Delayed Block Transfer Function in the Frequency Domain

When the impulse response of a transfer system is long, it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast Fourier transform (FFT) with a finite length window. The bias error in the estimate is large especially around the resonant frequency of the transfer system. In this paper, therefore, we propose an alternative new method to obtain an accurate estimate of the transfer function. The delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window. Based on these transfer functions, the total characteristics of the transfer system are estimated accurately. In the latter half of the paper, we derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods. By thoroughly comparing the resultant expressions, the superiority and the usefulness of the proposed method are theoretically confirmed. Finally, the simulation experiments show the advantages of the proposed method.