Question: Assume you sample a continuous-time signal x(t) at Fs = 500 Hz for a total time duration of 100 milliseconds to obtain x[n]. Further, assume that x(t) was sinusoidal. You then perform an FFT on x[n] to obtain the magnitude spectrum as shown below. All the FFT magnitude values are shown; assume there was no zero padding, no windowing, no shifting or centering of the FFT output, and no aliasing occurred in the sampling process
(a) How many samples of x(t) did you obtain?
(b) What is the real-world frequency resolution (Δf) of the FFT?
(c) What was the real-world frequency of x(t)?
(d) Exactly how many periods of x(t) were sampled?