what are the basic difference between z and fourier transform..at what we will be traversing from Z to Fourier transform????????
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what are the basic difference between z and fourier transform..at what we will be traversing from Z to Fourier transform????????
HOPE THE FOLLOWING ABOUT THE PROPERTIES OF THE TWO TRANSFORMS WILL MAKE THINGS CLEAR:
FOURIER TRANSFORM:
The time and frequency domains are alternative ways of representing signals. The Fourier transform is the mathematical relationship between these two representations. If a signal is modified in one domain, it will also be changed in the other domain, although usually not in the same way. For example, it was shown in the last chapter that convolving time domain signals results in their frequency spectra being multiplied. Other mathematical operations, such as addition, scaling and shifting, also have a matching operation in the opposite domain. These relationships are called properties of the Fourier Transform, how a mathematical change in one domain results in a mathematical change in the other domain.
Z TRANSFORM:
Just as analog filters are designed using the Laplace transform, recursive digital filters are developed with a parallel technique called the z-transform. The overall strategy of these two transforms is the same: probe the impulse response with sinusoids and exponentials to find the system's poles and zeros. The Laplace transform deals with differential equations, the s-domain, and the s-plane. Correspondingly, the z-transform deals with difference equations, the z-domain, and the z-plane. However, the two techniques are not a mirror image of each other; the s-plane is arranged in a rectangular coordinate system, while the z-plane uses a polar format. Recursive digital filters are often designed by starting with one of the classic analog filters, such as the Butterworth, Chebyshev, or elliptic. A series of mathematical conversions are then used to obtain the desired digital filter. The z-transform provides the framework for this mathematics. The Chebyshev filter design program presented in Chapter 20 uses this approach, and is discussed in detail in this chapter.
Z transform is for discrete signals.
Fourier is for continous signals. Fourier transform can be used for discrete sequences by formulating the function as continuous using delta functions;
Also - the Fourier transfrorm does not deal with the entire complex plane.
Think of the z-transform as being the solution (provider) to discrete-time difference equations,
whereas the Laplace transform is the solution (provider) to continuous-time differential equations.
THEN fourier series and fourier transform are meant for continuous signal or discrete signal analysis or simply for both.....
i think ther are related to one and othre
because Z tells about the system on the basis of roc
where as the fourier does no tell
Quote:
Originally Posted by electronics_kumar
Fourier series is only for continous periodic signals. But transform is for any signal. Fourier series operation is a subset of transform
The continuous Fourier transform is for solutions along the +/- jw axis of the s-plane.
The FFT is for equally spaced solutions along the z-plane's unit circle.
I suggest you to check out Digital Signal Processing books to get a clearer explaination about traversing from z transform to fourier transform