33 36 Measuring Room Impulse Responses Perceptually the conference room seemed

33 36 measuring room impulse responses perceptually

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3.6 Measuring Room Impulse Responses Perceptually, the conference room seemed to be an acoustically “dead” room with negligible reverberation. This observation was quantified using the Gaussian noise recordings, including the signals from the reference microphone mounted in front of the loudspeaker, to estimate the room impulse responses and reverberation times. The Gaussian test signals were similar to those used in other impulse response measuring experiments [77][95]. Recall the room impulse response model of Equation 2.6: ) ( ) , ( ~ * ) ( ) ( ) ( t v t d h t s t x m s m m + = r ) , ( ~ ) ( t d h s m r is the source-output to microphone-output impulse response, which is the convolution of the room impulse response with the microphone-channel impulse response. ) , ( ~ ) ( t d h s m r can be measured when s ( t ) is known and is sufficiently white over the duration of an array recording. The reference microphone provided the known source signal, s ( t ), while its Gaussian properties yielded sufficient wide- band power over the duration of the recording. Since there were no anechoic measurements of the microphone system, there was no way to recover the actual room impulse response from ) , ( ~ ) ( t d h s m r . However, if the microphone system is linear and behaves similar to a bandpass filter, then ) , ( ~ ) ( t d h s m r is a band-limited approximation to the true room impulse response, ) , ( ) ( t d h s m r . 3.6.1 Least-Squares Fit to Input-Output Data A room impulse response estimation procedure was developed based on the discrete-time form of Equation 2.6: ] [ ] , [ ~ * ] [ ] [ ) ( n v n d h n s n x m s m m + = r (3.3) As discussed in Chapter 2, the impulse responses are highly dependent on m d r and ) ( s d r , as well as the environmental factors. However, it will be assumed that the environment was constant over the duration of each Gaussian array recording, which is 5 seconds long, and that the room impulse responses remained 34
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fixed as well for this duration. Under these conditions, the explicit dependence on the source location, ) ( s d r , can be dropped, and Equation 3.3 can be re-written as: ] [ ] [ ~ * ] [ ] [ n v n h n s n x m m m + = Considering only one microphone signal at a time, the microphone index, m , can also be dropped from the notation: (3.4) ] [ ] [ ~ * ] [ ] [ n v n h n s n x + = Room impulse responses have infinite duration in nature. However, their power becomes negligible in comparison to the power of the direct-path sound in finite time (See Section 3.6.3), and they can be modeled accurately by finite-duration sequences. If the duration of the truncated, discrete-time room impulse response is I points, then the convolution, represented by “*” in Equation 3.4 can be expanded as follows: (3.5) ] [ * ] [ ] [ ~ ] [ 1 0 n v i n s i h n x I i + = = Hence, the goal is to estimate for ] [ ~ n h 1 0 I n using the data from the N -point Gaussian noise recordings where N>>I . This was done using the block-processing scheme described in Section 3.4 in conjunction with a DFT-based method that minimized the sum of squares error between the DFT of the modeled microphone signals and the DFT of the observed microphone signals.
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