I have to disagree with you on these points. You once mentioned several DSP books you are using in your courses. My recollection is that they all explain this reasonably well.... I had thought of using impulse function but then it wasn't making sense to me in the given context.
... An impulse train can't produce such a spectrum.
... I have checked some books but no one explains Nyquist theorem the way it should be explained.
The logic is very simple for any sampling shape (pulse, impulse etc.), but is easies with an impulse function. The arguments can be made very simply and at a high level using basic transform properties.
First, the idea of sampling is modeled simply as the multiplication of an impulse train times the input signal. The act of multiplication in the time domain allows us to use the convolution property, which says that the frequency spectrum will be the convolution of the signal spectrum with the impulse train spectrum. We know that the transform of an impulse train is an impulse train, so convolution of signal spectrum with an impulse train creates a signal frequency spectrum at every harmonic of the sample rate.
So, you are correct that the impulse spectrum does not give that shape. All it does is create the shifted versions of the signal spectrum. It is the signal spectrum that gives that shape.
Now, in reality we can't make an impulse train for sampling. But think about it. Any periodic sampling shape will have Fourier series components at harmonics of the sampling frequency. The only difference is that the amplitudes of the impulses that represent the Fourier coefficients are not the same at all frequencies. Actually, typically the amplitude decrease as frequency increases. But the amplitude is not critical because you still are going to get shifted versions of the signal spectrum, and the Nyquist criterion is still applicable.
So, you see, very basic ideas are used here. The specifics will depend on the exact signal spectrum and exact nature of the sampling process, but if you only care about general effects, such as frequency locations, the basic ideas tell you all you need to know. The signal bandwidth and the sampling rate are the primary factors.
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