Page 41 - Analog and Digital Filter Design

38 Analog and Digital Filter Design

Digital Filter Types

Digital filters are becoming more widespread in use and are replacing analog
filters in many systems. Digital filters process signals in the time domain. Analog
signals have first to be sampled and digitized at discrete (clock) intervals using
an analog-to-digital converter.

Because the analog signal is sampled, care has to be taken to prevent errors such
as aliasing. Aliasing, which was described earlier, occurs when the analog signal
has spectral energy at frequencies above half the sampling frequency. The analog
and sampling signals mix in such a way that it is impossible to recover the origi-
nal signal when it is converted back to analog. To prevent aliasing, the highest
frequency of the input signal must be filtered. In telecommunications, the upper
voice frequency is limited to 3.4kHz with a very steep skirt (Le., a sharp roll-
off), so that there is no discernable energy at 4kHz or higher. The voice fre-
quency is then sampled at 8 kHz.

What would happen if an analog signal at, say, 5 kHz is passed then sampled
at 8 kHz? Mixing between the 5 kHz signal and the 8 kHz signal would cause
signals to be generated at the sum and difference frequencies. Thus signals at
3kHz and 13kHz would be produced. When converted back to analog, the
13 kHz signal would be outside the passband of the output filter, but the 3 kHz
signal would be inside the passband and thus appear at the output as an alias.

Once digitized, the signals are digitally filtered by either a dedicated IC or
a digital signal processor (DSP) using a filtering software. Within every digital
filter there are delay elements, multiplying functions and adders, which process
the digitized signal. There are two types of digital filter: Finite Impulse Response
(FIR) filters, which are also described as nonrecursive filters; and Infinite
Impulse Response (IIR) filters, which are recursive because part of the output
signal is fed back to the input.

The recursive approach in digital filtering processes uses negative feedback in
order to obtain a sharp roll-off using the minimum of delay, summing, and
multiplying elements. The feedback comprises a small fraction of the output
signal. Because of the delays, any sudden change in the input signal affects the
output for some time (possibly forever, if there is any instability in the design).
Recursive filters are said to have an Infinite Impulse Response (IIR). Some
designs are sensitive to the filter coefficients used as multiplying factors, and
truncating the coefficient (limiting the number of decimal places) can result in
positive feedback and hence oscillation.

Nonrecursive, or moving average, filters take several successive samples then sum
them (perhaps with a scaling factor at each tapping point) to produce the
average of several samples. As time goes on the samples ripple through the filter,