wave packets

frequency point is the delay that a single frequency component is subject to

when it passes through the filter, and the quantity (13) is, indeed, a delay in

samples. Vice versa, in order to interpret the group delay let us consider a local

approximation of the phase response by the tangent line at one point. Locally,

propagation can be considered linear and, therefore, a signal having frequency

components focused around that point has a time-domain envelope that is de-

layed by an amount proportional to the slope of the tangent. For instance, two

sinusoids at slightly different frequencies are subject to beats and the beat fre-

quency is the difference of the frequency components (see fig. 6). Therefore,

beats are a frequency local phenomenon, only dependent on the relative dis-

tance between the components rather than on their absolute positions. If we

are interested in knowing how the beat pattern is delayed by a filter, we should

consider local variations in the phase curve. In other words, we should consider

the group delay.

frequency band, and preservation of the shape of such packets is important.

Vice versa, in sound processing it is more meaningful to consider the set of

frequency components in the audio range as a whole, and the phase delay is