On Restoring Prematurely Truncated Sine Sweep Room Impulse Response Measurements
When measuring room impulse responses using swept sinusoids, it often occurs that the sine sweep room response recording is terminated soon after either the sine sweep ends or the long-lasting low-frequency modes fully decay. In the presence of typical acoustic background noise levels, perceivable artifacts can emerge from the process of converting such a prematurely truncated sweep response into an impulse response. In particular, a low-pass noise process with a time-varying cutoff frequency will appear in the measured room impulse response, a result of the frequency-dependent time shift applied to the sweep response to form the impulse response. Here, we detail the artifact, describe methods for restoring the impulse response measurement, and present a case study using measurements from the Berkeley Art Museum shortly before its demolition. We show that while the difficulty may be avoided using circular convolution, nonlinearities typical of loudspeakers will corrupt the room impulse response. This problem can be alleviated by stitching synthesized noise onto the end of the sweep response before converting it into an impulse response. Two noise synthesis methods are described: the first uses a filter bank to estimate the frequency-dependent measurement noise power and then filter synthesized white Gaussian noise. The second uses a linearphase filter formed by smoothing the recorded noise across perceptual bands to filter Gaussian noise. In both cases, we demonstrate that by time-extending the recording with noise similar to the recorded background noise that we can push the problem out in time such that it no longer interferes with the measured room impulse response.