The signal x(t) = cos (14*pi*t) is sampled at a sampling interval of T = 0.1 seconds. Can we recover the signal from its samples (why or why not).


I attached my attempt at a solution.

What I did was this: I did a fourier transform on the signal, X(w), which resulted in two delta functions: one located at -14pi, the other at 14pi. Now, the fourier transform of the sampled signal, Xs(w) equals X(w) plus X(w) shifted by integer multiples of n*2*pi/Ts which equals 20*pi.

From my plot of Xs(w), there are delta functions interspersed to the left and right of the original X(w). I don't know if the original signal can be recovered with an anti-aliasing filter.

 

Lotta work -- and completely unnecessary.

2πf = 14π
f=7 Hz.
fs(minimum) = 14 Hz.
1/14 = 71.4 milliseconds

The sampling frequency must be twice the highest frequency component. A sampling frequency of 10 Hz., corresponding to a sampling period of 100 milliseconds, just won't make it.

 

that's a whole lot easier, ugh.

thanks for the help.