Digital Signal Processing Reference
In-Depth Information
4,0
3,0
2,0
1,0
0,0
2,5
1,0
-0,5
-2,0
2,5
1,5
0,5
-0,5
1,25
0,50
-0,25
-1,00
1,25
1,00
0,75
0,50
0,25
0,00
-0,25
0,75
Delta-pulse
Channel 0: Pulse r esponse h ( t) of a bandpass filter fr om 256 - 512 Hz
Channel 1: Pulse r esponse h ( t) of a l owpass fi l ter fr om 0 - 256 Hz
Channel 2: Pulse r esponse h (t ) of a bandpass filter fr om
128 - 256 Hz
Channel 3: Pulse r esponse h (t ) of a lowpass filter fr om 0 - 127 Hz
Channel 4: Pulse r esponse h (t ) of a bandpass filter fr om
64 - 127 Hz
-0,50
0,6
0,4
0,2
0,0
-0,2
0,30
Channel 5: Pulse r esponse h (t ) of a lowpass filter fr om 0 - 63 Hz
Channel 6: Pulse r esponse h (t ) of a bandpass filter fr om
32 - 63 Hz
-0,25
0,30
0,20
0,10
0,00
-0,10
Channel 7: Pulse r esponse h (t ) of a lowpass filter fr om 0 - 31 Hz
475
500
525
550
Centre
ms
Extract from the list of the filter coefficients corresponding to the pulse response
Channel 0
FIR coeff .
Channel 1
FIR coeff.
Channel 2
FIR coeff .
Channel 3
FIR coeff.
Channel 4
FIR coeff.
Channel 5
FIR coeff.
Channel 6
FIR coeff .
Channel 7
FIR coeff .
Number
Centre
Illustration 234:
The internal structure of pulse reponses of digital subband filters
The Illustration shows 8 pulse responses of 8 digital filters the bandwidths of which are in a particular
relation to each other. The pulse responses of the three lowpass filters at the top of the table - and thus the
filter coefficients of these digital filters - result from the lower lowpass filter by omitting (from bottom to
top) every other value (downsampling !) Thus the duration of the pulse resonse is halved. According to the
Uncertainty Principle
UP
this means doubling the bandwidth of the filter. The same is true of the pulse
responses of the four bandpass filters.
Even adjacent highpass and lowpass filters - e.g. channel 0 and channel 1 - which both cover a particular
frequency range demonstrate quite clearly that their internal structures are similar (cf. the readings of the
table). And now for a test question: What is the relationship between the mid-frequency of the bandpass
filters and the bandwidth of the relevant lowpass filters?
