Digital Signal Processing and Its Applications

Table of Content

Chapter 1 Introduction

1.1 Need and Basic Elements of Digital Signal Processing

1.2 Advantages of Digital Signal Processing

1.3 Classification of Signals

1.3.1 Multichannel and Multidimensional Signals

1.3.2 Continuous-Time Versus Discrete-Time Signals

1.3.3 Continuous-Valued Versus Discrete-Valued Signals

1.3.4 Deterministic Versus Random Signals

1.4 Classification of Continuous-Time and Discrete-Time Signals

1.4.1 Energy Signals and Power Signals

1.4.2 Periodic Signals and Aperiodic Signals

1.4.3 Even and Odd Signals

1.5 Types of Signals – Basic Discrete-Time and Continuous-Time Signals

1.5.1 Unit Impulse Function

1.5.2 Unit Step Function

1.5.3 Ramp Signal ur(t)

1.5.4 Exponential Signal

1.6 Classification of Systems

1.6.1 Systems with and without Memory

1.6.2 Invertibility and Inverse Systems

1.6.3 Causal and Non-Causal Systems

1.6.4 Stability [Stable System and Unstable System]

1.6.5 Time-Invariant System or Time-Variant System

1.6.6 Linear System or Non-Linear System

1.7 Concept of Frequency in Continuous-Time and Discrete-Time Signals (Analog

And Digital Signals)

1.8 Sampling Theorem

1.9 Reconstruction of a Signal from Samples

1.10 Analog-to-Digital Conversion

Solved Problems (1.1 to 1.18)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilab Programs

Chapter 2 Discrete-Time System Analysis

2.1 Linear Convolution Sum

2.1.1 Convolution Sum Definition

2.1.2 Properties of Convolution Sum

2.1.3 Steps Involved in Linear Convolution

Solved Problems (2.1 to 2.7)

2.2 Circular Convolution

2.2.1 Matrix Method

Solved Problems (2.8)

2.2.2 Concentric Circle Method

Solved Problems (2.9)

2.2.3 DFT and IDFT Method

Solved Problems (2.10)

2.3 Linear Convolution Using Circular Convolution

Solved Problems (2.11)

2.4 Correlation

2.4.1 Autocorrelation

2.4.2 Cross-Correlation

Solved Problems (2.12 to 2.14)

2.5 Z-Transform

2.5.1 Definition

2.5.2 Properties of Z-Transform

2.5.3 Relationship between Z-Transform and DTFT

2.5.4 Relationship between Z-Transform and DFT

2.5.5 Region of Convergence (ROC)of Z-Transform

Solved Problems (2.15 to 2.20)

2.6 Inverse Z-Transform

2.6.1 Power Series Method

2.6.2 Partial Fraction Method

2.6.3 Residual Method

Solved Problems (2.21 to 2.24)

2.7 Discrete-Time System Representations -Solution by Z-Transform

Solved Problems (2.25 to 2.30)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilab Programs

Chapter 3 Discrete Fourier Transform (DFT) and Its Computation Using FFT

3.1 DFT and IDFT Pair

3.2 Relationship between Discrete-Time Fourier Transform and Discrete Fourier

Transform

3.3 Properties of DFT

3.3.1 Periodicity

3.3.2 Linearity

3.3.3 Circular Shift of a Sequence (Time Domain)

3.3.4 Circular Shift (Frequency Domain)

3.3.5 Time Reversal of the Sequence

3.3.6 Complex Conjugate Properties

3.3.7 Circular Correlation

3.3.8 Parseval’s Theorem

3.3.9 Multiplication of Two Sequences

3.3.10 Convolution of Two Sequences

Solved Problems (3.1 to 3.10)

3.4 Fast Fourier Transform (FFT) (DFT Computation Method)

3.4.1 Decimation in Time FFT Algorithm(DIT-FFT)

3.4.2 Comparison of DFT Using Formula (Direct Computation) and by Using

FFT Algorithm

Solved Problems (3.11 to 3.16)

3.5 IDFT (Inverse Discrete Fourier Transform) Using DIT-FIT Algorithm

Solved Problems (3.17 to 3.25)

3.6 Decimation-in-Frequency Algorithm (DIF-FFT) [Derivation]

Solved Problems (3.26 to 3.32)

3.7 Use of FFT Algorithms in Linear Filtering and Correlation

3.8 Filtering of Long Data Sequences: DFT Based Using Overlap-Save Method and

Overlap-Add Method

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilab Programs

Chapter 4 FIR Filter Design

4.1 Symmetric and Antisymmetric FIR Filter: Condition

4.2 Amplitude and Phase Response of Symmetric and Antisymmetric FIR Filters

4.2.1 Symmetric Odd Order Filter (Even Length)

4.2.2 Symmetric Even Order Filter (Odd Length)

4.3 Comparison of Symmetric and Antisymmetric FIR Filter

4.4 Selection of Filters

4.5 Linear Phase Response – Linear Phase Filter

Solved Problems (4.1)

4.6 FIR Filter Design Methods

4.6.1 Need for Windowing Techniques in Designing FIR Filter

4.6.2 Desirable Characteristics of the Window

4.6.3 Procedure for Designing FIR Filter Using Window Function

4.6.4 Effect of Window Function on the Desired Frequency Response

4.6.5 Rectangular Window

4.6.6 Gibbs Phenomenon

4.6.7 Effect of Window Length M in Filter Design

4.6.8 To Avoid Oscillations in Passband and Stopband Filter Design

4.6.9 Different Types of Windowing Techniques

4.6.10 Derivation of Impulse Response for Lowpass Filter

Solved Problems (4.2 to 4.15)

4.6.11 Derivation of Impulse Response of Highpass Filter

Solved Problems (4.16 to 4.17)

4.6.12 Derivation of Impulse Response of Bandpass Filter

Solved Problems (4.18)

4.6.13 Derivation of Impulse Response of Band Reject Filter

Solved Problems (4.19 to 4.21)

4.7 Design for FIR Filters Using Frequency Sampling Techniques

4.7.1 Type of Filters for Which Frequency Sampling Method is Suitable

4.7.2 Steps Involved in Designing FIR Filter Using Frequency Sampling

Method

4.7.3 Advantage of Frequency Sampling Techniques

Solved Problems (4.22 to 4.24)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Review Questions

Big Questions

Unsolved Problems

Scilab Programs

4.7.4Fourier Series Method

Solved Problems (4.25 to 4.29)

Short Questions

Big Questions

Chapter 5 FIR Filter Realization Structures

5.1 Direction Realization of Linear Phase FIR Filter

5.2 IIR Filter Design by Approximation of Derivatives

Solved Problems (5.1 to 5.2)

5.3 Cascade Realization

5.4 Polyphase Realization of FIR Filter

5.5 Lattice Structure

5.6 Frequency Sampling Structure

Solved Problems (5.3 to 5.19)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilap Programs

Chapter 6 IIR Filter Design

6.1 IIR Digital Filter Equation

6.2 Merits of IIR Filters

6.3 Demerits of IIR Filter

6.4 Design Stages for Digital IIR Filters

6.5 Need for Digital Transformation

6.6 Different Transformation Techniques to Obtain a Digital Filter from an Analog

Filter

6.7 IIR Filter Design by Impulse-Invariance Method

6.7.1 Design Procedure

6.7.2 Disadvantage of Impulse Invariance Method −Aliasing

6.7.3 Minimize Aliasing in Impulse Invariant Method

6.7.4 Steps Involved in Converting Analog Filter to Digital Filter

6.8 IIR Filter Design by the Bilinear Transformation

6.8.1 Advantage of Bilinear Transformation

6.8.2 Bilinear Transformation Mapping for Designing IIR Filter

6.8.3 Frequency Compression or Frequency Warping

6.8.4 Summary of Steps Involved in IIR Digital Filter Design Using Bilinear

Transformation

6.8.5 Prewarping

6.8.6 Advantage of Bilinear Transformation Technique

6.8.7 Disadvantage of Bilinear Transformation Technique

6.8.8 Difference between Bilinear Transformation Technique and Impulse

Invariant Technique

6.9 Butterworth IIR Filter

6.9.1 Derivation of Filter Order ‘N’ and Poles ‘Sk’ for Butterworth Filter

6.9.2 Butterworth Filter Properties

6.9.3 Design Procedure for Designing a Digital IIR Butterworth Filter Using

Impulse Invariance Method

6.9.4 Design Procedure for Designing a Digital IIR Butterworth Filter Using

Bilinear Transformation Method

6.10 Chebyshev IIR Filter Design

Solved Problems (6.1 to 6.27)

6.11 Frequency Transformation in Analog Domain

Solved Problems (6.28 to 6.34)

6.12 Digital Frequency Transformation

Solved Problems (6.35 to 6.37)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilab Programs

Chapter 7 IIR Filter Realization Structures

7.1 Direct-form Structures

7.1.1 Direct form I Realization

7.1.2 Direct form II Realization (Canonic form)

7.2 Cascade form Structure

7.3 Parallel form Structure

7.4 Lattice and Lattice –Ladder Structures for IIR Systems

Solved Problems (7.1 to 7.12)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilab Programs

Chapter 8 Finite Word Length Effect

8.1 Introduction

8.2 Arithmetic Type Used in DSP

8.3 Comparison of Fixed Point and Floating Point Arithmetic

8.4 Representation of Numbers in Fixed Point Arithmetic

Solved Problems (8.1 to 8.6)

8.5 Representation of Numbers in Floating –Point Arithmetic

Solved Problems (8.7)

8.6 Quantization

8.6.1 Quantization Noise or Quantization Error

8.6.2 Quantization Levels

8.6.3 Quantization Step Size or Resolution (Δ)

8.6.4 Quantization Methods or Techniques

8.6.5 Steady State Input Quantization Noise Power

8.6.6 Signal to Noise Ratio

8.6.7 Steady State Output Noise Power

Solved Problems (8.8 to 8.13)

8.7 Errors Resulting from Truncation and Rounding

8.7.1 Fixed Point Representation

8.7.2 Floating Point Representation

8.7.3 Probability of Error or Probability Density Function of Error Due to

Truncation and Round – Off

8.8 Quantization Error in IIR Filters

Solved Problems (8.14 to 8.22)

8.9 Quantization of Coefficients in FIR Filters or Coefficient Quantization in FIR

Filters or Parameter Quantization in FIR Filters

Solved Problems (8.23 to 8.25)

8.10 Product or Round of Errors in IIR Digital Filters or Product Quantization in IIR

Digital Filters

8.10.1 Product Quantization Methods

8.10.2 Block Diagram Representation of Quantization

8.10.3 To Control the Round off Noise or Product Quantization Noise

8.11 Limit-Cycle Oscillations in Recursive Systems or Limit-Cycle Oscillations in

IIR System

8.11.1 Limit-Cycles

8.11.2 Single-Pole System or First-Order IIR Filter

8.11.3 Limit-Cycle Behaviour in Two-Pole Filter or Second-Order IIR Filter

8.11.4 Dead Band

8.11.5 Limit-Cycle in Parallel – form Realization

8.11.6 Limit-Cycle in Cascade Realization

Solved Problems (8.26 to 8.32)

8.11.7 Overflow Limit-Cycle

8.12 Saturation Arithmetic

8.12.1 Disadvantage of Saturation Arithmetic

8.12.2 Need for Scaling

8.12.3 Condition for Scaling

Solved Problems (8.33 to 8.37)

8.13 Scaling Methods

8.13.1 L1Norm

8.13.2 L2Norm

8.13.3 L∞Norm

8.14 Sample and Hold Circuit

8.15 Quantization Effects in the Computation of the DFT

8.15.1 Quantization Errors in the Direct Computation of the DFT

Solved Problems (8.38)

8.15.2 Quantization Errors in FFT Algorithms

Solved Problems (8.39)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Two mark Questions

Unsolved Big Questions

Scilab Programs

Chapter 9 Multirate Signal Processing

9.1 Principle of Multirate Digital Signal Processing

9.1.1 Need for Multirate DSP

9.1.2 Sampling Rate Conversion

9.1.3 Multirate Digital Signal Processing Systems

9.1.4 Applications of Sampling Rate Conversion in Multirate Signal Processing

Systems

9.1.5 Applications of QMF (Quadrature Mirror Filter)

9.1.6 Key Factors or Key Terms Used in Multirate DSP

9.1.7 Areas in Which Multirate Signal Processing are Used

9.1.8 Advantage of Multirate Signal Processing

9.1.9 Problems to be Avoided While Designing Multirate System

9.2 Up sampling

9.3 Decimation

9.4 Interpolation

9.5 Spectrum of the Down sampled Signal

9.6 Aliasing Effect

Solved Problems (9.1)

9.7 Spectrum of Decimated Signal

9.8 Spectrum of Upsampled Signal

9.9 Anti-Imaging Filter (Need for Anti-Imaging Filter)

Solved Problems (9.2 to 9.3)

9.10 Sampling Rate Conversion by a Rational Factor (I/D) or Sampling Rate Conversion

by a Factor (L/M)

9.11 Need for Multistage Implementation of Sampling Rate Conversion

9.12 Filter Design and Implementation for Sampling Rate Conversion

9.13 Polyphase Structure

9.14 Sampling Rate Conversion by an Arbitrary Factor Need for This Method

Solved Problems (9.4)

9.15 Subband Coding − Applications of Multirate Signal Processing

9.15.1 Analysis Filter Bank

9.15.2 Synthesis Filter Bank

9.15.3 Subband Coding Filter Bank

9.16 QMF − Quadrature Mirror Filter Bank

9.17 Adaptive Filters

Short Questions and Answers

Multiple Choice Questions with Answer Key

Unsolved Big Questions

Scilab Programs

Chapter 10 Discrete Random Signal Processing and Power Spectrum

10.1 Ergodic Signal

10.2 Mean

10.3 Variance

10.4 Covariance

Solved Problems (10.1)

10.5 Energy Density Spectrum

10.6 Wiener−Khintchine Theorem

Solved Problems (10.2)

10.7 Use of Windowing in Spectrum Estimation

10.8 The Use of the DFT in Power Spectrum Estimation

10.9 Estimation of the Autocorrelation and Power Spectrum of Random Signals:

The Periodogram

10.10 Non Parametric Methods for Power Spectrum Estimation

Solved Problems (10.3 to 10.13)

Short Questions and Answers

Multiple Choice Questions with Answer Key

Two mark Questions

Unsolved Big Questions

Scilab Programs

Chapter 11 Application of DSP to Speech Processing

11.1 Subband Coding of Speech Signals (Vocoders)

11.2 Echo Cancellation in Telephone Network

11.3 Musical Sound Processing

11.4 Speech Noise Cancellation (Using Adaptive Filters)

11.5 FM Stereo Generation

11.6 Speech Compression and Coding

11.7 Speech Recognition

Short Questions and Answers

Scilab Programs

Chapter 12 Application of DSP to Image Processing

12.1 Image Enhancement

12.2 Image Restoration and Image Denoising

12.3 Edge-Base Image Segmentation

12.4 Automated Objected Recognition

12.5 Image Compression

12.6 Video Compression

12.7 Watermarking

Scilab Programs

Chapter 13 Biomedical Applications of DSP

13.1 Fetal ECG Monitoring

13.2 Fetal ECG from Maternal ECG

13.3 DSP –Based Closed Loop Controlled Anaesthesia

13.4 Adaptive Filtering of EMG and ERG from Human EEG

Chapter 14 Discrete Cosine Transform and Haar Transform

14.1 Discrete Cosine Transform

14.1.1 Need for Discrete Cosine Transform

14.1.2 Definition of DCT

14.1.3 DCT Properties

14.1.4 DCT Computation Using Scilab

14.2 The Haar Transform

14.2.1 Haar Transform for Continuous-Time Function

14.2.2 Haar Transform for Discrete-Time Sequence

14.2.3 Haar Transform Pair

14.2.4 Normalized Haar Transform

14.2.5 Haar Transform Properties

14.2.6 Haar Transform Using Scilab

14.3 Energy Compaction Properties of DCT and Haar Transform

14.3.1 Discrete Cosine Transform (DCT)

14.3.2 The Discrete Haar Transform

Chapter 15 Digital Signal Processors

15.1 Introduction to DS Processors (Programmable DSPs)

15.1.1 Architecture

15.1.2 Features (DSP Architecture Features)

15.1.3 Addressing Modes (Examples from TMS320C5X)

15.1.4 Introduction to Commercial DSP Processors with Architectural Features

15.1.5 Comparison of Fixed Point DSP and Floating-Point DSP

15.1.6 Instructions Set TMS320C5X – An Overview

15.2 Architectural Features of TMS320 from First Generation to Fifth Generation

Short Questions and Answers

Two Mark Questions

Big Questions

Appendix A – Introduction to Open Source Software Scilab