DiscreteSignal Analysis and DesignISBN: 9780470187777
174 pages
February 2008

This book provides an introduction to discretetime and discretefrequency signal processing, which is rapidly becoming an important, modern way to design and analyze electronics projects of all kinds. It presents discretesignal processing concepts from the perspective of an experienced electronics or radio engineer, which is especially meaningful for practicing engineers, technicians, and students. The approach is almost entirely mathematical, but at a level that is suitable for undergraduate curriculums and also for independent, athome study using a personal computer.
Coverage includes:

First principles, including the Discrete Fourier Transform (DFT)

Sine, cosine, and theta

Spectral leakage and aliasing

Smoothing and windowing

Multiplication and convolution

Probability and correlation

Power spectrum

Hilbert transform
The accompanying CDROM includes Mathcad® v.14 Academic Edition, which is reproduced with permission and has no time limitation for use, providing users with a sophisticated and worldfamous tool for a wide range of applied mathematics capabilities.
DiscreteSignal Analysis and Design is written in an easytofollow, conversational style and supplies readers with a solid foundation for more advanced literature and software. It employs occasional reexamination and reinforcement of particularly important concepts, and each chapter contains selfstudy examples and fullpage Mathcad® Worksheets, workedout and fully explained.
1. Define the goals of the book.
2. Define discrete signals.
3. The advantages of discretesignal analysis and design.
4. Describe the DFT and IDFT.
5. Discuss the Mathcad program.
6. Discuss MATLAB and less expensive approaches.
7. Discuss Multisim program from National Instruments Co.
8. Discuss the Mathtype program.
9. Mention LabVIEW.
10. Mention Search Engines.
11. Discuss the personal productivity software capability.
Chapter 1: First Principles
1. Sequence structure in time domain and frequency domain.
2. Twosided time and frequency.
3. The discrete Fourier transform.
4. The inverse discrete Fourier transform.
5. Frequency and time scaling.
6. Number of samples needed.
7. Complex frequency domain sequences. The phasor concept.
8. Time x(n) vs frequency X(k).
Chapter 2: Sine, Cosine and Theta.
1. Onesided sequences.
2. Combinations of twosided phasors
3. Time and spectrum transformations.
4. Transforming twosided phasor sequences into onesided sine, cosine, Θ.
5. Example 21, nonlinear amplifier distortion and square law modulator.
6. Example 22, analysis of the ramp function.
Chapter 3: Spectral Leakage and Aliasing.
1. Spectral leakage. Noninteger values of time and frequency.
2. Scaling of frequency reduces leakage. Example 31.
3. Aliasing in the twosided frequency domain.
4. Aliasing in the positive frequency domain.
5. Example 32. Analysis of frequency domain aliasing.
6. Time domain aliasing.
Chapter 4: Smoothing and Windowing.
1. Smoothing the rectangular window, without noise and with noise.
2. Smoothed sequences near the beginning and end.
3. Signal to noise ratio of a smoothed sequence.
4. Threepoint smoothing and seven point smoothing.
5. Windowing in the time and frequency domains.
6. The rectangular window (review Ch. 3).
7. The Hamming Window.
8. The Hanning (Hann) Window.
9. Relative merits of the three windows.
10. Lobe amplitudes of the three types of windows.
11. Behavior of windows near k = 1 and 2.
12. Scaling the windows for improved frequency resolution.
Chapter 5: Multiplication and Convolution
1. Sequence multiplication.
2. Polynomial multiplication.
3. Discrete Convolution basic equation.
4. Relating convolution to polynomial multiplication.
5. The “fold and slide” concept.
6. Circular discrete convolution (try to avoid).
7. Sequence time and phase shift.
8. The DFT and IDFT of discrete convolution.
9. Fig 56. Compare convolution and multiplication.
10. Deconvolution.
Chapter 6: Probability and Correlation
1. Expected value of noiseless sequence.
2. Include some additive noise.
3. Envelope detection of noisy sequence.
4. Power of noiseless sequence.
5. Power of noisy sequence.
6. Sequence averaging.
7. Variance (AC component).
8. Gaussian (normal) distribution.
9. Cumulative distribution (CDF).
10. Autocorrelation of a sequence.
11. Cross correlation of two sequences.
12. Autocovariance.
13. Crosscovariance.
14. Correlation coefficient.
Chapter 7: Power spectrum.
1. Finding the power spectrum using Eq 71.
2. Twoside phasor spectrum, oneside power spectrum.
3. Example 71. See Fig 72.
4. Random Gaussian noise spectrum.
5. Measuring power spectrum.
6. Spectrum analyzer example.
7. WienerKintchine theorem.
8. System power transfer Eq 76.
9. Cross power spectrum.
10. Example of calculating phase noise.
Chapter 8: Hilbert Transform.
1. The perfect Hilbert transformer.
2. Example of a Hilbert transform of a square wave.
3. Illustrate smoothing of the Example.
4. Explanation of peaks in Hilbert of square wave.
5. Mathematics of the Hilbert transform.
6. The analytic signal.
7. Example of construction of analytic signal.
8. Singlesideband RF signals.
9. SSB design.
10. The basic allpass network.
11. 90° cascaded phase shift audio network.
12. Why the 90° network is not equivalent to a Hilbert transformer.
13. Filter method SSB transmitter.
14. Phasing method SSB receiver.
15. Filter method SSB receiver.
Appendix A: Additional discretesignal information
16. Discrete derivative.
17. State variable solutions.
18. Using the discrete derivative.
Glossary.
Index.
William E. Sabin, MSEE, Life Member IEEE, has worked at a professional engineering level in the electronics industry for forty years in almost all areas of signal processing, including analog, discrete, and digital. He has coedited three books on the subject of radio systems and circuits and is the author of about forty technical articles in electronics journals.

Every chapter includes examples of practical uses of Discrete Signal Analysis & Design.
 Presents introductory digital signal processing concepts presented in a unique way that will be useful to graduate students; written by an experienced radio engineer.
 Includes Mathcad 14.0 for Students software giving practicing engineers and students alike all the tools they need to use this book. This software package is useful for the buyer long after they have mastered the text.
 This Mathcad 14.0 for Students software package offers significant personal and process productivity advantages for product development, engineering design projects and hundreds of other applications where calculations are key. This is not a timed out version of this product. It is the actual software package and the user receives a single user license.
“DiscreteSignal analysis and Design is written in an easytofollow, conversational style and supplies readers with a solid foundation for more advanced literature and software. It employs the occasional reexamination and reinforcement of particularly important concepts and each chapter contains selfstudy examples and fullpage Mathcad Worksheets, workedout and fully explained.” (International Journal Microstructure & Materials Properties, 2009)
"This volume is valuable for students, academic libraries, mathematicians, and working professionals, especially Mathead users." (CHOICE, August 2008)DiscreteSignal Analysis and Design (US $168.00)
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