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
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