# ch4 - Chapter 4: IIR Filter Design • Introduction Analog...

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Unformatted text preview: Chapter 4: IIR Filter Design • Introduction Analog Filter Basics, Butterworth Filters, Chebyshev Filters, Elliptic Filters* • Design of Digital IIR Filters from Analog Filters pulse Invariant Transformation, Bilinear ransformation Impulse Invariant Transformation, Bilinear Transformation • IIR Filters Design Using Matlab Signal Processing Toolbox Prepared by Lim H.S. Last edited on 26 Mar 2009. Introduction • Analog Filter Basics o The most common design method for digital IIR filter is based on designing an analog filter and then transforming it to an equivalent digital filter. o This approach has been widely used for many reasons: 1. Analog approximation techniques are highly advanced. 2. They usually yield closed-form solutions. 3. Extensive tables are available for analog filters design 4. Many applications require the digital simulation of analog filters. 2 Introduction • Analog Filter Basics (cont.) o The advantages of digital IIR filters: 1. Analog filters can be readily transformed into equivalent digital IIR filters. This is impossible with FIR filters as they have no analog counterpart. 2. Require less filter coefficients than FIR filter to achieve similar frequency response. Hence, the IIR filter is computationally more efficient. 3 Introduction • Analog Filter Basics (cont.) o Analog filters are specified in a manner similar to digital filters; the main difference is that frequencies are specified in the Ω domain (in rad/s), rather than in the ω domain. o Thus, a low-pass analog filter is specified in terms of its pass-band ge frequency stop and edge frequency pass and ripple edge frequency Ω p , stop-band edge frequency Ω s , pass-band ripple δ p , and stop-band attenuation δ s . o For analog filters, the pass-band magnitude response is usually required to be in the range [1- δ p , 1]. 4 Introduction • Analog Filter Basics (cont.) o Analog filters specifications: 2 ) 1 ( p δ- 2 | ) ( | Ω j H a 5 2 s δ p Ω s Ω Ω Introduction • Analog Filter Basics (cont.) o Recall the definitions will be convenient to introduce the following auxiliary s s p p A A δ δ 10 10 log 20 ) 1 ( log 20- =-- = o It will be convenient to introduce the following auxiliary parameters: o The parameter d is called the discrimination factor ; the parameter k is called the selectivity factor . s p s p k d Ω Ω =        --- =-- 2 / 1 2 2 1 1 ) 1 ( δ δ 6 Introduction • Butterworth Filters o A low-pass Butterworth filter is defined in terms of its squared- magnitude frequency response N c a j H 2 2 ) / ( 1 1 ) ( Ω Ω + = Ω where N is the order of the filter and Ω c is the 3-dB cut-off frequency. o | H a ( j Ω )| 2 decreases monotonically with increasing Ω ....
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## This note was uploaded on 08/27/2009 for the course FET etm taught by Professor Hi during the Spring '09 term at Multimedia University, Cyberjaya.

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ch4 - Chapter 4: IIR Filter Design • Introduction Analog...

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