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Other Measurement Techniques

Since we are trying to find an impulse response, what we are really doing is using our test signal (swept sine wave for TDS) to model an ideal impulse function. As we increase the amount of energy per unit time contained in our test signal, our measurement becomes more and more like the 'real' impulse response. We must have as much energy in our signal as possible in order to maintain a high signal-to-noise ratio for our measurement. This is especially important in an environment where ambient noise levels are high (in real-world venues, we must consider HVAC, industrial sounds, and possibly even things like audience noise).

One convenient measure of how much energy our signal contains per unit time is the crest factor. The crest factor of a signal is simply the ratio of peak value of the signal and the RMS value of the signal:

crest factor = (peak value) / (RMS value).

Ideally, we would like our crest factor to be as close to 1 as possible. Since our peak value and RMS value would be the same, we cannot have any more energy per unit time in our signal, and our input signal can be said more closely resemble an idealized impulse.

Our swept sine wave input has a crest factor of sqrt(2), which is approximately 1.4.

Another kind of input signal, which has gained a great deal of popularity in the last few years, is called an MLS, or Maximum Length Sequence. An MLS signal is simply a series of pseudo-random pulses generated by an MLS random number generator. Usually, these pulses are white or pink noise signals (pink noise is like random white noise, but it has equal power for each octave in the frequency domain).

The crest factor for MLS is very close to 1, so it makes sense to use this kind of input signal when we need a high signal-to-noise ratio for our measurement. MLS works well for the noisy real-world environments that are ever so prevalent in acoustics testing.

So why do we still use swept sine waves?

If we want to measure the impulse response of a system using MLS, we input an pseudo-random MLS signal and measure the output of the system. In order to get the impulse response, we must compute the cross-correlation between the input and the output. A cross-correlation is a way of determining how similar two signals are using a weighted moving average. A correlation is like a convolution, except neither signal is 'flipped'). If we can use convolution to compute the output of a system with a known impulse response, then we can use correlation to compute the system impulse response from a given input and an output. Or, put differently, if convolution is like multiplication in the frequency domain, correlation is like division in the frequency domain.

In order to compute frequency response from our impulse response, we must use the FFT. This is where swept-sine wave techniques may be better in some cases. When we take an FFT of a time-domain signal, any frequency that is not centered inside an FFT bin may not be measured at its full value. How this happens in the frequency domain depends on the time-domain window used in the FFT (a square window has a sinc function as its Fourier transform).

In any case, as a given frequency moves away from the 'kernel' (this is the frequency domain equivalent of our 'window'), the measured value in the frequency domain starts to dip as the frequency moves between the FFT bins. This is usually called scallop loss, but some people also call it picket fence loss because of the way the dips look in the frequency domain. Another, more simpler way of explaining this loss is by realizing that FFT windows tend to attenuate signals at both ends of the window (in order to make it periodic and prevent aliasing). Since the window reduces overall power in the time domain, the same power is lost in the frequency domain, and the amplitude measured in the frequency domain at a particular frequency is not always the "real" amplitude. The FFT bins may contain contributions from 'other' frequencies, and may even contain broadband noise, which causes the signal-to-noise ratio of our measurement to decrease.

When we use swept-sine waves to measure the response of a system, we are using a tracking filter in the frequency domain and directly measuring frequency response, and the measurement can be spaced at either linear frequency steps, or at logarithmic frequency steps. Using swept-sine measurements, our amplitude and frequency measurements are more precise. Our frequency response using swept-sine wave techniques may be more accurate and more precise than using other techniques. Of course, as stated above, MLS is more resistant to ambient noise because the signal contains more energy per unit time. Also, if an impulse response is desired, MLS may be the way to go.

In the real-world, there are many more considerations that are constantly coming up. Recent editions of publications like the AES Journal contain many arguments that could lead one to go either way when considering which technique to use, depending on each given situation.

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