Ideal sampling of audio signals-Periodic spectrum
Discritizing a signal in the ideal sense is equivalent to multiplying by a Dirac delta impulse train.  The Fourier transform of an impulse train is also an impulse train.  Lastly, a multiplication in the time domain is equivalent to a convolution in the frequency domain.  So when we discritize a signal, we are convolving that signal’s frequency transform with an impulse train, resulting in a frequency spectrum that repeats at intervals equal to the sample rate, making it periodic.