DSP for MATLAB and LabVIEW. Volume II, Discrete frequency transforms /
This book is Volume II of the series DSP for MATLAB and LabVIEW. This volume provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (D...
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
San Rafael, Calif. :
Morgan & Claypool Publishers,
[2008]
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| Series: | Synthesis lectures on signal processing (Online) ;
#5. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book Software download |
Table of Contents:
- The discrete time Fourier transform
- Overview
- In the previous volume
- In this volume
- In this chapter
- Software for use with this book
- Introduction to transform families
- Fourier family (constant unity-magnitude correlators)
- Laplace family (time-varying-magnitude correlators)
- The DTFT
- Inverse DTFT
- A few properties of the DTFT
- Linearity
- Conjugate symmetry for real x[n]
- Periodicity
- Shift of frequency
- Convolution
- Even and odd components
- Multiplication by a ramp
- Frequency response of an LTI system
- From impulse response
- From difference equation
- References
- Exercises
- The z-transform
- Overview
- Software for use with this book
- Definition & properties
- The z-transform
- The inverse z-transform
- Convergence criteria
- Summary of ROC facts
- Trivial poles and zeros
- Basic properties of the z-transform
- Common z-transforms
- Transfer functions, poles, and zeros
- Pole location and stability
- Conversion from z-domain to time domain
- Difference equation
- Table lookup
- Partial fraction expansion
- Contour integration in the complex plane
- Transient and steady-state responses
- Frequency response from z-transform
- For generalized transfer function
- Relation to DTFT
- Finite impulse response (FIR)
- Infinite impulse response (IIR) single pole
- Cascaded single-pole filters
- Off-unit-circle zeros and decaying signals
- Transfer function & filter topology
- Direct form
- Direct form transposed
- Cascade form
- Parallel form
- Lattice form
- References
- Exercises
- The DFT
- Overview
- Software for use with this book
- Discrete Fourier series
- Sampling in the z-domain
- From DFS to DFT
- DFT-IDFT pair
- Definition-forward transform (time to frequency)
- Definition-inverse transform (frequency to time)
- Magnitude and phase
- N, scaling constant, and DFT variants
- MathScript implementation
- A few DFT properties
- General considerations and observations
- Bin values
- Periodicity in n and k
- Frequency multiplication in time domain
- Computation of DFT via matrix
- DFT of common signals
- Frequency resolution
- Bin width and sample rate
- The FFT
- N-pt DFT from two N/2-pt DFTs
- Decimation-in-time
- Reassembly via butterfly
- Algorithm execution time
- Other algorithms
- The Goertzel algorithm
- Via single-pole
- Using complex conjugate poles
- Magnitude only output
- Linear, periodic, and circular convolution and the DFT
- Cyclic/periodic convolution
- Circular convolution
- DFT convolution theorem
- Linear convolution using the DFT
- Summary of convolution facts
- The overlap-add method
- DFT leakage
- On-bin/off-bin: DFT leakage
- Avoiding DFT leakage-windowing
- Inherent windowing by a rectangular window
- A few common window types
- DFT leakage v. window type
- Additional window use
- DTFT via padded DFT
- The inverse DFT (IDFT)
- Computation of IDFT via matrix
- IDFT via DFT
- IDFT phase descrambling
- Phase zeroing
- Phase shifting
- Equalization using the DFT
- References
- Exercises.