1. T-61.3010 Digital Signal Processing and Filtering
Based on the book by Sanjit K. Mitra
Digital Signal Processing, A Computer-Based Approach
McGraw-Hill, 1998 (2nd Edition, 2001) 3rd Edition 2006
Olli Simula Helsinki University of Technology
Laboratory of Computer and Information Science 1 1

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3. Contents of Mitra’s book
1 Signals and Signal Processing Characterization and Classification of Signals 1.2 Typical Signal Processing Operations 1.3 Examples of Typical Signals 1.4 Typical Signal Processing Applications 1.5 Why Digital Signal Processing  3 3

4. Contents of Mitra’s book (cont.)‏
Discrete-Time Signals and Systems Discrete-Time Signals 2.2 Typical Sequences and Sequence Representation 2.3 The Sampling Process 2.4 Discrete-Time Systems 2.5 Time-Domain Characterization of LTI Discrete-Time Systems 2.6 Simple Interconnection Schemes 2.7 Finite-Dimensional LTI Discrete-Time Systems Classification of LTI Discrete-Time Systems Correlation of Signals Random Signals Summary Problems Matlab Exercises  4

5. Contents of Mitra’s book (cont.)‏
3 Discrete-Time Fourier Transform The Continuous-Time Fourier Transform 3.2 The Discrete-Time Fourier Transform 3.3 Discrete-Time Fourier Transform Theorems 3.4 Energy Density Spectrum of a Discrete-Time Sequence 3.5 Band-Limited Discrete-Time Signals 3.6 DTFT Computation Using Matlab The Unwrapped Phase Function 3.8 The Frequency Response of an LTI Discrete-Time System 3.9 Phase and Group Delays Summary Problems Matlab Exercises  5 5

6. Contents of Mitra’s book (cont.)‏
4 Digital Processing of Continous-Time Signals Introduction 4.2 Sampling of Continuous-Time Signals 4.3 Sampling of Bandpass Signals Analog Lowpass Filter Design 4.5 Design of Analog Highpass, Bandpass, and Bandstop Filters 4.6 Anti-Aliasing Filter Design 4.7 Sample-and-Hold Circuit 4.8 Analog-to-Digital Converter 4.9 Digital-to-Analog Converter Reconstruction Filter Design Effect of Sample-and-Hold Operation Summary Problems Matlab Exercises  6 6

7. Contents of Mitra’s book (cont.)‏
5 Finite-Length Discrete Transforms Orthogonal Transforms 5.2 The Discrete Fourier Transform 5.3 Relation Between the Fourier Transform and the DFT, and Their Inverses 5.4 Operations on Finite-Length Sequences 5.5 Classification of Finite-Length Sequences DFT Symmetry Relations 5.7 Discrete Fourier Transform Theorems 5.8 Fourier-Domain Filtering 5.9 Computation of the DFT of Real Sequences Linear Convolution Using DFT Discrete Cosine Transform Discrete Haar Transform Energy Compaction Properties Summary Problems Matlab Exercises 7 7

8. Contents of Mitra’s book (cont.)‏
6 z-Transform Definition and Properties 6.2 Rational z-Transforms 6.3 Region of Convergence of a Rational z-Transform The Inverse z-Transform 6.5 z-Transform Properties 6.6 Computation of the Convolution Sum of Finite-Length Sequences 6.7 The z-Transform Function 6.8 Summary 6.9 Problems Matlab Exercises 8 8

9. Contents of Mitra’s book (cont.)‏
7 Discrete-Time Systems in the Transform Domain Transfer Function Classification Based on Magnitude Characteristics 7.2 Transfer Function Classification Based on Phase Characteristics Types of Linear-Phase Transfer Functions 7.4 Simple Digital Filters 7.5 Complementary Transfer Functions 7.6 Inverse Systems 7.7 System Identification 7.8 Digital Two-Pairs 7.9 Algebraic Stability Test Summary Problems Matlab Exercises 9 9

10. Contents of Mitra’s book (cont.)‏
8 Digital Filter Structures Block Diagram Reprensentation 8.2 Equivalent Structures 8.3 Basic FIR Digital Filter Structures 8.4 Basic IIR Filter Structures 8.5 Realization of Basic Structures Using Matlab 8.6 Allpass Filters 8.7 Tunable IIR Digital Filters 8.8 IIR Tapped Cascaded Lattice Structures 8.9 FIR Cascaded Lattice Structures Parallel Allpass Realization of IIR Transfer Functions Digital Sine-Cosine Generator Computational Complexity of Digital Filter Structures Summary Problems Matlab Exercises  10 10

11. Contents of Mitra’s book (cont.)‏
9 IIR Digital Filter Design Preliminary Considerations 9.2 Bilinear Transform Method of IIR Filter Design 9.3 Design of Lowpass IIR Digital Filters 9.4 Design of Highpass, Bandpass, and Bandstop IIR Digital Filters 9.5 Spectral Transformations of IIR Filters 9.6 IIR Filter Design Using Matlab 9.7 Computer-Aided Design of IIR Digital Filters 9.8 Summary 9.9 Problems Matlab Exercises 11 11

12. Contents of Mitra’s book (cont.)‏
10 FIR Digital Filter Design Preliminary Considerations FIR Filter Design Based on Windowed Fourier Series Computer-Aided Design of Equiripple Linear-Phase FIR Filters Design of Minimum-Phase FIR Filters FIR Digital Filter Design Using Matlab Design of Computationally Efficient FIR Digital Filters Summary Problems Matlab Exercises 12 12

13. Contents of Mitra’s book (cont.)‏
11 DSP Algorithm Implementation § Basic Issues Structure Simulation and Verification Using Matlab Computation of the Discrete Fourier Transform Fast DFT Algorithms Based on Index Mapping DFT and IDFT Computation Using Matlab Sliding Discrete Fourier Transform DFT Computation over a Narrow Frequency Band Number Representation Arithmetic Operations Handling of Overflow Tunable Digital Filters Function Approximation Summary Problems Matlab Exercises 13 13

14. Contents of Mitra’s book (cont.)‏
12 Analysis of Finite Word-Length Effects The Quantization Process and Errors Quantization of Fixed-Point Numbers Quantization of Floating-Point Numbers Analysis of Coefficient Quantization Effects A/D Conversion Noise Analysis Analysis of Arithmetic Round-Off Errors Dynamic Range Scaling Signal-to-Noise Ratio in Low-Order IIR Filters Low-Sensitivity Digital Filters Reduction of Product Round-Off Errors Using Error Feedback Limit Cycles in IIR Digital Filters Round-Off Errors in FFT Algoritms Summary Problems Matlab Exercises  14 14

15. Contents of Mitra’s book (cont.)‏
13 Multirate Digital Signal Processing Fundamentals The Basic Sample Rate Alteration Devices Multirate structures for Sampling Rate Conversion Multistage Design of Decimator and Interpolator The Polyphase Decomposition Arbitrary-rate Sampling Rate Converter Nyquist Filters Summary Problems Matlab Exercises 15 15

16. Contents of Mitra’s book (cont.)‏
14 Multirate Filter Banks and Wavelets Digital Filter Banks Two-Channel Quadrature-Mirror Filter Bank Perfect ReconstructionTwo-Channel FIR Filter Bank L-Channel QMF Banks Multilevel Filter Banks Discrete Wavelet Transform Summary Problems Matlab Exercises 16 16

17. Contents of Mitra’s book (cont.)‏
15 Applications of Digital Signal Processing Dual-Tone Multifrequency Signal Detection Spectral Analysis of Sinusoidal Signals Spectral Analysis of Nonstationary Signals Spectral Analysis of Random Signals Musical Sound Processing Digital Music Synthesis Discrete-Time Analytic Signal Generation Signal Compression Transmultiplexers Discrete Multitone Transmission of Digital Data Oversampling A/D Converter Oversampling D/A Converter Sparse Antenna Array Design Summary Problems Matlab Exercises  17 17

18. Contents of Mitra’s book (cont.)‏
A Discrete-Time random Signals A.1 Statistical Properties of a Random Variable A.2 Statistical Properties of a Random Variable A.3 Wide-Sense Stationary Random Signal A.4 Cocept of Power in a Random Signal A.5 Ergodic Signal A.6 Transform-Domain Representation of a Random Signal A.7 White Noise A.8 Discrete-Time Processing of Random Signals   18 18

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