Basic IIR Digital Filter
Structures
Basic IIR Digital Filter
Structures
The causal IIR digital filters we are
concerned with in this course are
characterized by a real rational transfer
function of z 1 or, equivalently by a constant
real coefficient diff

The Transfer Function
The Transfer Function
Taking the z-transforms of both sides we get
A generalization of the frequency response
function
The convolution sum description of an LTI
discrete-time system with an impulse
response h[n] is given by
y[n] =

Stability Condition of an LTI
Discrete-Time System
Stability Condition of an LTI
Discrete-Time System
Proof: Assume h[n] is a real sequence
Since the input sequence x[n] is bounded we
have
x[n] Bx <
BIBO Stability Condition - A discretetime is BIBO st

Signals and Signal Processing
Signals play an important role in our daily
life
A signal is a function of independent
variables such as time, distance, position,
temperature, and pressure
Some examples of typical signals are shown
next
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Digital Filter Design
Digital Filter Specifications
Usually, either the magnitude and/or the
phase (delay) response is specified for the
design of digital filter for most applications
In some situations, the unit sample response
or the step response may

Digital Filter Structures
Digital Filter Structures
The convolution sum description of an LTI
discrete-time system can, in principle, be
used to implement the system
For an IIR finite-dimensional system this
approach is not practical as here the impulse

Discrete-Time Systems:
Examples
Discrete-Time Systems
A discrete-time system processes a given
input sequence x[n] to generates an output
sequence y[n] with more desirable
properties
In most applications, the discrete-time
system is a single-input, sing