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 P4.22.
1. Determine the frequency response characteristic of the prefilter that whitens the noise, in terms of sn( f ), the noise power spectral density.
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.
