Transcript Slide 1

Digital Signal
Processing
1
Digital Signal Processing
Topic 10: The Fast Fourier
Transform
1. Calculation of the DFT
2. The Fast Fourier Transform algorithm
3. Short-Time Fourier Transform
2
1. Calculation of the DFT
3
The DFT
4
Computational Complexity
5
Goertzel’s Algorithm
6
Goertzel’s Algorithm
7
2. Fast Fourier Transform FFT
8
Decimation in Time (DIT) FFT
9
Decimation in Time (DIT) FFT
10
Decimation in Time (DIT) FFT
11
Decimation in Time (DIT) FFT
12
One-Stage DIT Flowgraph
13
Multiple DIT Stages
14
Two-Stage DIT Flowgraph
15
Multi-Stage DIT FFT
16
FFT Implementation Details
17
8-pt DIT FFT Flowgraph
18
FFT for Other Values of N
19
Inverse FFT
20
DFT of Real Sequences
21
3. Short-Time Fourier Transform (STFT)
22
Fourier Transform of AM Sine
23
Fourier Transform of AM Sine
24
FT of Short Segments
25
The Spectrogram
26
Short-Time Fourier Transform
27
STFT Window Shape
28
STFT Window Shape
29
STFT Window Length
30
STFT Window Length
31
Spectrograms of Real Sounds
32
Narrowband vs. Wideband
33
Spectrogram in MATLAB
34
STFT as a Filterbank
35
STFT as a Filterbank
36
STFT Analysis-Synthesis
37
STFT Analysis-Synthesis
38
STFT Analysis-Synthesis
39
STFT Analysis-Synthesis
40