FIR Filter Design PDF

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FIR Filter Design...

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DISPRO

2014

FIR Filter Design Digital Filters  Digital Filter Specifcatons FIR Filter Design based on Windowed Series

Frequency Transformatons

Domain

Filter

Introduction to Digital Filters  In signal processing, the functon of a flter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.

Two Types of Filters Analog Filter  uses analog electronic circuits made up from components such as resistors, capacitors and op-amps to produce the required fltering effect  widely used in such applicatons as noise reducton, video signal enhancement, graphic equalizers in hi-f systems, and many other areas Digital Filter  uses a digital processor to perform numerical calculatons on sampled values of the signal  processor may be a general-purpose computer such as a PC, or a specialized DSP (Digital Signal Processor) chip IIR FIR Impulse Response fnite infnite System Functon H(z)=P(z) H(z)=P(z)/D(z Structure diagram Have feedback No feedba Phase response Exact linear phase h[n]= h[n-N] Zero-poles Only have zeros Both zeros and poles Advantages of using Digital Filters 1.A digital flter is programmable, i.e. its operaton is determined by a program stored in the processor's memory. This means the digital flter can easily be changed without affectng the circuitry (hardware). An analog flter can only be changed by redesigning the flter circuit.

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2.Digital flters are easily designed, tested and implemented on a general-purpose computer or workstaton. 3.The characteristcs of analog flter circuits (partcularly those containing actve components) are subject to drift and are dependent on temperature. Digital flters do not suffer from these problems, and so are extremely stable with respect both to tme and temperature. 4.Unlike their analog counterparts, digital flters can handle low frequency signals accurately. As the speed of DSP technology contnues to increase, digital flters are being applied to high frequency signals in the RF (radio frequency) domain, which in the past was the exclusive preserve of analog technology. 5.Digital flters are very much more versatle in their ability to process signals in a variety of ways; this includes the ability of some types of digital flter to adapt to changes in the characteristcs of the signal. 6.Fast DSP processors can handle complex combinatons of flters in parallel or cascade (series), making the hardware requirements relatvely simple and compact in comparison with the equivalent analog circuitry. Digital Filter Specifications The magnitude response of a digital low pass flter may be given as

In the pass band, we require that bandwidth w with a deviaton

In the stopband, we require that the bandwidth w with a deviaton

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Selection of Filter Type Advantages in using an FIR filter: 1.Can be designed with exact linear phase 2.Filter structure always stable with quantzed coefficients Disadvantages in using an FIR filter : 1.Order of an FIR flter is considerably higher than that of an equivalent IIR flter meetng the same specifcatons 2.Leads to higher computatonal complexity for FIR FIR Design Three commonly used approaches to FIR filter design: 1.Windowed Fourier series approach 2.Frequency sampling approach 3.Computer-based optmizaton methods Finite Impulse Response Filters The transfer functon is given by

The length of Impulse Response is N Zeros can be placed anywhere on the z-plane FIR: Linear phase For linear phase the second term in the fundamental phase relatonship must be identcally zero for all index values. Hence 1.The maximum phase factor has zeros which are the inverses of the those of the minimum phase factor 2.The phase response is linear with group delay (normalised) equal to the number of zeros outside the unit circle

FIR Filter Design Based on Windowed Series

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Gibbs Phenomenon  The causal FIR flter obtained by simply truncatng the impulse response coefficients of the ideal flters exhibit an oscillatory behavior in their respectve magnitude responses which is more commonly referred to as the Gibbs phenomenon. FIR Filter Design Based on Windowed Series The magnitude characteristc of a physically realizable flter is:

An FIR flter of length M has a transfer functon given by:

The difference equaton of an FIR flter is expressed as:

Design of FIR filters: Windows 1.Start with ideal infnite duraton 2.Truncate to fnite length. (This produces unwanted ripples increasing in height near discontnuity.) 3.Modify h(n) Weight w(n) is the window

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Windowing Techniques

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Comparison of various Windows

Frequency Sampling Method In this approach we are given h(k) and need to fnd This is an interpolaton problem and the soluton is given in the DFT part of the course. It has similar problems to the windowing approach

About Digital Filter Design Estmaton of the Filter Order IIR: The order of G(z) is determined from the transformaton being used to convert Ha(s) into G(z)

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Frequency-Domain Filter Transformations Lowpass to Highpass Transformaton 

Let HLP() be the frequency response of a lowpass flter with a cutoff frequency equal to c and HHP() be the frequency response of a highpass flter with the same cutoff frequency.

Lowpass to Bandpass Transformation  Let HLP1() and HLP2() be the frequency response of the low pass flters with cutoff frequencies equal to c1 and c2, respectvely. Let HBP() be the frequency response of a bandpass flter with low and high cutoff frequencies c1 and c2. (NB: c1 < c2)

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Lowpass to Bandstop Transformation oLet HLP1() and HLP2() be the frequency response of the lowpass flters with cutoff frequencies c1 and c2, respectvely. Let HBS() be the frequency response of a highpass flter with low and high cutoff frequencies c1 and c2, respectvely. (Note: c1 < c2 )

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