Digital Filter Design Process

Digital filters are used in a wide variety of signal processing applications, such as spectrum analysis, digital image
processing, and pattern recognition. Digital filters eliminate a number of problems associated with their classical
analog counterparts and thus are preferably used in place of analog filters. Digital filters belong to the class of
discrete-time LTI (linear time invariant) systems, which are characterized by the properties of causality, recursibility,
and stability. They can be characterized in the time domain by their unit-impulse response, and in the transform
domain by their transfer function. Obviously, the unit-impulse response sequence of a causal LTI system could be of
either finite or infinite duration and this property determines their classification into either finite impulse response
(FIR) or infinite impulse response (IIR) system. To illustrate this, we consider the most general case of a discretetime
LTI system with the input sequence denoted by x(kT) and the resulting output sequence y(kT). As it can be seen
from (1), if for at least one v, a n ¹ 0, the corresponding system is recursive; its impulse response is of infinite
duration (IIR system). If a n = 0, the corresponding system is nonrecursive (FIR system); its impulse response is of
finite duration and the transfer function H(z) is a polynomial in z-1 . Commonly, bm is called the mth forward
filter coefficient and a n the nth feedback or reverse filter coefficient.
The design of digital filters involves the following basic steps:
· Determine the desired response. The desired response is normally specified in the frequency domain in terms of
the desired magnitude response and/or the desired phase response.
· Select a class of filters (for example, linear-phase FIR filters or IIR filters) to approximate the desired response.
· Select the best member in the filter class.
Implement the best filter using a general purpose computer, a DSP, or a custom hardware chip.
· Analyze the filter performance to determine whether the filter satisfies all the given criteria.