9solution - ECEN 455: Assignment 9 Optional Problems: 1....

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Unformatted text preview: ECEN 455: Assignment 9 Optional Problems: 1. (CSE: 8.17) When the additive noise at the input to the modulator 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. Towards this end, consider the configuration shown in Figure P-8.17. (a) Determine the frequency-response characteristic of the prefilter that whitens the noise. If the power spectral density of the additive noise is S n ( f ) , then the PSD of the noise at the output of the prewhitening filter is S ( f ) = S n ( f ) | H p ( f ) | 2 . In order for S ( f ) to be flat (white noise), H p ( f ) should be such that H p ( f ) = 1 radicalbig S n ( f ) . (b) Determine the frequency-response chracteristic of the filter matched to s ( t ) . Let h p ( t ) be the impulse response of the prewhitening filter H p ( f ) , i.e., h p ( t ) = F- 1 [ H p ( f )] . Then, the input to the matched filter is the signal s ( t ) = s ( t ) h p ( t ) . The frequency response of the filter matched to s ( t ) is S m ( f ) = S * ( f ) e- j 2 ft = S * ( f ) H * p ( f ) e- j 2 ft where t is some nominal time-delay at which we sample the filter output. (c) Consider the prefilter and the matched filter as a single generalizedd matched filter. What is the frequency-response characteristic of this filter? The frequency response of the overall system, prewhitening filter followed by the matched filter, is given by G ( f ) = S m ( f ) H p ( f ) = S * ( f ) | H p ( f ) | 2 e- j 2 ft...
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9solution - ECEN 455: Assignment 9 Optional Problems: 1....

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