Given. The impulse response, hp (n), of an ideal low pass filter with is given by...

 

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Given. The impulse response, hp (n), of an ideal low pass filter with is given by hp(n) = ain(uk) *H₂(W) passband gain 1 and cutoff frequency, -@. Using the information given above, what is the impulse response, hap (n), of an ideal bandpass filter with passband gain 1 and cutoff frequencies and ₂? H₂(W) -TL -"-W₂ -W₁ W #R Problem 2. Given: The modulation property of the DTFT says the DTFT of cos(won)x(n) is [X(w-wo) + X(w+wa)]; where X (as) is the DTFT of x(n) 761 2sini and we TU W₁ Wz R W₂+01 2 if x (n) = Then, a. Sketch X(w) including labels for amplitude and frequency. (Hint, look at the relationship provided in problem 1) b. If x(n) is the impulse response of a filter, what kind of filter is it? (Low pass, High pass, bandpass, notch?) c Sketch is [X(-) + X(w+wo)], including labels for amplitude and frequency d. If cos(wen)x(n) is the impulse response of a filter, what kind of filter is it? (Low pass, High pass, bandpass, notch?), Given. The impulse response, hp (n), of an ideal low pass filter with is given by hp(n) = ain(uk) *H₂(W) passband gain 1 and cutoff frequency, -@. Using the information given above, what is the impulse response, hap (n), of an ideal bandpass filter with passband gain 1 and cutoff frequencies and ₂? H₂(W) -TL -"-W₂ -W₁ W #R Problem 2. Given: The modulation property of the DTFT says the DTFT of cos(won)x(n) is [X(w-wo) + X(w+wa)]; where X (as) is the DTFT of x(n) 761 2sini and we TU W₁ Wz R W₂+01 2 if x (n) = Then, a. Sketch X(w) including labels for amplitude and frequency. (Hint, look at the relationship provided in problem 1) b. If x(n) is the impulse response of a filter, what kind of filter is it? (Low pass, High pass, bandpass, notch?) c Sketch is [X(-) + X(w+wo)], including labels for amplitude and frequency d. If cos(wen)x(n) is the impulse response of a filter, what kind of filter is it? (Low pass, High pass, bandpass, notch?),

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Lets break down the problems step by step Problem 1 The impulse response of an ideal low pass filter ... View the full answer