Digital Signal Processing Reference
In-Depth Information
llu
Filter bank
"IOU"
Time d omain
FF T
FF T- Filter
IFFT
An alogo utput
Ad di tio n
Sour ce signal
1,00
0,50
0,00
-0,50
-1,00
1,00
0,50
0,00
-0,50
-1,00
1,00
0,50
0,00
-0,50
-1,00
1,00
0,50
0,00
-0,50
-1,00
1,00
0,50
0,00
-0,50
-1,00
0,50
0,25
0,00
-0,25
-0,50
Filter ed signal 0 - 250 Hz
Filter ed signal 251 - 500 Hz
Filter ed signall 501 - 750 Hz ( M om entar ily, the sour ce contains pr actically no fr equencies between fr equencies between
501 und 750 Hz)
F
ilter ed signal 751 -1000 Hz ( M om entar ily , the sour ce contains pr actically no fr equencies between fr equencies between
751 und 1000 Hz)
Sum of 4 filter ed signals = aggr egate signal = sour ce signal
295.0
297.5
300.0
302.5
305.0
307.5
310.0
ms
Illustration 232:
Proof of the "subband" principle
This physical experiment is proof that the sum of the output signals of the n-filter is identical with the
original signal. The subband filters used in this experiment must, however, fulfil certain criteria which are
subsumed under the expression "quadrature mirror filter".
What is the idea behind this? Real (physical) signals usually have the property of being
"frequency weighted", which means that the energy of a signal is for a certain period of
time largely concentrated on one or several frequency ranges. This becomes obvious
when we look at the time domain of audio-lingual signals such as those in Illustration 67
and Illustration 71: the frequencies of vowels have different characteristics from those of
consonants. Besides, the duration of low-frequency proportion of such signals is often
greater than the high-frequency one (e.g. in the burst pulse).
It thus can assumed that at times the dicrete values of the source signal in a subband equal
zero. It would than be possible to compress this zero sequence very effectively using, for
example, RLE encoding.
But first, the folowing problems are evident: If the frequency band of the source signal
sampled by f
A
is, for example, divided into n equally large frequency bands, each of these
n-filtered output signals will initially contain the same number of discrete values (for each
time unit) as the original source signal. Each of these n signals at these n filter outputs
would have the n-fold value of the sampled values of the source signal.
