1. Lecture 9 FIR and IIR Filter design using Matlab
2007/11/16
Prof. C.M Kyung

2. FIR and IIR Filter
GOAL
Linear-Time-Invariant (LTI) system and Impulse response
z-Transform
Characteristics of FIR and IIR filters
Design procedure of FIR and IIR filters

3. FIR and IIR Filter LTI System
Input (x(t) or x[n]) and Output (y(t) or y[n]) is defined first
For a given system, it can be either LTI or non-LTI depending on how we define the input and output.
Linearity
For arbitrary and , the output of the system for
is the sum the output for and (superposition)
Time-invariance
Time-shift in input results in time-shift in output by same amount for time-invariant systems.

4. FIR and IIR Filter Impulse Response Definition Importance
Impulse response is the output of the system when impulse signal
or is applied as the input of the system.
Importance
Impulse response “fully describes” the system if the system is LTI.
Why and how?
Why the impulse response CANNOT fully describe a non-LTI system?
Fourier transform of the impulse response shows the characteristic of the system is frequency domain.

5. FIR and IIR Filter z-Transform Definition Example Note
The z-transform of a sequence is defined as
Example
For , ,
Note
z-transform is reduced to discrete-time Fourier transform (DTFT) if is substituted by .
This means that z-transform on the unit-circle on the complex plain is same as DTFT.
Laplace Transform CTFT ~ z-Transform  DTFT

6. Ideal frequency-selective filter
FIR and IIR Filter
Ideal frequency-selective filter
A filter whose frequency response is unity over a certain frequency range and zero for other frequencies.
Frequency response of an ideal low-pass filter
However, an ideal low-pass filter is noncausal.

7. FIR and IIR Filter FIR / IIR filter Definition FIR IIR
If the length of the impulse response is finite, the filter is an FIR (finite impulse response) filter. Otherwise, the filter is an IIR (infinite impulse response) filter.
FIR
Inherently BIBO (bounded-input, bounded-output) stable
Nonzero pole does not exist in its transfer function
Easy to implement
Can be designed to have linear phase property
IIR
Sometimes unstable
Nonzero pole exists in its transfer function
Lower filter order than a corresponding FIR filter
Usually have nonlinear phase property

8. Filter Design Procedure
FIR and IIR Filter
Filter Design Procedure
Design continuous-time IIR filter
Obtain desired using Butterworth, Chebyshev methods
Convert it to discrete-time IIR filter using impulse invariance
Impulse invariance :  ,
if ,
Obtain discrete-time FIR filter by windowing the IIR filter
Windowing :
Commonly used windows : rectangular, Bartlett, Hanning, Hamming,
Blackman, Kaiser, …
However, windowing does not give the optimum solution and other approaches can be used.

9. FIR and IIR Filter
Frequency response of various filters

10. FIR and IIR Filter Problem Statements
Design several types of FIR and IIR filters
IIR – butterworth, chebyshev type1, chebyshev type 2, …
FIR – using different windows ( Hamming, Hanning, Bartlett, … )
Remove the noise in acoustic signal using the filters
What are the differences between the filters ?
Understand the effect of sampling frequency on the sampled signal distortion (aliasing)

11. Experiment Requirements
FIR and IIR Filter
Experiment Requirements PC
Matlab software (with signal processing toolbox)

12. FIR and IIR Filter References
Fundamentals of Signal & System using the web and matlab Edward W. Kamen, Bonnie S. Heck
Discrete-Time Signal Processing
- Alan V. Oppenheim, Ronald W. Schafer