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Impulse response using inverse discrete-time Fourier transform.

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An ideal low-pass filter is described in the frequency-domain by

H_d(e^(jw)) = 1 . e^(-jaw) , |w| <= w_c
0 , w_c < |w| <= PI

where w_c is called the cutoff frequency and a (denoting symbol alpha) is called the phase delay.

Determine the ideal impulse response h_d(n) using the inverse discrete-time Fourier transform.

Please note that notation X_y indicates "X subscript y" in above description.

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Solution Preview

Let hd[n] be the time-domain impulse response and Hd(ejw) be its discrete-time fourier transform.:
Time domain  frequency domain

To solve this problem, we can ...

Solution Summary

The expert examines impulse response using inverse discrete-time Fourier transform.