Digital Signal Processing Reference
In-Depth Information
Filter
coefficients
Peak
The samples of
Si-function are the
filter coefficients
Peak
Expected
transfer
function of the
LP filter
Symmetric spectrum
Illustration 213:
A “filter development site”
The maximum number of filter coefficients is here n = 1024. The number desired must be set at the top in
the menu under A/D. In this case n = 16 was selected so as to avoid the list becoming too long and to show
that even with this small number the result (in the case of a relatively broadband TP filter) is quite
acceptable. These 16 filter coefficients can be seen at the bottom of the diagram as the vague suggestion of
an Si function. The FFT shows the characteristics of this lowpass in the frequency domain in the central
section of the diagram.
Values from n = 64 are recommended to obtain a good lowpass and from 256 for a bandpass. The
narrower the frequency range of the filter, the longer the Si shaped pulse response has to last according to
the Uncertainty Principle, and the more coefficients are normally required.
The following points are especially important:
(a) Never select the bandwidth of a filter higher than half the final sampling frequency (see text), otherwise
you will contravene the Sampling Principle.
(b) The further apart the bands of the total periodic spectrum are to be the higher the sampling frequency
selected must be.
