Question

difference between Fourier transform and Z-Transform?

Answer 1

Fourier transform is the analysis and synthesis of continuous time varying signals Fourier Transform can be generalized that is to define a signal by basis signals and For periodic signals using periodic signals like SINE and COS .. where as Z transform deals with discrete time signals simply the signals that aren't moniterd for continuous time .. As one domain is never enuf to completely define a signal

Answer 2

The Fourier Transform is used to analyze periodic signals, while the z-transform analyzes difference equations.

The z-transform is defined as
$$
\Large
X(z) = \mathcal{Z}\{x[n]\} = \sum_{n=-\infty}^{\infty} x[n] z^{-n}
$$
The discrete version of the Fourier Transform is the z-transform constrained to the unit circle in the complex plane:
$$
\Large
X_{2\pi}(\omega) = \sum_{n=-\infty}^{\infty} x[n] \,e^{-i \omega n}.
$$
This connection between the Fourier Transform and the Z-Transform is discussed here:
http://en.wikipedia.org/wiki/Discrete-time_Fourier_transform#Relationship_to_the_Z-transform