For this problem, now assume that you are trying to detect a known discrete-time
ID: 3223873 • Letter: F
Question
For this problem, now assume that you are trying to detect a known discrete-time signal s[n] in IID Gaussian white noise V [n]. Assume that the noise V [n] is zero mean with a variance 2 v .
Assume that the transmitted signal s[n] is one period of a DT sinusoid, i.e., s[n] = ( sin((2/8)n), 0 n 7 0, otherwise
(a) Sketch the impulse response h[n] for the matched filter.
(b) Three ECE 521 students are discussing how to improve the output SNR for this system. Rank the three suggestions below from best to worst in terms of improving output SNR
Prabha: Double the amplitude of s[n] to be 2 sin((2/8)n) while keeping the signal length and frequency unchanged.
Stew: Double the length of s[n] so it contains two periods of sin((2/8)n) for 0 n 15 while keeping the amplitude and frequency unchanged.
Fran: Double the frequency of s[n] to be (2/4) while keeping the amplitude and length unchanged (0 n 7).
Explanation / Answer
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For this problem, now assume that you are trying to detect a known discrete-time signal s[n] in IID Gaussian white noise V [n]. Assume that the noise V [n] is zero mean with a variance 2 v .
Assume that the transmitted signal s[n] is one period of a DT sinusoid, i.e., s[n] = ( sin((2/8)n), 0 n 7 0, otherwise
(a) Sketch the impulse response h[n] for the matched filter.
(b) Three ECE 521 students are discussing how to improve the output SNR for this system. Rank the three suggestions below from best to worst in terms of improving output SNR
Prabha: Double the amplitude of s[n] to be 2 sin((2/8)n) while keeping the signal length and frequency unchanged.
Stew: Double the length of s[n] so it contains two periods of sin((2/8)n) for 0 n 15 while keeping the amplitude and frequency unchanged.
Fran: Double the frequency of s[n] to be (2/4) while keeping the amplitude and length unchanged (0 n 7).
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