Digital Signal Processing Reference
In-Depth Information
12,5
10,0
7,5
5,0
2,5
0,0
-2,5
5,0
2,5
0,0
-2,5
-5,0
10,0
7,5
5,0
2,5
0,0
-2,5
5,0
2,5
0,0
-2,5
-5,0
10,0
7,5
5,0
2,5
0,0
-2,5
-5,0
7,5
5,0
2,5
0,0
-2,5
-5,0
-7,5
0,08
0,06
0,04
0,02
0,00
200
100
0
-100
-200
0,08
0,06
0,04
0,02
0,00
200
100
0
-100
-200
0,09
0,06
0,03
0,00
200
100
0
-100
-200
Amplitude spectrum
Bessel
Pulse response h(t)
Impulse response h(t)
Phase spectrum
Butterworth
Impulse response h(t)
Pulse response h (t)
Chebycheff
Impulse response h(t)
Pulse response h (t)
0 0100 150 200 250 300 350 400 450 500
0 550 75 100
150
200
250
300
ms
Hz
Illustration 141:
Traditional analog filter types
These three types are used in analog technology - in particular in the low frequency domain - depending
on the area of application. In each series top left you see the pulse response h(t) of each filter type, among
them the linear distortion of a sequence of rectangular pulses at the output of this filter. Top right, the
amplitude curve and below this the phase curve.
How important a linear phase curve can be in the conducting state region can be seen in the case of the
BESSEL filter using the sequence of periodic rectangular pulses. Only then is the symmetry of the signal
and its „form conservation“ optimally preserved. Only in this case are all the frequencies (sinusoidal
oscillations) contained in the signal delayed by exactly the same value.
In the case of the CHEBYCHEFF filter the non-linear phase curve - careful! filtering is a linear process -
leads to the overshoot of the pulse form. On the other hand the steepness of the sides is very good. The rip-
ple content of h(t) or of the sequence of periodic rectangular pulses is equivalent to the cutoff frequency of
the conducting state region. The BUTTERWORTH filter is a frequently used compromise between the
other two types.
All these filter types are available in different qualities (orders). Filters of a higher order generally require
greater circuit complexity and/or components with very small tolerances. The filter types presented here
are of the 4th order.
In the case of the BESSEL filter great store is set by a linear phase response, on the other
hand the filter steepness between the conducting state region and the blocking state region
is poor, the same is true of the amplitude curve in the conducting state region.
In the case of the CHEBYCHEFF filter great importance is attached to edge steepness. On
the other hand, the phase response is very non-linear and the amplitude curve in the
conducting state region is extremely „ripply“.
