Z-transform

Contour Integral and Residue Theory for Inverse $z$-Transform

Contour Integral and Residue Theory for Inverse $z$-Transform
  1. What is Z-transform and inverse Z-transform?
  2. What is residue theorem formula?

What is Z-transform and inverse Z-transform?

Z-Transform is basically a discrete time counterpart of Laplace Transform. Z-transform of a general discrete time signal is expressed in the equation-1 above. The range of values of 'Z' for which above equation is defined gives ROC (Reason of Convergence) of Z-transform.

What is residue theorem formula?

From the residue theorem (which produces a factor 2πi that cancels the similar factor in the definition of J), we getf(t)=J=(residue atz=a+ik)+(residue atz=a-ik).

Coherence Coherence between two signals How to convey the underlying idea using spectral decomposition and orthogonal projections?
Coherence between two signals How to convey the underlying idea using spectral decomposition and orthogonal projections?
What is coherence between two signals?What is the difference between correlation and coherence?What is meant by coherence function where is it used?W...
Scalogram Why does a signal with constant frequency have spots that changes colors at a specific value of scale (and so frequency) in the scalogram?
Why does a signal with constant frequency have spots that changes colors at a specific value of scale (and so frequency) in the scalogram?
What does a scalogram show?What is the difference between CWT and DWT?What is scalogram matlab? What does a scalogram show?The scalogram is the abso...
Sampling Minimum Sampling Frequency
Minimum Sampling Frequency
MINIMUM NUMBER OF SAMPLES f. The sampling theorem states that a real signal, f(t), which is band-limited to f Hz can be reconstructed without error fr...