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A framework for digital filter

design

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Introduction to digital filters

Types of digital filters

Comparison between FIR and IIR filters

Filter design steps

Summary

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Introduction

A filter is a system or network that selectively

changes the wave shape, amplitude-frequency

orphase-frequency characteristics of a signal in

a desired manner.

Common filtering objectives o To remove or reduce noise.

o To extract information from signals.

o To separate two or more signals previously combined to make anefficient use of an available communication channel.

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Digital filter - Introduction

It refers to the specific hardware / software routine thatperforms the filtering algorithm and achieves the filteringobjectives.

It operates on digitized analog signals or just sequenceof numbers stored in a computer memory.

It plays very important roles in DSP.

In comparison with Analog filters; it is preferred inapplications such as data compression, biomedical

signal processing, speech processing, imageprocessing, data transmission, digital audio, telephoneecho cancellation.

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Real time Digital Filters

A simplified block diagram with analog input and analog output.

A analog signal is sampled periodically & converted in digital samples

such as x(n), n = 0,1,2,3..

Digital processor implements the filtering operation, by mapping inputsignal x(n) into the output sequence y(n) based on the algorithm.

DAC converts the digitalized output signals into analog signals.

Again filtered to get smooth and remove unwanted noise and high

frequency components.

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Digital filters - advantages It can have characteristics such as true linearphase response.

The performance does not vary with environmental changes, like thermalvariations. It also eliminates the need to calibrate periodically.

In case of adaptive filters, frequency response can be adjusted if it isimplemented on a programmable processor.

No need to replicate the it, as a single filter can filter several input signals orchannels.

Both filtered and unfiltered data can be saved for further use.

The advancements in VLSI technology helps in fabricating digital filters insmall size, to consume low power and to keep the cost down.

In practice, the precision achievable with analog filters is restricted where as

in digital filters, the precision is limited only by the wordlength used. Performance of the digital filters can be repeated from unit to unit.

Digital filters can be used at very low frequencies , found in manybiomedical applications.

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Digital filter - disadvantage

Speed limitation The maximum bandwidth of signalsthat digital filters can handle, in real time, is much lowerthan for analog filters.

Finite word length effects

Digital filters are subject toADC noise resulting from quantizing a continuous signal,

and to round off noise incurred during computation. Inhigher order recursive filters, the accumulation of roundoff noise could lead to instability.

Long design and development times The design anddevelopment times for the digital filters, especiallyhardware developments can be much longer than foranalog filters.

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Types of digital filters

Basic form ofDigital filter.

Finite Impulse Response (FIR) filters

with impulse response of finite duration N.

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Infinite Impulse Response (IIR) filters

with impulse response of infinite duration.

Recursive form ofIIR filter.

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Comparisons - FIR vs. IIR

FIR filters can have exactly linearphase response.

FIR filters realized non recursively,are always stable.

Round off noise and coefficient

quantization error are less in FIRfilters.

FIR requires more coefficients forsharp cutoff filters.

FIR has no analog counterpart. Itis easier to synthesize filters of

arbitrary frequency responses. FIR is algebraically more difficult

to synthesize, ifCAD support notavailable.

The phase response ofIIR arenonlinear, especially at the bandedges.

The stability ofIIR filters cannot be

always guaranteed.

Round off noise and coefficientquantization error are more in IIRfilters.

IIR requires less coefficients.

Analog filters can be readilytransformed in to equivalent IIR

filters.

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Filter design steps

Specification of the filter requirements.

Calculation of suitable filter requirements.

Representation of the filter by a suitablestructure(realization).

Analysis of the effects of finite wordlength

on filterperformance. Implementation of filter in software and/ or

hardware.

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Summary A common framework for designing FIR and IIR

filters, from specification to implementation.

A simple designing procedure involves 5 keysteps:

Filter specification.

Calculation of suitable filter coefficients.

Realization of the filter using a suitable structure.

Quantization of filter coefficients and variables to suitable

wordlengths and analysis of any resultant errors. Implementation in hardware / software as coding of the filterin a processor which will perform the actual filtering on inputdata.