# signal sampling and recovery

Discussion in 'Homework Help' started by jut, Nov 16, 2009.

1. ### jut Thread Starter Senior Member

Aug 25, 2007
224
2
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.

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2. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
Lotta work -- and completely unnecessary.
Code ( (Unknown Language)):
1.
2. 2πf = 14π
3. f=7 Hz.
4. fs(minimum) = 14 Hz.
5. 1/14 = 71.4 milliseconds
6.
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.

3. ### jut Thread Starter Senior Member

Aug 25, 2007
224
2
that's a whole lot easier, ugh.

thanks for the help.