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Three Fourier analysis of systems problems

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Fourier Analysis of Systems:

1. A linear time-invariant continuous-time system has the frequency response function H(Ï?)=5cos(2Ï?), compute the system's impulse response h(t):

2. A signal with the highest frequency component at 10 kHz is to be sampled. To reconstruct the signal, the sampling must be done at a minimum frequency of:

3. An ideal low-pass digital filter has the frequency function H(Ï??) as shown in the figure (see attached doc). Determine the unit-pulse response h[n] of the filter. Note: The discontinuities occur at -Ï?/4 and +Ï?/4.

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