Digital Signal Processing Reference
In-Depth Information
T ime domain
Spectr um
Freq. domain
d-pulse
BP filter
1,00
0,10E-3
Time duration of pulse response 250 ms
Sample rate 1024
Bandwidth 100 Hz
0,75
0,75E-2
0,50
0,50E-2
0,25
0,25E-2
0,00
0,00E00
25
50
75
100
125
150
175
200
225
250
-500
-250
0
250
500
ms
Hz
1,00
0,20E-2
Time duration of pulse response 125 ms
Sample rate 2048
Bandwidth 200 Hz
0,75
0,15E-2
0,50
1,00E-3
0,25
0,50E-3
0,00
0,00E00
25
50
75
100
125
-1000
-750
-500
-250
0
250
500
750
100
ms
Hz
1,00
0,20E-2
Time duration of pulse response 31 ms
Sample rate 8192
Bandwidth 800 Hz
0,75
0,15E-2
0,50
1,00E-3
0,25
0,50E-3
0,00
0,00E00
15.0
20.0
25.0
30.0
35.0
40.0
45
-4000
-3000
-2000
-1000
0
500
1500
2500
3500
ms
Hz
Illustration 218:
Importance of the sampling rate for the filter curve
The relations are once again illustrated using the example of a bandpass. In the above circuit the same
coefficients file was used for a bandpass in the convolution module or the digital filter. The top pulse
response and the top filter curve corresponds to the state of affairs in the “filter development system”. In
the case of a bandpass a blocklength of at least 256 should be selected.
If in the above circuit the sampling rate is increased to 8192 (compared with 256) the bandwidth and mid-
frequency increase by the factor 8. The “filter form” however does not change. Because it is determined
exclusively by the filter coefficients.
• The number of the filter coefficients is a measure of the quality of the filter. With
DASY
Lab
a maximum of 1024 filter coefficients are possible in the convolution
module. If the number is greater so is also the amount of calculation necessary. This
can lead to difficulties in real time processing.
• The sampling frequency must also be at least double the highest cutoff frequency of
the bandpass. The Sampling Principle also applies here, of course. The highest signal
frequency which passes through the bandpass and not the bandwidth is decisive.
