Nyquist-Shannon sampling theorem, which is a modified version of the Nyquist sampling theorem, says that the sampling frequency needs to be twice the signal bandwidth and not twice the maximum frequency component, in order to be able to reconstruct the original signal perfectly from the sampled version.
If B is the bandwidth of the signal, then Fs > 2B is required, where Fs is sampling frequency. The signal bandwidth can be from DC to f1 (or) from f1 to f2 where B = f2-f1.
The above concept comes into picture when frequency translation is achieved with under-sampling
Suppose a signal fc = 70MHz, f1 = 60MHz & f2 = 80MHz. Highest frequency component present in the signal is f2 = 80MHz. if Fs > 2*(f2) => Over sampling. 2*(f2-f1)<Fs<2*(f2) => undersampling. Suppose if Fs is chosen as 40MHz; Divide the whole band into frequency zones of fs/2. The signal will appear in the first frequency zone (0 to fs/2) with spectral inversion some times (Depending which frequency zone the signal was present before sampling).
Q: Suppose a signal fm = 1kHz (sinusoidal), sampled at fs = 1.5kHz, and passed through a LPF with cut-off frequency 800Hz. The sinusoidal is present at which frequency ??
Mail me to know the answer..
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And here comes the confusing point.. For a complex signal, the sampling frequency required is same as highest frequency component (not double) or same as bandwidth. I don’t have a reasonable explanation now. I’ll come up with something sometime later..
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