Signal Sampling and Reconstruction:
The process of sampling is a bridge between continuous-time and discrete-time systems. Sampling is a process of converting a continuous-time signal to a discrete-time signal, and under certain conditions, the continuous-time signal can be completely recovered from its sampled sequence.
Aliasing or Spectrum Folding:
When fs < 2fm, the copies overlap, and hence, the perfect reconstruction becomes impossible. If this Nyquist criterion is not considered, the folded back portion overlaps the original spectrum. This results in a new shape of the reconstructed spectrum filtered by LPF. And this, undoubtedly, gives a signal different from X(t). This problem is called "aliasing".
Convolution:
The two most important attributes of systems are linearity and time-invariance. In this lecture, we develop the fundamental input-output relationship for systems having these attributes. It will be shown that the input-output relationship for LTI systems is described in terms of a convolution operation. The importance of the convolution operation in LTI systems stems from the fact that knowledge of the response of an LTI system to the unit impulse input allows us to find its output to any input signal.
