ABSTRACT
Signals are basically time functions that represent changes of a certain physical phenomenon. Traditional signal processing operations-for example, amplifi cation and fi ltering-are performed on raw signals in the time domain. However, it is sometimes advantageous to process signals while in the frequency domain, where they are viewed from another perspective. Mathematical tools (transforms) are therefore needed to perform mapping of signals from the time to the frequency domain and vice versa. Discrete-time transforms are those transforms that deal with sampled signals. Through such operations, N samples of a certain continuous time signal are transformed into an equal number of discrete frequency components describing the signal spectrum. The resulting components from this forward transform are usually complex; that is, they are expressed as magnitude and phase. To be usable, the reverse process of a transform-the inverse transform-should be valid; that is, it should be possible to get back a signal in the time domain from its spectrum. Frequency transforms are used extensively in several signal processing applications, such as the following:
1. Data transmission and storage, where it is necessary to reduce (compress) the amount of data to be transmitted and stored.
