Howtosignalprocessing
- What is the difference between Z-transform and Fourier transform?
- Why Z-transform better than Fourier transform?
- What is the relationship between Fourier and Z-transform?
- What is convergence in Z-transform?
What is the difference between Z-transform and Fourier transform?
Fourier transforms are for converting/representing a time-varying function in the frequency domain. Z-transforms are very similar to laplace but are discrete time-interval conversions, closer for digital implementations. They all appear the same because the methods used to convert are very similar. Save this answer.
Why Z-transform better than Fourier transform?
The z-transform, on the other hand, is especially suitable for dealing with discrete signals and systems. It offers a more compact and convenient notation than the discrete-time Fourier Transform.
What is the relationship between Fourier and Z-transform?
There is a close relationship between Z transform and Fourier transform. If we replace the complex variable z by e –jω, then z transform is reduced to Fourier transform. The frequency ω=0 is along the positive Re(z) axis and the frequency ∏/2 is along the positive Im(z) axis.
What is convergence in Z-transform?
The region of convergence, known as the ROC, is important to understand because it defines the region where the z-transform exists. The z-transform of a sequence is defined as. X(z)=∞∑n=−∞x[n]z−n. The ROC for a given x[n], is defined as the range of z for which the z-transform converges.
