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In order to recover the original signal. You must get the maximum frequency of the original signal, and at least set the sampling frequency to 4 times. In your case: sampling frequency >= 4*50 = 200 samples/sec. The bigger the sampling freq. the best you can recover the signal.
Sampling frequency must be twice the highest frequency component present in the given signal.
the higher the sampling frequency the better will the signal be recovered.
Although the Nyquist criterion says the freq needs to be at least twice the freq. in reality depending on the
signal quality requirement and the available sampling options it should be at least 4 to 5 times.
You also have to satisfy the relationship Fi/Fs = M/N.
Fi = 50Hz, N = 512, M = # of cycles you want to sample - say 4. Then,
See, the cycle frequency is 50 Hz, i.e. 50 cycles/ second. That is 1 cycle will have the time period of 1/50 seconds. Also that the sampling is given by 512 samples/ cycle that means there are 512 samples in 1/50 seconds of time(which is 1 cycle). Therefore, to find the time between the samples is,
(1/50)/512 = 1/(50X512) is nothing but the sampling time. So, (50X512) will give us Fs, the sampling frequency.
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