Digital Signal Processing Reference
In-Depth Information
Time domain
Frequency domain
Eye diagram
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5, 0
4, 5
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3,75
2,50
1,25
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-0,25
-3,00
5,0
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Bessel-
LP filter
Butterworth -
LP filter
Tschebycheff-
LP filter
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FFT - Tiefpass
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ms
Hz
V
Sig
nal
Oscilloscope
clock
of binary pattern
Illustration 257:
Low-pass filtering of the bit stream to restrict the transmission bandwidth
At the top left you can see the bit patterns which are generated by the encoder, in the centre the relevant
Si-shaped spectrum. The frequency of the basic pulse rate is in this case 200 Hz. Because of its large
bandwidth the signal cannot be modulated. It is important to find an optimum filter which allows the
original bit pattern to be reconstructed in the receiver and which at the same time reduces the bandwidth
to a minimum range. A sampling frequency of 200 Hz means that at best a signal of 100 Hz can be filtered
out. This is attempted using four different types of filters (with the same cutoff frequency of 100 Hz and
with the same - 10th - order).
At the top you can see the experiment using a BESSEL filter, below that with a BUTTERWORTH filter, fol-
lowed by an experiment with a CHEBYCHEFF lowpass filter (see Illustration 141) and finally, at the bot-
tom, using an FFT filter (see Illustration 206 ff). The BESSEL filter has a very pronounced edge, but an
almost linear phase response. BUTTERWORTH and CHEBYCHEFF filters both have a relatively steep
edge, but a non- linear phase response. The “ideal” FFT filter, by contrast, has an extremely negative
edge and complete phase linearity.
The eye diagram is a standard method in measuring technology to find out whether a bit pattern is recon-
structible. The larger the free area of the eye, the better. According to this method both the BESSEL and the
FFT filter meet these requirements. The non-linearity of the phase response obviously leads to an extreme
distortion of the pulse forms of the other two filters. This can also be seen in the time domain.
