FIGURE 8.0-3 (A) Autocorrelation function of the PRBN square wave, n(t). (B) Approximate autopower spectrum of n(t). (The small negative level in the autocorrelation function was neglected.) Vn(t) is used to make a random noise input for neuro-sensory systems (e.g., light, sound) being studied by a noise technique.
At low frequencies, the peak amplitude of the PDS is a2. At a frequency of ra 10, the magnitude of ®m(ra) is down 10% from peak. That is, ®m(ra10) = 0.9a2. Solving algebraically by trial and error, when (©At/2) = 0.56 rad, ^m(®10) = 0.9a2, and ©10 = 5.60 E4 r/s and f10 = 8.91 E3 Hz. Thus, the PDS of the raw dc-offset TTL output of this PRBN generator is substantially "white" (flat) out to about 9 kHz, given the 50-kHz clock and 32-state shift registers.
Recall that if the raw n(t) is conditioned by being passed through a linear low-pass filter, G(jra), the autopower spectrum at the filter output, z, is given by
If the conditioned PRBN, z(t), is used to identify H(jra), then by the development above,
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