unilateral means limit is 0 to infinite and bilateral means -infinite to +infinite in laplace transform
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discrete fourier transformer uses digital signals whereas the fast fourier transform uses both analog and digital.
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
There is no such thing as a "bilateral country". You would usually use the word "bilateral" to do something that involves a mutual relationship between TWO countries - for example, a "bilateral treaty", "bilateral relations", "bilateral talks", etc. If more than two countries (or in general, parties) are involved, the word "multilateral" is also used.