Digital filters - Signals, Processes, and Systems - page 328

Sider Generator Formula Data window Time domain List S pect rum F req. dom ain

5,0

Filter-coefficient 512 = 4,7815

Pulse response

2,5

0,0

-2,5

Number of filter-coefficients

-5,0

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

ms

0, 050

Symmetrical spectrum

0, 045

0, 040

0, 035

0, 030

0, 025

0, 020

0, 015

0, 010

0, 005

0, 000

-500 -250 0 250 500

Hz

Illustration 217: Development of a digital bandpass filter

This shows how the pulse response of a bandpass differs from that of a lowpass. In the final analysis it is a
the pulse response of a (symmetrical) lowpass which is multiplied by the mid-frequency of the bandpass.

First create the pulse response for a lowpass which should have the same bandwidth as the bandpass. The
bandwidth in the above case goes from roughly -12 Hz to + 12 Hz. Here we see how important the
symmetrical representation of the frequency domain is in the “filter development site”.

Then select on Channel 1 of the generator a sinusoidal signal with the mid-frequency of the bandpass (here
100 Hz) and the amplitude 1 instead of an offset of 1. Then you will see a state of affairs as shown above.
Illustration 219 shows these common features in greater detail.

A prerequisite for the successful development of digital filters are the correct basic
conditions:

• First establish how high the sampling frequency in the planned DSP system can be
selected. The higher the better. You then have the opportunity to make the intervals
between the periodic filter spectra of the digital signal as large as possible.