DSP (2012)
Fourier Analysis of Signals Using the DFT
Fourier Analysis of Signals
Using the DFT
Fourier Analysis of Signals
NCTU EE
1
DSP (2012)
Fourier Analysis of Signals Using the DFT
DFT Analysis of Sinusoidal Signals
Effect of Windowing
Given a con
DSP (2012)
Computation of DFT
Computation of DFT
Efficient algorithms for computing DFT Fast Fourier Transform.
(a) Compute only a few points out of all N points
(b) Compute all N points
What are the efficiency criteria?
Number of multiplications
Number
DSP (2012)
Discrete Fourier Transform
Discrete Fourier Transform
What is Discrete Fourier Transform (DFT)?
(Note: Its not DTFT discrete-time Fourier transform)
A linear transformation (matrix)
Samples of the Fourier transform (DTFT) of an aperiodic (wit
DSP (Spring, 2012)
Filter Design
Filter Design
Introduction
Filter An important class of LTI systems
We discuss frequency-selective filters mostly: LP, HP,
We concentrate on the design of causal filters.
Three stages in filter design:
Specification: ap
DSP (Spring, 2012)
Structures for Discrete-Time Systems
Structures For Discrete-Time Systems
Realization (implementation) of digital filters
Structures of IIR and FIR filters, their advantages and disadvantages efficiency and error
Example:
Given H ( z )
DSP (Spring, 2012)
Transform Analysis of LTI Systems
Transform Analysis of LTI Systems
Introduction
Frequency response of LTI systems
Linear constant-coefficient difference equations
Magnitude and phase
Minimum phase
Linear phase
An LTI system can comple
DSP (Spring, 2012)
Sampling of Continuous-time Signals
Sampling of Continuous-time Signals
Advantages of digital signal processing, e.g., audio/video CD.
Things to look at:
Continuous-to-discrete (C/D)
Discrete-to-continuous (D/C) perfect reconstruction
DSP (Spring, 2012)
The z-Transform
The z-Transform
Introduction
Why do we study them?
A generalization of DTFT.
Some sequences that do not converge for DTFT have valid z-transforms.
Better notation (compared to FT) in analytical problems (complex varia
DSP (Spring, 2012)
Discrete-Time Signals and Systems
Discrete-Time Signals and Systems
Introduction
Signal processing (system analysis and design)
Analog
Digital
History
Before 1950s: analog signals/systems
1950s: Digital computer
1960s: Fast Fouri