Improved analysers using Log-Swept sine techniques

10 February 2009

How research designed to assist with the measurement of acoustic spaces has benefited audio T&M techniques.

For many years, test and measurement devices for audio manufacturers relied on sending sine-wave tones at a variety of frequencies through the equipment on test, and seeing what harmonic distortion the equipment produced as a result. Today, as in most areas, science has moved on, and our ability to test and measure audio equipment has improved dramatically. However, we still employ sine waves for audio T&M — we just use them differently. And in fact, one recent advance, the use of log-swept sine waves in test equipment, stemmed from research into acoustics rather than electronics.

Rooms with a VU
Many of you reading this will not be surprised. While acoustics and electronics might seem distant, even unrelated subjects, they are both concerned with what happens when energy (sound in the case of acoustics, and an electrical signal in electronics) is introduced into a system (a room on the one hand, an arrangement of circuits on the other). Since these concepts were first understood, engineers have tried various means to measure and describe the effect of the system on the energy. And for the past few years, acousticians who have wanted to measure the effect that large rooms have on audio at different frequencies and amplitudes have begun making use of so-called ‘impulse responses’ and a process known as deconvolution to analyse the rooms.

From input signal to impulse response
The maths behind this idea can be ferociously complex, but the underlying concept is simple: if you put a high-energy, precisely controlled wide-band audio test signal containing as much harmonic content as possible into a room, you will excite its resonant frequencies and modes, and the acoustic result will be a
much altered, reverberant version of the signal you put in. Because you know the precise qualities of the original test signal, if you can somehow ‘remove’ the original signal from the reverberant version, the resulting time-domain response will describe the net acoustic affect the room has on any sound that passes through it. Needless to say, the aforementioned ‘deconvolution’ allows you to do exactly that, and the time-domain signal you end up with is known as the 'impulse response' of the room. Applying a Fast
Fourier Transform (FFT) to this to express it in the frequency domain then gives you the frequency response of the room. And of course, the idea applies equally well to deriving the frequency response of electronic
circuits as it does to acoustics. This is useful in T&M applications, not least for checking that your device is correctly passing audio within the audible human range.

Distortion and Farina's solution
From using deterministically generated, and therefore repeatable wideband white-noise as the test signals (also known as MLS or Maximum Length Sequence), T&M devices developed further and began to offer analysis based on linear-swept sine waves. The problem with all of these approaches was (and remains) distortion. No real-world piece of audio equipment is free of it, and the harmonics show up in every impulse response, rendering the eventual frequency response readings inaccurate.

Deliverance from this problem has also come from the world of acoustics. In the midto-late 1990s, Professor Angelo Farina, an Italian acoustician working at the University of Parma, showed in research that using an exponentially (or log) swept sine wave test signal, or in other words one where the frequency was being increased exponentially as it was fed into the room or system, resulted in the impulse responses relating to the harmonic distortion components of the system being separated out in time and turning up at the output at slightly different times to the fundamental impulse response of the system. Because the impulse responses for the different harmonics do not overlap time-wise when an exponential sweep
is used, it is possible to separate the impulse responses of the room or system from each other by recording the output digitally and then cutting the recording into smaller audio snippets, one for each of the harmonic impulse responses. By separately Fast- Fourier-transforming the individual impulse responses for the distortion components and summing their resultant frequency responses, you can also quickly determine the Total Harmonic Distortion (THD) in the system.

When Professor Farina presented his findings in a white paper at the European AES conference in Paris in 2000, he called it 'Simultaneous Measurement of Impulse Response and Distortion with a Swept-Sine
Technique', and it became influential. After all, it provided a relatively quick and easy way to measure frequency response and THD, all by using a single log-swept sine-wave input — or chirp. The paper caught the attention of the design team at Audio Precision, and when the APx Series, the company's next range of T&M audio analysers, was launched in 2005, they incorporated swept-sine chirp signals, alongside other more traditional methods of analysis.

Advantages of chirp
There are several advantages to using chirp signals in an audio T&M analyser. Building up an approximation to a complete frequency response by sending discrete stepped sinewave tones through the system and measuring the responses is a slow process, even with modern DSPs, and doesn't recreate a complete frequency response, merely sampling the response in several places. Chirp-based testing, on the other hand generates the whole response and is relatively fast — on AP's eight-channel APx585 analyser, 14 measurements are computed from one chirp signal being fired into the equipment under test, including measurements of magnitude, phase, group delay at different frequencies, and even interchannel
crosstalk, which is evaluated by delaying the chirp signals by known amounts on the different channels, and then comparing the small impulse responses that 'bleed through' at the expected delayed times from the other channels.

The length of the chirp is itself userdefinable; the shortest time available is a quarter of a second, which suffices for testing of equipment with a reasonable signal-to-noise ratio (SNR), or where it's important to have the shortest testing time possible per unit under test, such as on a very busy factory production line. In lowquality equipment where testing with a low SNR could cause distortion in the readings, the SNR can be improved by using a longer chirp. The maximum on the APx585 is four and a half seconds; however, this not only makes the acquisition time longer, but also adds considerably to the process overall, as deconvolving the resultant output and performing the Fast Fourier Transforms on the impulse responses takes a great deal of processing power.

Perhaps the greatest advantage of logswept sine waves is that they are just that —sine waves. As test engineers, we feel comfortable with the concept of analysis based on sinusoidal signals — they provide
decent signal-to-noise performance, and we note with relief that the figures you obtain from a log-swept sine analysis, while more accurate, are not radically different from those you might obtain from a stepped-sine analysis and are expressed in the same way.

The future
Of course, there's always room for improvement. Clever though it is for the APx Series analysers to separate out the distortion harmonics and then recombine them to create a THD reading, they don't currently offer a way to measure the combined THD+N figure that most engineers still prefer to quote. At present there is no way to measure a system's noise— although of course in a well-designed, lownoise system, the THD+N figure would not differ much from the THD. There are as yet no filters for removing potential interference signals from the input, such as 50 or 60Hz mains hum, nor is there provision for multichannel devices that deliberately offset some of their output channels, like home theatre receivers and in-car surround systems that delay their rear surround channels with respect to the Left, Centre and Right channels. At present, these delays would confuse the analyser when in six-channel surround testing mode. However, these features may be added in future upgrades. And of course, the introduction of log-swept chirp has already widened the palette of reliable testing options open to the T&M engineer, adding a fast and efficient means of obtaining accurate frequency response measurements for the equipment under test. Things can only improve further.

MATT BELL was talking to Dr Tom Kite, Vice- President of Engineering at Audio Precision

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