foldover

frequency modulation

digital frequencies

Discrete-Time Fourier

thus implying that the reconstruction process can not be implemented exactly.

However, it is possible to give a practical realization of the reconstruction filter

by an impulse response that approximates the sinc function.

called aliasing or foldover and is avoided by forcing the continuous-time original

signal to be bandlimited to the Nyquist frequency. In other words, a filter in

the continuous-time domain cuts off the frequency components exceeding the

Nyquist frequency. If aliasing is allowed, the reconstruction filter can not give a

perfect copy of the original signal.

out of the frequency range of hearing. However, some sound synthesis techniques,

such as frequency modulation, exploit aliasing to produce additional spectral

lines by folding onto the base band spectral components that are outside the

Nyquist bandwidth. In this case where the connotation is positive, the term

foldover is preferred.

signal domain, which switches from a continuous to a discrete set of points. We

have also seen how this operation is transposed in the frequency domain as a

periodic replication. It is now time to clarify the meaning of the variables which

are commonly associated to the word "frequency" for signals defined in both the

continuous and the discrete-time domain. The various symbols are collected in

table 1.1, where the limits imposed by the Nyquist frequency are also indicated.

With the term "digital frequencies" we indicate the frequencies of discrete-time

signals.

a function of frequency, for discrete-variable functions obtained by sampling

continuous-time signals with sampling interval T . This transform is called the

Discrete-Time Fourier Transform (DTFT) and is expressed by