When the additive noise at the input to the demodulator is colored, the filter matched to the signal no longer maximizes the output SNR. In such a case, we may consider the use of a prefilter that "whitens" the colored noise. The prefilter is followed by a filter matched to the prefiltered signal. Toward this end, consider the configuration shown in Figure P-10.10.
1. Determine the frequency-response characteristic of the prefilter that whitens the noise.
2. Determine the frequency-response characteristic of the filter matched to s(t).
3. Consider the prefilter and the matched filter as a single "generalized matched filter." What is the frequency-response characteristic of this filter?
4. Determine the SNR at the input to the detector.
