the room and a widely varying frequency response at any one location.
There are several ways to avoid these room problems. An ideal approach, though often an expensive or impractical one, is to measure in an "anechoic" environment, a space without nearby reflecting boundaries. The outdoors can be such an environment, preferably with the speaker placed on a high tower, since the ground too is a source of reflections. But outdoor measurements put us at the mercy of the elements. Even a moderate breeze can add intolerable noise to the measured audio levels, and rain, snow, or cold weather obviously make outdoor measurements impractical in most parts of our country. (Years ago I tried outdoor speaker measurements and found, in addition to the other problems, that my neighbors did not share my enthusiasm for audio testing!) For most practical purposes, anechoic measurements must be made in an anechoic chamber-literally, an echo-free room. Such chambers are lined on all interior surfaces with sound-absorbing wedges of glass fiber or similar material, and the working floor is actually an open metal mesh several feet above the actual bottom of the chamber. Such rooms are quite expensive to build, and, unfortunately, they are anechoic only above a certain low frequency (which depends on the size of the room). Only a large and wealthy enterprise can afford an anechoic chamber large enough to be useful in the lowest audio octaves.
Until a couple of decades ago, the only way to measure a speaker with out such a costly facility was to place it in a more or less normal room and pretend that the room was not there. That pretense was enhanced by such measures as aver aging the outputs of several micro phones at different locations, swinging or rotating the micro phones to achieve a similar result, using a "warble tone" (a sine wave whose frequency varies up and down rapidly in a small range, which is equivalent to multi-microphone or moving-microphone systems in its effect on room-resonance aberrations), or some combination of these techniques. I still make room-response measurements with a sine wave whose frequency sweeps from 20 to 20,000 Hz in about 1 minute while warbling one-third of an octave up and down at a rate of about 5 Hz.
An alternate method of measurement has long been recognized as theoretically possible, but its implementation became practical only with the advent of powerful, fast, and affordable computers. There is a mathematical relationship, de fined by the Fourier transform, be tween the frequency and time properties of a signal. If the shape of an impulse signal is known, its equivalent frequency spectrum can be computed, and vice versa. The computation is tedious, and only the availability of computers has made it practical for applications such as this.
If a loudspeaker is driven with a short pulse (which sounds like a "tick"), the output of the pickup microphone can be processed with what is known as the fast Fourier transform, or FFT, and converted into the corresponding frequency spectrum, which is (for our purposes) the speaker's "frequency response." This technique was first used by a commercial loudspeaker manufacturer more than fifteen years ago, when KEF pioneered digital loudspeaker measurements with the aid of a powerful Hewlett-Packard minicomputer.
In the following years, a few other companies adopted similar techniques, although the cost of suitable computers was beyond the means of The tens of thousands of computations required to generate a frequency response plot with the IQS FFT analyzer take only a few seconds.
many small manufacturers and almost any individual. About five years ago, a practical FFT signal-analysis system was developed for the Apple Il series of personal computers, and it is now available from IQS, Inc. of Garden Grove, California. For more than four years, we have been using the IQS 401-L signal-analysis system as an adjunct to our room-response measurements.
The IQS system generates pulses that are appropriate for the desired measurement band (about 10 microseconds wide for the full audio range). The pulses are amplified and used to drive the speaker, and the microphone picks up the sound and returns it to the computer in electrical form for analysis. A frequency response curve can be generated from a single pulse, but up to 128 pulses can be averaged to improve the signal-to-noise ratio. We usually use the sixteen-pulse train. It is possible to perform this measurement in a very noisy environment thanks to the signal-averaging ability of the system; the short duty cycle of the pulse lets us drive the speaker (if necessary) to extremely high levels that could damage its drivers if they were sustained.
The acoustic waveform emitted by any speaker (and analyzed in electrical form) is quite different from the driving impulse we use in our measurements, which has a frequency spectrum that is essentially flat up to 20,000 Hz and beyond.
The response aberrations of a speaker typically change the pulse shape by stretching it and adding a period of "ringing." The signal is sampled 46,488 times a second for most audio measurements, yielding a maximum frequency response of 23.244 kHz. The analyzer's sampling rate can be set to a number of values between 200 and 60,000 Hz, corresponding to upper frequency limits of 100 to 30,000 Hz. When the range is selected the analyzer automatically sets the pulse width, the repetition rate, and the cutoff frequency of the ant-aliasing filter needed to prevent false responses (as in the case of digital sound recording).
The amplitude levels of the pulse waveform during the sampling pro cess are stored in the computer for processing. Typically, several hundred samples are processed for a waveform whose duration is a few milliseconds. These data undergo a mathematical procedure, involving multiplication of each sample level by sine and cosine values, in accordance with the FFT algorithm. The final result (assuming the normal sampling rate) is a display on the computer monitor of the frequency spectrum of the waveform over a range of 180 to 23,244 Hz. By using other sampling rates, measurements can be made as low as 0.5 Hz or as high as 30,000 Hz.
The tens of thousands of computations required to generate a frequency-response plot with the IQS FFT analyzer take only a few seconds, giving us a rapid acoustic-measurement capability that would not have been possible before the availability of low-cost computers and the FFT technique itself. Aside from its speed, however, the FFT analyzer helps us to reduce or eliminate room effects from our measurements by displaying the acoustic impulse and any reflections from room boundaries or other discontinuities.
The display's time scale is normally a few milliseconds long for full-frequency-range measurements.
For example, if we see a reflection occurring about 3 milliseconds after the main signal, we know that it has traveled roughly 3 fen farther than the direct signal (sound travels about 1.1 feet per millisecond).
From this we can usually determine the source of the reflection and either remove the cause (by shifting a piece of furniture, for example, or by covering it with sound-absorbent material) or truncate the signal just before the reflection arrives in our analysis window. If the speaker's own impulse output has essentially disappeared before the first reflection arrives, removing the reflection will not affect our response measurement other than to make it easier to interpret.
The IQS FFT analyzer can per form a number of other measurements on the impulse response of a speaker, including phase response and group delay, and it can plot two traces on a single readout to show the response at different angles to the speaker's forward axis or generate three-dimensional "waterfall" plots to show the relationship be tween time, frequency, and amplitude in a single display. We also use it, on its lowest frequency range, to measure the transmission of low-
frequency and infrasonic signals through the mounting feet of a record player. Although the FFT technique is not a universal problem solver, it is one of the most powerful audio measurement tools available today.
Also see: THE HIGH END (Jul. 1985)