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T-61.3010 T-61.3010 Digital Digital Signal Processing Signal Processing

and Filteringand 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 SimulaHelsinki University of Technology

Laboratory of Computer and Information Science

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Contents of Mitra’s book

1 Signals and Signal Processing 11.1 Characterization and Classification of Signals1.2 Typical Signal Processing Operations1.3 Examples of Typical Signals1.4 Typical Signal Processing Applications1.5 Why Digital Signal Processing 

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Contents of Mitra’s book (cont.)• Discrete-Time Signals and Systems

41 2.1 Discrete-Time Signals2.2 Typical Sequences and Sequence Representation2.3 The Sampling Process2.4 Discrete-Time Systems2.5 Time-Domain Characterization of LTI Discrete-Time Systems2.6 Simple Interconnection Schemes2.7 Finite-Dimensional LTI Discrete-Time Systems 2.8 Classification of LTI Discrete-Time Systems 2.9 Correlation of Signals2.10 Random Signals2.11 Summary2.12 Problems2.13 Matlab Exercises 

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Contents of Mitra’s book (cont.)

3 Discrete-Time Fourier Transform 117

3.1 The Continuous-Time Fourier Transform3.2 The Discrete-Time Fourier Transform3.3 Discrete-Time Fourier Transform Theorems3.4 Energy Density Spectrum of a Discrete-Time Sequence3.5 Band-Limited Discrete-Time Signals3.6 DTFT Computation Using Matlab 3.7 The Unwrapped Phase Function3.8 The Frequency Response of an LTI Discrete-Time System3.9 Phase and Group Delays 3.10 Summary3.11 Problems3.13 Matlab Exercises 

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Contents of Mitra’s book (cont.)

4 Digital Processing of Continous-Time Signals 171

4.1 Introduction4.2 Sampling of Continuous-Time Signals4.3 Sampling of Bandpass Signals 4.4 Analog Lowpass Filter Design4.5 Design of Analog Highpass, Bandpass, and Bandstop Filters4.6 Anti-Aliasing Filter Design4.7 Sample-and-Hold Circuit4.8 Analog-to-Digital Converter4.9 Digital-to-Analog Converter4.10 Reconstruction Filter Design4.11 Effect of Sample-and-Hold Operation4.12 Summary4.13 Problems4.14 Matlab Exercises 

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Contents of Mitra’s book (cont.)5 Finite-Length Discrete Transforms

2335.1 Orthogonal Transforms5.2 The Discrete Fourier Transform5.3 Relation Between the Fourier Transform and the DFT, and Their Inverses5.4 Operations on Finite-Length Sequences5.5 Classification of Finite-Length Sequences 5.6 DFT Symmetry Relations5.7 Discrete Fourier Transform Theorems5.8 Fourier-Domain Filtering5.9 Computation of the DFT of Real Sequences5.10 Linear Convolution Using DFT5.11 Discrete Cosine Transform5.12 Discrete Haar Transform5.13 Energy Compaction Properties 5.14 Summary5.15 Problems5.16 Matlab Exercises

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Contents of Mitra’s book (cont.)

6 z-Transform 3016.1 Definition and Properties6.2 Rational z-Transforms6.3 Region of Convergence of a Rational z-Transform 6.4 The Inverse z-Transform6.5 z-Transform Properties6.6 Computation of the Convolution Sum of Finite-Length

Sequences6.7 The z-Transform Function6.8 Summary6.9 Problems6.10 Matlab Exercises

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Contents of Mitra’s book (cont.)

7 Discrete-Time Systems in the Transform Domain 353

7.1 Transfer Function Classification Based on Magnitude Characteristics7.2 Transfer Function Classification Based on Phase Characteristics 7.3 Types of Linear-Phase Transfer Functions7.4 Simple Digital Filters7.5 Complementary Transfer Functions7.6 Inverse Systems7.7 System Identification7.8 Digital Two-Pairs7.9 Algebraic Stability Test7.10 Summary7.11 Problems7.12 Matlab Exercises

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Contents of Mitra’s book (cont.)8 Digital Filter Structures

4278.1 Block Diagram Reprensentation8.2 Equivalent Structures8.3 Basic FIR Digital Filter Structures8.4 Basic IIR Filter Structures8.5 Realization of Basic Structures Using Matlab8.6 Allpass Filters8.7 Tunable IIR Digital Filters8.8 IIR Tapped Cascaded Lattice Structures8.9 FIR Cascaded Lattice Structures 8.10 Parallel Allpass Realization of IIR Transfer Functions8.11 Digital Sine-Cosine Generator8.12 Computational Complexity of Digital Filter Structures8.13 Summary8.14 Problems8.15 Matlab Exercises 

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Contents of Mitra’s book (cont.)

9 IIR Digital Filter Design 4899.1 Preliminary Considerations9.2 Bilinear Transform Method of IIR Filter Design9.3 Design of Lowpass IIR Digital Filters9.4 Design of Highpass, Bandpass, and Bandstop IIR Digital Filters9.5 Spectral Transformations of IIR Filters9.6 IIR Filter Design Using Matlab9.7 Computer-Aided Design of IIR Digital Filters9.8 Summary9.9 Problems9.10 Matlab Exercises

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Contents of Mitra’s book (cont.)10 FIR Digital Filter Design

52310.1 Preliminary Considerations10.2 FIR Filter Design Based on Windowed Fourier Series10.3 Computer-Aided Design of Equiripple Linear-Phase FIR Filters10.4 Design of Minimum-Phase FIR Filters10.5 FIR Digital Filter Design Using Matlab10.6 Design of Computationally Efficient FIR Digital Filters10.7 Summary10.8 Problems10.9 Matlab Exercises

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Contents of Mitra’s book (cont.)11 DSP Algorithm Implementation §

58911.1 Basic Issues11.2 Structure Simulation and Verification Using Matlab11.3 Computation of the Discrete Fourier Transform11.4 Fast DFT Algorithms Based on Index Mapping 11.5 DFT and IDFT Computation Using Matlab11.6 Sliding Discrete Fourier Transform11.7 DFT Computation over a Narrow Frequency Band11.8 Number Representation11.9 Arithmetic Operations11.10 Handling of Overflow11.11 Tunable Digital Filters11.12 Function Approximation11.13 Summary11.14 Problems11.15 Matlab Exercises

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Contents of Mitra’s book (cont.)

12 Analysis of Finite Word-Length Effects 665

12.1 The Quantization Process and Errors12.2 Quantization of Fixed-Point Numbers12.3 Quantization of Floating-Point Numbers 12.4 Analysis of Coefficient Quantization Effects12.5 A/D Conversion Noise Analysis12.6 Analysis of Arithmetic Round-Off Errors12.7 Dynamic Range Scaling12.8 Signal-to-Noise Ratio in Low-Order IIR Filters12.9 Low-Sensitivity Digital Filters12.10 Reduction of Product Round-Off Errors Using Error Feedback12.11 Limit Cycles in IIR Digital Filters12.12 Round-Off Errors in FFT Algoritms12.13 Summary12.14 Problems12.15 Matlab Exercises 

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Contents of Mitra’s book (cont.)

13 Multirate Digital Signal Processing Fundamentals739

13.1 The Basic Sample Rate Alteration Devices13.2 Multirate structures for Sampling Rate Conversion13.3 Multistage Design of Decimator and Interpolator13.4 The Polyphase Decomposition13.5 Arbitrary-rate Sampling Rate Converter13.6 Nyquist Filters13.7 Summary13.8 Problems13.9 Matlab Exercises

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Contents of Mitra’s book (cont.)

14 Multirate Filter Banks and Wavelets799

14.1 Digital Filter Banks14.2 Two-Channel Quadrature-Mirror Filter Bank14.3 Perfect ReconstructionTwo-Channel FIR Filter Bank14.4 L-Channel QMF Banks14.5 Multilevel Filter Banks14.6 Discrete Wavelet Transform140.7 Summary14.8 Problems14.9 Matlab Exercises

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Contents of Mitra’s book (cont.)15 Applications of Digital Signal Processing

85515.1 Dual-Tone Multifrequency Signal Detection15.2 Spectral Analysis of Sinusoidal Signals15.3 Spectral Analysis of Nonstationary Signals15.4 Spectral Analysis of Random Signals 15.5 Musical Sound Processing15.6 Digital Music Synthesis15.7 Discrete-Time Analytic Signal Generation15.8 Signal Compression15.9 Transmultiplexers15.10 Discrete Multitone Transmission of Digital Data15.11Oversampling A/D Converter15.12 Oversampling D/A Converter15.13 Sparse Antenna Array Design15.14 Summary15.15 Problems15.16 Matlab Exercises 

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Contents of Mitra’s book (cont.)

A Discrete-Time random Signals 929A.1 Statistical Properties of a Random VariableA.2 Statistical Properties of a Random Variable A.3 Wide-Sense Stationary Random SignalA.4 Cocept of Power in a Random Signal A.5 Ergodic SignalA.6 Transform-Domain Representation of a Random Signal A.7 White NoiseA.8 Discrete-Time Processing of Random Signals 

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