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Transfer-Function Measurementwith Maximum-Length Sequences*
DOUGLAS DRA Laboratories, D. RIFE VA 22170, USA

Sterling, AND

JOHN VANDERKOOY** Audio Research Group, University of Waterloo, Waterloo, Ont. N2L 3Gl, Canada

A comprehensive analysis of tranfer-function measurement based on maximum-length sequences (MLS) is presented. MLS methods employ efficient cross correlationbetween input and output to recover the periodic impulse response (PIR) of the system being measured. For perfectly linear noiseless systems, the PIR so obtained is shown to be identical to the system's response to a simple periodic square pulse. In the face of external noise and nonlinearities, the MLS approach is shown to be as robust as timedelay spectrometry (TDS). Like TDS, MLS methods are alsocapable of rejecting or selecting nonlinear (distortion) components when measuring weakly nonlinear systems. An MLS coherence function is defined that is not unlike the coherence function usually associated with dual-channel FFT analyzers. Finally, a new low-cost instrument based on the IBM-PC makes MLS measurements generally available and affordable.

0 INTRODUCTION The use of maximum-lengthsequences (MLS) to measure the impulse response of linear systems is not new; the basic idea can be traced back at least two decades [ 1]. Binary MLSs are periodic two-level pseudorandom sequences of length L = 2/v - 1, where N is an integer, which yield essentially an impulse under circular autocorrelation [2]. The basic idea is to apply an analog version of an MLS to a linear system, sample theresulting response, and then cross-correlate that response with the original sequence. The result of the cross correlation is essentially the system impulse response. Schroeder [3] used MLS methods to measure the impulse response of concert halls and also derived the reverberant decay curve by reverse-integrating the square of the measured response. Alrutz, as described in Ando [4], refined thetechnique by speeding up the cross-correlation calculation with an algorithm adapted from Hadamard spectroscopy [5]. More recently, Borish and Angell [6], independently of Alrutz, discovered * Presented at the 83rd Convention of the Audio Engineering Society, New York, 1987 October 16- 19;revised 1988 August 16. Member of the Guelph-Waterloo ** program for graduate work in physics,
J. Audio Eng. Soc.,Vol. 37, No. 6, 1989 June

and published essentially the same cross-correlation algorithm. While these references show that MLS measurements are practicable and generally provide high noise immunity, they focus rather narrowly on either computational algorithms or specific applications such as room acoustic measurements. We feel that a wider view of MLS methods is called for. With thedevelopment of the first commercial MLS instrument by one of the authors (DR) [7], it became possible to perform many experiments which led to a wider and more comprehensive theoretical framework. The results convinced us that the MLS approach is not only viable but actually preferable for many applications over other techniques, including dual-channel fast Fourier transform (FFT), periodic pulse testing,and time-delay spectrometry (TDS) [8]. We show that, under ordinary conditions, the impulse response obtained from an MLS measurement is identical to that obtained directly by periodic pulse excitation, except that noise and distortion immunity is now comparable to TDS. Furthermore, with preemphasis and preaveraging techniques, we show that the overall noise immunity of MLS is actually superior tothat of TDS for most applications. In periodicpulse testing, the impulseresponseis measured by applying a narrow pulse to the system. If
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RIFE AND VANDERKOOY

PAPERS

the pulse is narrow enough, the system's impulse response is obtained directly without the need for further processing. But the narrow pulse has a very high crest factor and hence a very low energy content, and many...