Effect of the shape of time window in estimating the transfer characteristics of the acoustic system having group delay or reverberation
Yoichi Takebayashi, K. Kido · The Journal of the Acoustical Society of America · 1978
This paper describes the effect of the shape of the time window on the errors in estimating the coherence function and the transfer function of the system having group delay or reverberation. It is well known that the windowing determines the spectral resolution and the sidelobes, and the proper time window should be selected from the point of view. The windowing has another effect when the system has group delay. Because the cross-power spectrum obtained from DFTs is equivalent to the circular convolution of the input and the output sequences and the signals come to contain the uncorrelated components in the initial and the final parts of the windows due to group delay, the estimation of the coherence function is biased towards zero. The estimation is improved by using the Hanning window if the delay is sufficiently shorter than the window duration, but the rectangular window is superior to the Hanning window if the delay is longer than about 0.18 times the window duration. The analytical and the experimental results are presented numerically. For the system having reverberation, a similar discussion is also given.