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Obtaining The Impulse Response: Part 2 In A Series On The Keys Of Loudspeaker Electroacoustic Measurements

Methods of obtaining the impulse response of a loudspeaker, and the pluses/minuses of each approach.

Editor’s Note: Part 1 of this series (here) provided a primer on the essentials of several loudspeaker measurements, including frequency response, sensitivity, input voltage/power and more. Here the authors further the discussion with a look at the key issue of impulse response and related factors.

To use time-selective measurement techniques, one must first obtain the impulse response of a loudspeaker as set up in the test room. There are several methods available, each having certain advantages and disadvantages.

Impulse Testing

The most direct way of obtaining the impulse response is to measure it directly through impulse testing.  This involves applying a narrow (e.g., 10 µs wide) voltage pulse to the loudspeaker and measuring its response with a microphone. A sufficiently large room is required such that the direct response from the loudspeaker has substantially decayed by the time the first room reflection arrives at the microphone.

The energy in the pulse is spread over a wide frequency range, resulting in a low signal-to-noise ratio (SNR), particularly at low frequencies, even with a pulse several tens of volts in magnitude. As a result, many averages must be used to improve the SNR. Impulse testing was first developed in the 1970s [1]. It has largely been replaced by other measurement techniques.

Maximum-Length Sequence Measurements

The MLS method of measuring an impulse response was originally presented by Borish and Angell in 1983 [2]. A maximum length sequence (MLS) is a type of pseudo-random binary sequence. It can be specified in terms of its order N, where N represents the number of binary digits (or shift registers) used to create the sequence. An MLS of order N has a length of 2^N-1 and contains every possible combination of the binary values 0 or 1 in its N digits, (except the zero vector, in which all digits are 0).

An MLS has some interesting properties that make it well suited to measuring impulse responses [3]. For practical purposes in audio testing, MLS signals are made symmetric (i.e., they are scaled to have values of +1 or -1 instead of 0 or 1).

One interesting property of a raw MLS signal is its crest factor (ratio of peak to rms level): All samples have a value of either +1 or -1 with a random distribution. Hence, the peak value and the rms value are both 1.0, resulting in a crest factor of 1.0, or 0 dB. This result only applies to a raw MLS, however. Once an MLS signal is passed through filters present in a typical audio measurement chain, the waveform is modified considerably, and its crest factor approaches a nominal 11 dB [3].

In loudspeaker testing, the MLS technique is based on exciting the device under test (DUT) with an MLS and measuring its output. The impulse response is obtained by circular cross correlation of the measured output with the MLS signal input to the DUT. Once the impulse response has been derived, like any quasi-anechoic technique, it can be windowed to remove the portion containing reflections, and then Fourier transformed to yield an estimate of the DUT’s transfer function.

By nature, an MLS signal is spectrally flat (like white noise). The signal is often filtered to have a pink noise spectrum (i.e., the rms level decreases linearly with frequency), which is more suitable for acoustic systems.

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One of the advantages of MLS testing over other techniques is that, when averaging is used, it has relatively high immunity to steady or impulsive noise that is not correlated with the MLS input sequence. A disadvantage, however, is that it’s impossible to separate the linear response of the system from nonlinearities, such as harmonic distortion. Loudspeakers always have relatively high levels of distortion compared to electronic systems. In an impulse response measured via MLS, this distortion and other nonlinearities appear as artifacts or peaks distributed along the impulse response.

Log-Swept Sine Measurements

A sine signal with continuously varying frequency is often called a chirp. Linearly swept sine chirps, wherein the sine frequency varies linearly with time, have been used in audio test for many decades, including in time delay spectrometry (TDS). TDS is another well-known quasi-anechoic measurement technique, first introduced in 1967 [4]. These methods are also subject to the limitation that non-linear effects such as distortion cannot be separated from the system’s linear response.

The value of chirp signals changed dramatically when the first logarithmic chirp technique was introduced by Farina in 2000 [5]. He discovered that when a log-swept sine chirp signal is used to stimulate a system, through deconvolution, it is possible to simultaneously derive the linear impulse response of the system as well as separate impulse responses for each harmonic distortion component.

For example, Figure 1 shows the result of deconvolution of the signal from an analog graphic equalizer stimulated with a log-swept sine chirp [6]. The linear system impulse response is shown at time zero, and the impulses of the harmonic distortion components appear logarithmically spaced in negative time.

Figure 1: Impulse response derived by deconvolution following a chirp measurement of an analog graphic equalizer. The amplitude axis has been enlarged to show the harmonic distortion impulses [6].

By carefully time-windowing and Fourier transforming the various impulses, the individual response functions can be recovered, from which many different measurements can then be derived mathematically. In other words, almost every common audio measurement can be obtained from a single, fast acquisition, dramatically decreasing test time.

Farina’s original paper focused on measuring the response of rooms and loudspeakers. Müller and Massarini [7], motivated by the requirement to measure high quality room impulse responses, showed that the log-swept sine chirp method is preferable to MLS for room measurements as well as for most DUTs, including electro-acoustic devices.

Kite [6] demonstrated that log chirp measurements of audio devices provide comparable results to traditional swept sine measurements and suggested an extension to measure crosstalk. The extension involves staggering the stimulus signals applied to each channel of a DUT such that each channel is offset from the previous one by a short time.  This enables crosstalk to be measured simultaneously with frequency response and distortion.

The log-swept sine chirp measurement became a hallmark of Audio Precision’s APx500 audio analyzer platform, first introduced in 2006 with the launch of the APx585 8-channel audio analyzer. Since its introduction, the APx platform has had two chirp measurements intended for electronic audio test, named Continuous Sweep and Frequency Response.

The Continuous Sweep measurement provides a multitude of audio results including level, gain, phase, harmonic distortion, group delay, crosstalk, impulse response and more. The Frequency Response measurement contains a subset of these results for users who simply want to quickly measure a device’s level and gain versus frequency, and its deviation from flatness.

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