Sampling Sinusoids
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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: No file selected