2. What is a filter?
To attenuate one frequency or a range of frequencies out of mix of
different frequencies.
Selectively filtering one frequency or range of frequencies.
An LTI system performs filtering process among the various components
at its input.
It acts a frequency shaping filter.
4. Main uses of filters
Signal Separation
eg)measure the heart beat of baby’s heart in womb-
corrupted by breathing and heartbeat of mother.
Signal Restoration
eg)audio recording with poor equipment-shaky
camera-blurred image
Removal of undesirable noise
Signal detection
Spectral analysis
5. Main Classification of Filters
Analog Filter-process only analog signals,x(t),y(t)
Digital Filter-process only digital signals,x(n),y(n)
6. Ideal filter characteristics
The filters have a constant gain(unity gain) passband
characteristics and zero gain in their stopband.
Linear phase response.
14. Classification of Digital Filters
FIR-Finite Impulse Response
-impulse response h(n) is of finite duration
Eg: h(n)={1,2,3,4}
IIR-Infinite Impulse Response
-impulse response h(n) is of infinite duration
Eg: h(n)=[(1/2)^n -(0.1)^n]u(n)
22. IIR Analog filter design
The design of IIR filter involves design of a digital filter in
the analog domain and transforming the design into the
digital domain.
The system function describing an analog filter may be
written as
where 𝑎𝑘 and 𝑏𝑘 are the filter coefficients.
23. IIR-analog cont…
Conversion techniques are to be effective, the technique
should possess the following properties:
i) The 𝑗Ω axis in the s-plane should map onto the unit
circle in the z-plane.
ii) The left half plane of the s-plane should map inside of
the unit circle in the z-plane to convert a stable analog filter into a
stable digital filter.