Processing for compression - The MPEG - page 54

decay due to the capacitor discharging through the resistor (in series with the source impedance which is assumed
here to be negligible). The figure also shows the response to a squarewave at (b). With other waveforms the
process is inevitably more complex.
Figure 3.2: (a) The impulse response of a simple RC network is an exponential decay. This can used to calculate
the response to a square wave, as in (b).
Filtering is unavoidable. Sometimes a process has a filtering effect which is undesirable, for example the limited
frequency response of an audio amplifier or loss of resolution in a lens, and we try to minimize it. On other
occasions a filtering effect is specifically required. Analog or digital filters, and sometimes both, are required in
ADCs, DACs, in the data channels of digital recorders and transmission systems and in DSP. Optical filters may
also be necessary in imaging systems to convert between sampled and continuous images. Optical systems used
in displays and in laser recorders also act as spatial filters. [ 1 ]
Figure 3.3 shows that impulse response testing tells a great deal about a filter. In a perfect filter, all frequencies
should experience the same time delay. If some groups of frequencies experience a different delay from others,
there is a group-delay error. As an impulse contains an infinite spectrum, a filter suffering from group-delay error
will separate the different frequencies of an impulse along the time axis.
Figure 3.3: If a filter is not phase-linear, different frequencies will emerge at different times if an impulse is input.
This is undesirable in video circuitry.
A pure delay will cause a phase shift proportional to frequency, and a filter with this characteristic is said to be
phase-linear. The impulse response of a phase-linear filter is symmetrical. If a filter suffers from group-delay error it
cannot be phase-linear. It is almost impossible to make a perfectly phase-linear analog filter, and many filters have
a group- delay equalization stage following them which is often as complex as the filter itself. In the digital domain it
is straightforward to make a phase- linear filter, and phase equalization becomes unnecessary.
Because of the sampled nature of the signal, whatever the response at low frequencies may be, all PCM channels
(and sampled analog channels) act as low-pass filters because they cannot contain frequencies above the Nyquist
limit of half the sampling frequency.
[ 1 ] Ray, S.F., Applied Photographic Optics , Ch. 17, Oxford: Focal Press (1988)