51 Structures for the Realization of Linear Time Invariant LTI System Let us consider the first order system is given by The framework provided to the designer valuable information from specifications to implementation ID: 733562
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Slide1
Lect5
A framework for digital filter design Slide2
5.1 Structures for the Realization of Linear Time Invariant (LTI) System.
Let
us consider the first order system is given by
The framework provided to the designer valuable information from specifications to implementation
. Slide3
Introduction
to digital filter
A simplified block diagram of a real time digital filter with analogue input and output signals is shown in fig (5.6). Slide4
As we have seen the main properties of the LTI system are the association and commutation as shown in fig (5.2). Slide5
5.2 Type of digital filter: FIR and IIR
Digital
filters are broadly divided into two classes:-1) Infinite impulse response (IIR)2) Finite impulse response (FIR)Slide6
5.3 Choosing between FIR and IIR
The
choice between FIR and IIR filters depends on the relative advantages of the two filters1) FIR has linear phase response and this is important for data transition, biomedicine, digital audio and image processing. 2) FIR filters realized
nonrecursively are always stable3
) FIR requires more coefficients for sharp cut off than IIR.
4) Analogue
filters can be readily transformed into equivalent IIR digital filters meeting similar specifications. Slide7
5.4 Filter design steps
The
design of a digital filter involves five steps:- 1) Specification of the filter requirements. 2) Calculation of suitable filter coefficients. 3) Representation of the filter by suitable structure (realization).
4) Analysis of the effects of finite wordlength on filter performance.
5) Implementation of filter in software and/or hardware. Slide8
1) Specification of the filter requirements:-
The characteristics of digital filters are often specified in frequency domain. Fig (5.8) shows frequency response for low pass filter. The following are the main parameters:- Slide9
2. Coefficient calculation
The
coefficient of the digital filters are h(k) for FIR, 𝑎𝑘𝑎𝑛𝑑𝑏𝑘 for IIR. Calculations of IIR filter coefficients are based on the transformation of known analogue filter characteristics into equivalent digital filters. The two basic methods are used
(1) The impulse invariant (2) The bilinear transformationSlide10
3. Representation of a filter by a suitable structure (Realization)
Realization
involves converting a given transfer function H(z) into a suitable filter structure. 1. For IIR filters, three structures are used:- (a)Direct form(b) cascade form
(c) parallel form Slide11Slide12Slide13
2. For FIR filter three structure are used:-
(1)Direct form (or transversal)
(2) Frequency sampling (3)Fast convolution. Slide14Slide15
c. Fast convolution realization:Slide16
d. There are many other practical structures for digital filtersSlide17
5.5
Finite world length effects
In actual implementation, represents the filter coefficients by limited number of bits, typically 8 to 16 bits, and the arithmetic operations indicated in the difference equation are performed using finite precision arithmetic.