Discrete Linear System Summary

1.   Sampling is multiplication by a comb of delta functions:

á á   

2.   Fourier transformá á á 

á á   

3.   Alternative representation of FT:

á á   

á á á á á á á  á possibility of aliasing.

4.   Finite length sequence á convolution with sinc function.

5.   Windowingá  á multiply sequence in order to achieve balance between width and sidelobes of convolving function

6.   Leakage á sidelobes of window function may affect appearance of samples in the frequency domain.

7.   Circular convolution á sampling the function in the frequency domain á á periodicity in the time domain.

8.   Filtering of sampled data in frequency domain is convolution in the time domain over a periodic function.

9.   Stability determined as for continuous systems: stable if no poles in Right Half-Plane.