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Accuracy Applied: Part 1 In A Series On The Keys Of Loudspeaker Measurements

"Frequency response is the single most important aspect of the performance of any audio device. If it is wrong, nothing else matters." – Floyd Toole, 2009

Quasi-Anechoic Measurement Techniques

Due to the expense of – and limited access to – anechoic chambers, much work has been devoted to the development of “quasi-anechoic” measurement techniques which seek to enable measuring the frequency response of loudspeakers (and microphones) in an ordinary, semi-reverberant room.

These techniques are all time-selective; they work by stimulating the loudspeaker with a broadband signal and analyzing that portion of the measured response that contains the direct sound from the loudspeaker but excludes the portion containing reflections from the room surfaces.

Quasi-anechoic techniques take advantage of one of the foundations of signal processing – the equivalence of a linear system’s frequency response and its impulse response. In the frequency domain, a system’s frequency response, H(f) represents its output magnitude and phase (or real and imaginary parts) per unit input, as a function of frequency. In the time domain, its impulse response, h(t), represents the system’s output as a function of time when stimulated by a unit impulse or Dirac delta function.

These two representations of a dynamic system are equivalent, and one can be derived from the other using Fourier analysis. For example, the Fourier transform of the impulse response yields the frequency response. Similarly, the inverse Fourier transform of the frequency response yields the impulse response.

Figure 3: A loudspeaker measurement on-axis in a semi-reverberant space.

So how do time selective techniques work in practice? Consider the measurement setup depicted in Figure 3. A measurement microphone is positioned on-axis in front of a loudspeaker in a semi-reverberant room. To be in the far field of the loudspeaker, the distance d is chosen such that it is more than 3 times M, the largest significant dimension of the loudspeaker. The path length of the direct sound from the loudspeaker to the microphone is d, and the path length of the first reflection from the nearest reflecting surface (the floor in this case) is 2dR.

Based on this geometry, the time difference, T, between the direct sound arrival at the microphone and the first reflection is T=(2d_R-d)/c, where c is the speed of sound.

Figure 4 (upper graph) shows an impulse response measured 3.84 feet (1.17 meters) in front of a bookshelf speaker located 9.4 feet (2.86 meters) above the floor in a large room. The peak in the impulse response occurs at about time t = 3.5 milliseconds (ms), which corresponds to the direct path length (3.84 feet) divided by the speed of sound (334 microseconds or m/s).

Figure 4: A measured Impulse Response (top) and Energy Time Curve (bottom).

Although it’s difficult to see in the impulse response, there are small secondary peaks that occur at time t = 16.5 ms and later. These smaller peaks, which are due to the arrival of reflections from the floor, walls and other room surfaces are much easier to see in the lower graph in Figure 5, which is called the Energy Time Curve (ETC).

Figure 5: RMS Level and Phase response computed from the Impulse Response in Figure 4 after windowing.

The ETC, which was introduced in the 1960s [9], is essentially a plot of the envelope of the impulse response. It’s plot of magnitude on a logarithmic scale makes it much easier to see the arrival time of room reflections.

Time-selective or quasi-anechoic measurements would apply a window to the impulse response, eliminating any data after the first reflection arrives (about 15 ms, in this case), and then use a Fourier transform to compute the frequency response magnitude and phase (Figure 5). Typically, a rectangular window with cosine tapers at the beginning and end is used, to create smooth transitions. In Figure 5, the frequency response magnitude has been multiplied by the magnitude of the voltage signal applied to the loudspeaker to determine the RMS Level in dBSPL.

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Joe Begin, PE (Acoustical Engineering), a graduate of McGill University (B.Sc.) and the University of Canterbury (M.Sc.), has more than 35 years of experience in test and measurement. As director of applications and technical support at Audio Precision, he is involved in product management, audio and electroacoustic test applications engineering, and technical support.

References
1. IEC 60268-5:2003+A1:2007 – Sound system equipment, Part 5: Loudspeakers.
2. Private communication, J. Woodgate, 2017. IEC 60268-5 Maintenance Team Project Leader for IEC TC100.
3. IEC 61305-5:2003 – Household high-fidelity audio equipment and systems – Methods of measuring and specifying the performance – Part 5: Loudspeakers.
4. Toole, Floyd (2009). Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms. Taylor and Francis.
5. C. Struck and S. Temme (1992). Simulated Free Field Measurements. 93rd AES Convention.
6. L.L. Beranek (1986). Acoustics. Acoustical Society of America, New York.
7. ISO 3745:2012. Acoustics – Determination of sound power levels of noise sources using sound pressure – Precision methods for anechoic and hemi-anechoic rooms.
8. J. M. BERMAN, and L. R. FINCHAM. The application of digital techniques to the measurement of loudspeakers, JAES, 25, June (1977).
9. R. C. Heyser (1971) Determination of Loudspeaker Signal Arrival Times, Parts I, II and III. JAES, vol 19.

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