ABSTRACT
Fourier methods are commonly used for signal analysis and system design in modern telecommunications, radar, and image processing systems. Classical Fourier methods such as the Fourier series and the Fourier integral are used for continuous-time (CT) signals and systems, i.e., systems in which a characteristic signal,
s
(
t
), is defined at all values of
t
on the continuum –
∞
<
t
<
∞
. A more recently developed set of Fourier methods, including the discrete-time Fourier transform and the discrete Fourier transform, are extensions of basic Fourier concepts that apply to discrete-time (DT) signals. A characteristic DT signal,
s
[
n
], is defined only for values of
n
where
n
is an integer in the range –
∞
<
n
<
∞
. The following discussion presents basic concepts and outlines important properties for both the CT and DT classes of Fourier methods, with a particular emphasis on the relationships between these two classes. The class of DT Fourier methods is particularly useful as a basis for digital signal processing (DSP) because it extends the theory of classical Fourier analysis to DT signals and leads to many effective algorithms that can be directly implemented on general computers or special purpose DSP devices.
