DSP System Design: Complexity Reduced IIR Filter Implementation for Practical Applications

Symbols and Abbreviations

?(k)

Delta sequence, equal to 1 for k=0 and zero for k ?0

n(k)

Noise

u(k)

Step function

e(k)

Error signal

w i(k)

Update weight coefficient

z ?1

Unit delay operator

H(z)

Transfer function of the discrete-time filter

A(z)

Transfer function of an allpass filter

H bp(z)

Z transfer function of the bandpass filter

H notch(z)

Z transfer function of the notch filter

?

Normalized frequency ?=f/f s.

FFT

Fast Fourier Transform

FST

Fourier Summation Transform

DFT

Discrete Fourier Transform

dB

Decibel

SNR

Signal-to-Noise Ratio

rms

Root Mean-Square

exp

Exponential function ex

FIR

Finite Impulse Response

IIR

Infinite Impulse Response

LPF

LowPass Filter

HPF

HighPass Filter

BPF

BandPass Filter

LMS

Least-Mean-Square

PZP

Pole-Zero Pattern

VLSI

Very Large Scale Integration

VHSIC

Very High Speed Integrated Circuit

VHDL

VHSIC Hardware Description Language

HTML

Hyper Text Mark-up Language

M

Lowpass oversampling ratio

R

Bandpass oversampling ratio

L

Lowpass interpolation ratio

MSB

Most Significant Bit

LSB

Least Significant Bit

A/D

Analogue-to-Digital

ADC

Analogue-to-Digital Converter

DAC

Digital-to-Analogue Converter

SRD

Sample Rate Decreaser

SRI

Sample Rate Increaser

MIP

Minimum Phase filter

MAP

Maximum Phase filter

LPH

Linear Phase

MOS

Metal Oxide Semiconductor technology

COMB

Filter described by Nth-order difference equation.

MAVR

Moving A Verage Filter.

SLINK

Sink function defined for discrete signals

PCM

Pulse Code Modulation

PDM

Pulse Density Modulation

AM

Amplitude Modulation

FM

Frequency Modulation

AGDP

Arbitrary Group Delay Filter

f s

Sampling frequency

LLFT

Lowpass-to-Lowpass Frequency Transformation

AA

Anti-Aliasing

??

Sigma-Delta

PC

Personal Computer

TB

Transition Bandwidth

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