Digital Signal Processing Reference
In-Depth Information
The schematic circuit diagram of the
-
decoder with the two integrators can
be simplified. Hardly anything is changed in the output signal at the receiver if the
integrator changes its positiom from the end of the transmission channel to the input.
Linear processes can be changed round in sequence, as described in Chapter 7.
-encoder and
Δ
Δ
Why should this be done? In this way the two integrators in the
-encoder can be replaced
by a single integrator directly in front of the 1 bit ADC (see Exercise 10 in Chapter 7). We
now have the so-called sigma-delta modulator/encoder with a demodulator/decoder as
shown in Illustration 230. There the integrator is shown as a feedback adder. The capital
sigma (
Δ
) is the symbol for "sum total" in the technical and scientifc field. The circuit
variant is therefore known as a
Σ
Σ−Δ−
modulator/encoder.
The demodulator only consists of an analog LP filter. This recovers the analog input
signal from the digital
Σ−Δ−
modulated signal. It functions like a floating averager.
Noise shaping and decimation filter
The higher the oversampling the smaller the quantisation error. This is shown in both
Illustration 227 and Illustration 231. By the n-fold oversampling the quantisation noise
distributes itself over an n-fold higher frequency range as the horizontal bar in Illustration
231 shows.
A further reduction in this level of interference is possible by means of the
modula-
tor. This shaping effect known as “noise shaping” arises as a result of the re-grouping of
the integrator at the beginning of the 1 bit A/D converter. This gives preference to the slow
changes in the signal as the integrator is a kind of averager.
Σ−Δ−
The quantisation error increases linearly with the frequency and has therefore a highpass
characteristic. By this means only the level of interference is present after the retrieval of
the signal in the demodulator which corresponds to the (pink) triangular area.
The sampling frequency f
S
of the audio signal should be selected as high as possible in
this process, but the transmission rate is usually fixed and may be much lower than the
sampling rate. This “adjustment” is brought about by so-called “decimation filters” (see
Illustration 231). They divide up the bit sequence of the 1 bit A/D converter into blocks
with an odd-numbered bit number (e.g. 7). They then check whether more "0" or "1"
symbols occur within the block. The symbol which occurs more frequently is then
indicated at the output of the decimation filter. Of course, this is also a kind of averaging
with a lowpass characteristic.
Exploiting psycho-acoustic effects (MPEG)
The frequency domain so far does not seem to play a part in the encoding or compressing
of audio signals. However, hearing is entirely in the frequency domain, that is we hear
only sinusoidal signals of different frequencies. A really intelligent method of compres-
sion ought to include the frequency domain.
Audio-signals such as language and music do not contain redundant features, unlike text
where the letter "e" occurs much more freequently than "y". As a result it is difficult to
allocate a shorter code to a sound or tone.
