book

Practical Applications in Digital Signal Processing

by Richard Newbold

October 2012

Intermediate to advanced

1152 pages

28h 19m

English

Pearson

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The Purpose of This BookWho Should Read This BookHow This Book Is Organized
1.1. Definitions1.2. Defining Digital Frequencies1.3. Mathematical Representation of Digital Frequencies1.4. Normalized Frequency1.5. Representation of Digital Frequencies
2.1. Cartesian Form of Complex Numbers2.2. Polar Form of Complex Numbers2.3. Roots of Complex Numbers2.4. Absolute Value of Complex Numbers2.5. Exponential Form of Complex Numbers2.6. Graphs of the Complex Variable z2.7. Limits2.8. Analytic Functions2.9. Singularity2.10. Entire Functions2.11. The Complex Number ∞2.12. Complex Differentiation2.13. Cauchy-Riemann Equations2.14. Simply Connected Region2.15. Contours2.16. Line Integrals2.17. Real Line Integrals2.18. Complex Line Integrals2.19. Cauchy’s Theorem2.20. Table of Common Integrals2.21. Cauchy’s Integral2.22. Residue Theory2.23. References
3.1. A Brief Review of the Fourier Series3.2. A Brief Review of the Fourier Transform3.3. Review of the Discrete Fourier Transform (DFT)3.4. DFT Processing Gain3.5. Example DFT Signal Processing Application3.6. Discrete Time Fourier Transform (DTFT)3.7. Fast Fourier Transform (FFT)3.8. References

4.1. Complex Number Representation4.2. Mechanics of the Z-Transform4.3. Left-Sided Z-Transform4.4. Right-Sided Z-Transform4.5. Two-Sided Z-Transform4.6. Convergence of the Z-Transform4.7. System Stability4.8. Properties of the Z-Transform4.9. Common Z-Transform Pairs4.10. Inverse Z-Transform4.11. Pole and Zero Standard Form Plug-In Equations4.12. Applications of the Z-Transform4.13. Summary of Useful Equations4.14. References
5.1. Review of Digital FIR Filters5.2. Parks-McClellan Method of FIR Filter Design5.3. PM Implementation of Half Band Filters5.4. References
6.1. Poly Phase Filter (PPF)6.2. Half Band Filter6.3. Cascaded Integrator Comb (CIC) Filter6.4. References
7.1. A Typical Digital Signal Processing (DSP) System7.2. Conversion of a Complex Signal to a Real Signal7.3. Complex to Real Simulation Results7.4. Reference
8.1. Numerically Controlled Oscillator (NCO)8.2. Enhanced NCO Phase Accumulator8.3. NCO Synthesized Output Frequency Error8.4. Adding a Programmable Phase Offset to the NCO Output8.5. Design of an Industry-Grade NCO8.6. NCO Phase Dither8.7. References
9.1. Continuous Time (Analog) Fourier Transform9.2. Discrete Time (Digital) Fourier Transform9.3. Useful Equations9.4. References
10.1. Example Application of an Elastic Store Memory10.2. PCM Multiplexing Hierarchy10.3. DS-1C Multiplexer Design Overview10.4. Design of the Elastic Store Memory10.5. Hardware Implementation of the Elastic Store Memory10.6. Overall DS-1C Multiplexer Design Block Diagram10.7. Additional Information10.8. References
11.1. Digital Data Locked Design11.2. Digital Data Locked Steady State Behavior11.3. Digital Data Locked Transient Behavior11.4. Data Locked Loop Bit-Level Simulation11.5. Engineering Note11.6. Summary of Useful Equations11.7. References
12.1. Introductory Description12.2. Channelizer Functional Overview12.3. Channelizer Detailed Design Concepts12.4. Channelizer Software Simulation Results12.5. Channelizer Hardware Design Example12.6. Summary of Useful Equations12.7. References
13.1. Design of a Type I RMS AGC Circuit13.2. Design of a Type II RMS AGC Circuit13.3. References
A.1. Writing a C/C++ Main ProgramA.2. Calling Subroutines and Functions From a C/C++ MainA.3. Writing a FORTRAN SubroutineA.4. Writing a FORTRAN FunctionA.5. Passing Integer ArgumentsA.6. Passing Floating Point ArgumentsA.7. Passing Array ArgumentsA.8. Passing Pointer ArgumentsA.9. Compile/Link Mixed Language C/C++ FORTRAN ProgramsA.10. Parks-McClellan FORTRAN Subroutine Called from C MainA.11. References

Content preview from Practical Applications in Digital Signal Processing

Chapter Seven. Complex to Real Conversion

There are many instances where signal processing hardware and/or software operate on real signals. One example is passing a real digitized signal x_R(n) through a digital filter to shape the signal bandwidth. Another example is computing a histogram of a real discrete signal by collecting statistics on one or more of its parameters.

For the most part, when dealing with communication signals, it is either convenient or mandatory that a signal be processed in its complex form. That is, the signal x_R(n) is first converted from its real form to its complex form x_C(n) = a(n) + jb(n), where a(n) is the real part ...