Sampling Sinusoids

The questions below are due on Thursday February 27, 2025; 02:00:00 PM.

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Let f(t) represent the following continuous-time signal:

f(t)=4\cos(300\pi t)+2\sin(400\pi t)+\cos(600\pi t)

Part a. Let f_a[n] represent a discrete-time signal that is obtained by sampling f(t) with sampling frequency f_{sa}=100 Hz, so that

f_a[n] = f(n/f_{sa})

Determine the fundamental (shortest) period of f_a[n] (if one exists). Briefly explain.

Part b. Let f_b[n] represent a discrete-time signal that is obtained by sampling f(t) with sampling frequency f_{sb}=200 Hz, so that

f_b[n] = f(n/f_{sb})

Determine the fundamental (shortest) period of f_b[n] (if one exists). Briefly explain.

Part c. Let f_c[n] represent a discrete-time signal that is obtained by sampling f(t) with sampling frequency f_{sc}=300 Hz, so that

f_c[n] = f(n/f_{sc})

Determine the fundamental (shortest) period of f_c[n] (if one exists). Briefly explain.

Part d. Determine a sampling frequency f_{sd} for which

f_d[n]=f(n/f_{sd})

is not periodic (if such a frequency exists). Briefly explain.

Please upload a single pdf file that contains your answers to all parts of this problem:

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