Window Functions and Their Applications in Signal Processing.

• Author: Prabhu, K. M. M.
• Place / Publishing House: Milton : : Taylor & Francis Group,, 2013.; ©2014.
• Year of Publication: 2013
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (405 pages)

Table of Contents

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Foreword -- Preface -- Acknowledgments -- Abbreviations -- 1. Fourier Analysis Techniques for Signal Processing -- 1.1 Review of Basic Signals and Systems -- 1.1.1 Basic Continuous-Time Signals -- 1.1.2 Basic Discrete-Time Signals -- 1.1.3 System and Its Properties -- 1.1.4 LTI Systems -- 1.2 Continuous-Time Fourier Transform -- 1.2.1 Properties of the CTFT -- 1.2.2 Examples of CTFT -- 1.3 Discrete-Time Fourier Transform -- 1.3.1 Properties of DTFT -- 1.3.2 Examples of DTFT -- 1.4 Z-Transform -- 1.4.1 Examples of z-Transform -- 1.5 Discrete Fourier Transform -- 1.5.1 Properties of the DFT -- 1.5.2 Examples of DFT -- 1.6 Fast Fourier Transform -- 1.6.1 Decimation-in-Time FFT (DIT-FFT) -- 1.6.1.1 Computational Savings -- 1.6.1.2 In-Place Computation -- 1.6.2 Decimation-in-Frequency FFT (DIF-FFT) -- 1.6.3 Inverse DFT from FFT -- 1.6.4 Linear Convolution Using DIT-FFT and DIF-FFT -- References -- 2. Pitfalls in the Computation of DFT -- 2.1 Sampling, Reconstruction, and Aliasing -- 2.1.1 WKS Sampling Theorem -- 2.1.2 Reconstruction of Continuous-Time Signals from Discrete-Time Samples -- 2.2 Frequency Leakage Effect -- 2.2.1 Zero Leakage Case -- 2.2.2 Maximum Leakage Case -- 2.3 DFT as a Filter Bank -- 2.4 Picket-Fence Effect or Scalloping Loss -- 2.5 Zero-Padding and Frequency Resolution -- 2.5.1 Zero-Padding -- 2.5.2 Frequency Resolution -- References -- 3. Review of Window Functions -- 3.1 Introduction -- 3.2 Characteristics of a Window Function -- 3.3 List of Windows -- 3.3.1 Rectangular (Box Car) Window -- 3.3.2 Triangular (Bartlett) Window -- 3.3.3 Cos(x) Window -- 3.3.4 Hann (Raised-Cosine) Window -- 3.3.5 Truncated Taylor Family -- 3.3.6 Hamming Window -- 3.3.7 Cos3(x) Window -- 3.3.8 Sum-Cosine Window -- 3.3.9 Cos4(x) Window.

3.3.10 Raised-Cosine Family -- 3.3.11 Blackman Window -- 3.3.12 Optimized Blackman Window -- 3.3.13 Blackman-Harris Window -- 3.3.14 Parabolic Window -- 3.3.15 Papoulis Window -- 3.3.16 Tukey Window -- 3.3.17 Parzen (Jackson) Window -- 3.3.18 Dolph-Chebyshev Window -- 3.3.19 Kaiser's Modified Zeroth-Order Bessel Window Function Family -- 3.3.20 Kaiser's Modified First-Order Bessel Window Function Family -- 3.4 Rate of Fall-Off Side-Lobe Level -- 3.4.1 Theorem -- 3.4.2 Side-Lobe Fall-Off Rate in the Time-Domain -- 3.5 Comparison of Windows -- References -- 4. Performance Comparison of Data Windows -- 4.1 Definition of Window Parameters -- 4.2 Computation of Window Parameters -- 4.3 Discussion on Window Selection -- References -- 5. Discrete-TimeWindows and Their Figures of Merit -- 5.1 Different Classes of Windows -- 5.2 Discrete-Time Windows -- 5.2.1 Rectangular (Box Car) Window -- 5.2.2 Triangular (Bartlett) Window -- 5.2.3 Cosαx Window Family -- 5.2.4 Hann Window -- 5.2.5 Truncated Taylor Family of Windows -- 5.2.6 Hamming Window -- 5.2.7 Sum-Cosine Window -- 5.2.8 Raised-Cosine Window Family -- 5.2.9 Blackman Window -- 5.2.10 Optimized Blackman Window -- 5.2.11 Tukey Window -- 5.2.12 Blackman-Harris Window -- 5.2.13 Nuttall Window Family -- 5.2.14 Flat-Top Window -- 5.2.15 Parabolic Window -- 5.2.16 Riemann Window -- 5.2.17 Poisson Window -- 5.2.18 Gaussian Window -- 5.2.19 Cauchy Window -- 5.2.20 Hann-Poisson Window -- 5.2.21 Papoulis (Bohman) Window -- 5.2.22 Jackson (Parzen) Window -- 5.2.23 Dolph-Chebyshev Window -- 5.2.24 Modified Zeroth-Order Kaiser-Bessel Window Family -- 5.2.25 Modified First-Order Kaiser-Bessel Window Family -- 5.2.26 Saramäki Window Family -- 5.2.27 Ultraspherical Window -- 5.2.28 Odd and Even-Length Windows -- 5.3 Figures of Merit -- 5.4 Time-Bandwidth Product -- 5.5 Applications of Windows.

5.5.1 FIR Filter Design Using Windows -- 5.5.2 Spectral Analysis -- 5.5.3 Window Selection for Spectral Analysis -- References -- 6. Time-Domain and Frequency-Domain Implementations of Windows -- 6.1 Time-Domain Implementation -- 6.2 A Programmable Windowing Technique -- 6.3 Computational Error in Time and Frequency-Domains -- 6.4 Canonic Signed Digit Windowing -- 6.4.1 Window 1 -- 6.4.2 Window 2 -- 6.4.3 Window 3 -- 6.4.4 Window 4 -- 6.4.5 Window 5 -- 6.4.6 Window 6 -- 6.4.7 Window 7 -- 6.4.8 Window 8 -- 6.4.9 Window 9 -- 6.4.10 Window 10 -- 6.4.11 Window 11 -- 6.4.12 Window 12 -- 6.4.13 Window 13 -- 6.4.14 Window 14 -- 6.5 Modified Zeroth-Order Kaiser-Bessel Window Family -- 6.6 Summary -- References -- 7. FIR Filter Design Using Windows -- 7.1 Ideal Filters -- 7.1.1 Lowpass Filter -- 7.1.2 Highpass Filter -- 7.1.3 Bandpass Filter -- 7.1.4 Bandstop Filter -- 7.2 Linear Time Invariant Systems -- 7.3 FIR Filters -- 7.3.1 Advantages of FIR Filters -- 7.4 IIR Filters -- 7.4.1 Properties of IIR Filters -- 7.5 Structure of an FIR Filter -- 7.5.1 Filter Specifications -- 7.6 FIR Filter Design -- 7.6.1 Linear-Phase Filters -- 7.6.2 Types of FIR Filters -- 7.6.3 Frequency Response of Type 1 FIR Filter -- 7.6.4 Design Procedure for Filters -- 7.7 Kaiser-Bessel Windows for FIR Filter Design -- 7.7.1 Filter Design Using Kaiser-Bessel Zeroth-Order (I0-Sinh) Window -- 7.7.2 Filter Design Using Kaiser-Bessel First-Order (I1-Cosh) Window -- 7.8 Design of Differentiator by Impulse Response Truncation -- 7.9 Design of Hilbert Transformer Using Impulse Response Truncation -- References -- 8. Application of Windows in Spectral Analysis -- 8.1 Nonparametric Methods -- 8.1.1 Periodogram PSD Estimator -- 8.1.2 Modified Periodogram PSD Estimator -- 8.1.3 Spectral Analysis Using Kaiser-Bessel Window -- 8.1.4 Bartlett Periodogram -- 8.1.5 Welch Periodogram Method.

8.1.6 Blackman-Tukey Method -- 8.1.7 Daniel Periodogram -- 8.1.8 Application of the FFT to the Computation of a Periodogram -- 8.1.9 Short-Time Fourier Transform -- 8.1.10 Conclusions -- References -- 9. Applications of Windows -- 9.1 Windows in High Range Resolution Radars -- 9.1.1 HRR Target Profiling -- 9.1.2 Simulation Results -- 9.2 Effect of Range Side Lobe Reduction on SNR -- 9.2.1 Introduction -- 9.2.2 Loss Factor -- 9.2.3 Weighting Function -- 9.2.4 Results and Discussions -- 9.3 Window Functions in Stretch Processing -- 9.4 Application of Window Functions in Biomedical Signal Processing -- 9.4.1 Biomedical Signal Processing -- 9.4.2 FIR Filtering of Biomedical Signals -- 9.4.3 Moving Average Filtering of Biomedical Signals -- 9.4.4 QRS Detection in ECG Based on STFT -- 9.5 Audio Denoising Using the Time-Frequency Plane -- 9.5.1 Time-Frequency Plane -- 9.5.2 Audio Denoising Using Time-Frequency Plane -- 9.5.3 Block Thresholding -- 9.5.4 Effect of Windows -- 9.6 Effect of Windows on Linear Prediction of Speech -- 9.6.1 Linear Prediction Coder -- 9.6.2 Line Spectral Frequencies -- 9.6.3 LSF Variation due to Windows -- 9.7 Application of Windows in Image Processing -- 9.7.1 Windows for ISAR Images -- 9.7.2 Experimental Analysis -- 9.7.3 Results and Conclusions -- 9.8 Windows to Improve Contrast Ratio in Imaging Systems -- 9.8.1 Experimental Analysis -- 9.8.2 Results and Conclusions -- References -- Index.