Sampling and reconstruction (Advance level)

Time sampling - continuous time signal to discrete time signal

Reconstruction- discrete time signal to continuous time signal

The sampling works by the sample theorem:

We usually let x(t) be a band limited with all the X(w)=0 for |w|>B

Then x(t) can be uniquely determined by its samples x(nt).

ws = 2B is called Nyquist sampling frequency

Aliasing is an effect that cause different signals look the same like aliases of one another. This is an important technique in signal processing. Aliasing also refer to distortion or artifact that results happen if signal reconstructed from samples is different from the original one too.

In addition when ws < 2B, X(w-kws) will overlap each other. Thus, X(w) cannot be recovered. The low frequency component of Xs(w) also contains high frequency components in X(w). This phenomenon is called aliasing.

Reduce aliasing:

1. increase sampling frequence, 2. use anti-aliasing filter – lowpass filter

youtube video: Sampling, Aliasing

Set of videos for SAMPLING and RECONSTRUCTION

Practice Problems
Sampling-MIT questions Solution

Reconstruction-MIT questions Solution

Text book- Question Solution

Extra Resources
MIT lecture and video