In the auditory system case, nx ^ 0, n2 ^ 0, which is desirable. It is also desirable for ctz ^ x. ctz ^ x for a linear system with one more pole than zero (N - M = 1). (Wu shows other special conditions that will make ctz ^ x. In some cases ctz ^ 0, which makes TC impossible.) Thus, for broadband noise:
Wu examined the theoretical case where H(ra) is an ideal bandpass filter (IBPF), shown in Figure 8.2-3. The Q of the IBPF is simply Q = rao/2B. The PDS of the input noise is rectangular, and has an amplitude of Io msV/r/s for |ra| ô rai. Thus, the autocorrelation function of the noise is
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