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: | |
|---|---|
| Format: | Electronic |
| Language: | English |
| Published: |
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) :
Morgan & Claypool Publishers,
c2008.
|
| Series: | Synthesis lectures on signal processing (Online) ;
# 5. |
| Subjects: | |
| Online Access: | View fulltext via EzAccess |
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.