Digital Signal Processing Reference
In-Depth Information
Filter 1
LP
Decoder
Encoder
Up
sampling
Down
sampling
Filter 2
BP
Filter 2
BP
Encoder
Decoder
Demulti-
plexer
Multiplexer
•
•
•
•
•
•
+
Filter M
B
P
Filter M
B
P
Encoder
Decoder
M-Band subband encoding system (
Analysis
sectionl)
M-Band subband decoding system (
Synthesis
section)
f
Changing uncertainty
blocks as result of
narrowing the
frequency range
Δ
M = 4
M = 4
f
∗Δ
t = konstant
t
Illustration 235:
Block diagram of a subband coding system
The left-hand side shows the transmitter-related part of subband coding, the right-hand side the receiver-
related one. As described in the main part, there is no compression of data as a result of filtering and
downsampling alone. Data can only be comressed in the encoder. The M subband encoder signals are
combined in one channel by the multiplexer (parallel serial transduction) and split up into M channels by
the demultiplexer in the receiver (serial parallel transduction).
It is vital to understand the Uncertainty Principle
UP
in order to grasp the above mentioned process. The
bottom part of the table illustrates this process. The behaviour of the signal is largely determined by the
changing “uncertainty blocks”. Due to the bandwidth of the signal, which in this Illustration has been
reduced to one quarter, the uncertainty in the time domain increases fourfold, which in turn influences the
duration of the pulse response h(t). See also the detailed representation in Illustration 233.
The term "quadrature mirror filter" (QMF) is a reference to the symmetrical properties of
the filter. The transmission function of the adjacent connected bandpass filters is a result
of the mirroring of the lowpass transmission function of the “mother function” to clearly
defined "carrier frequencies" (see Illustration 236). At first glance, this resembles
Illustration 200, bottom, which illustrated the limiting case of the sampling principle. In
the subband process, the conducting state areas of adjacent filters are therefore ideally
clearly separated (see Illustration 236). As there are no ideal rectangular filters, however,
the result is only an approximation. The best choice for this process is the linear phase
FIR filter.
The pulse responses h(t) - i.e. the FIR filter coefficients - in Illustration 234 show the
internal affinity of such QM filters. Downsampling the pulse response h(t) (bottom) of the
lowpass filter from 0 to 31 Hz or -31 to +31 Hz results in the filter coefficients for a
lowpass of -63 to +63 Hz, -127 to +127 Hz, or -255 to +255 Hz. The bandpass pulse
response which seamlessly adjoins every lowpass with the same bandwidth is the result
of multiplying the Si-function (lowpass) by the mid-frequency of the relevant bandpass.
