The harmonic function cx[k] for a periodic continuous-time signal x(t) whose fundamental period is 4 is zero everywhere except at exactly two values of k, k = ±8. Its value is the same at those two points, cx[8] = cx[?8] = 3. What is the representation time used in calculating this harmonic function?
What will be an ideal response?
The harmonic function cx[k] for a periodic continuous-time signal x(t) whose fundamental period is 4 is zero everywhere except at exactly two values of k, k = ±8. Its value is the same at those two points, cx[8] = cx[?8] = 3. What is the representation time used in calculating this harmonic function?
32
If the signal has only two equal-value real impulses in its CTFS harmonic function it is a cosine. If the impulses in the harmonic function occur at k = ±8 that means that the frequency of that cosine is at the 8th harmonic of the fundamental. The cosine fundamental period is 4 so its frequency is 1/4. If 1/4 is the 8th harmonic of the fundamental frequency of the CTFS representation that fundamental frequency must be 1/32 and the representation time must be T=32.
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