Download presentation

1
**Fourier / Wavelet Analysis**

ASTR 3010 Lecture 19 Textbook : N/A

2
Fourier Transform in signal processing, (time and frequency)

3
**Add bunch of zeros in your data!**

Number of input data points number of frequency sampling in FT!

4
**Example of FFT in astronomy : defringing a spectrum**

heavily fringed raw spectrum power spectrum of the input defringed spectrum

5
**Limits on Fourier Transform**

it can only “see” one variable (period or time) at a time at sufficient precision!

6
**Short-Time Fourier Transform**

Using a window function in time Limited by the Uncertainty Principle : t*ω = constant

7
**STFT resolution problem**

Four different Gaussian windows

8
Wavelet Transform Wavelet transform can get two different information (i.e., time and frequency) simultaneously!

9
**Wavelet Transform where basis function is s : scale parameter**

τ : translation parameter

10
**Practical use of wavelet transformation**

Decomposition and recomposition of a signal

11
**PyWavelets pywt pywt.wavelist pywt.wavelet pywt.wavedec pywt.waverec**

['bior1.1', 'bior1.3', 'bior1.5', 'bior2.2', 'bior2.4', … 'coif1', 'coif2', 'db1', 'db2', 'db3', 'sym15', 'sym16', 'sym17', 'sym18', 'sym19', 'sym20'] pywt pywt.wavelist pywt.wavelet pywt.wavedec pywt.waverec import pywt pywt.wavelist()

12
**PyWavelets http://www.pybytes.com/pywavelets pywt pywt.wavelist**

pywt.wavelet pywt.wavedec pywt.waverec import pywt myw=pywt.wavelet(‘db4’) phi,psi,wx = myw.wavefun() plot(wx,phi,’r’) plot(wx,psi,’b’) Daubechies Wavelet : order 4

13
**PyWavelets http://www.pybytes.com/pywavelets pywt pywt.wavelist**

pywt.wavelet pywt.wavedec pywt.waverec import pywt myw=pywt.wavelet(‘sym20’) phi,psi,wx = myw.wavefun() plot(wx,phi,’r’) plot(wx,psi,’b’)

14
**Wavelets Decomposition Tree**

decomposition of a signal into several resolution levels. First, the original signal is decomposed by two complementary half-band filters (high-pass and low-pass filters) that divide a spectrum into high-frequency (detail coefficients; D1) and low-frequency (approximation coefficients; A1) components (bands). For example, the low-pass filter will remove all half-band highest frequencies. Information from only the low frequency band (A1), with a half number of points, will be filtered in the second decomposition level. The A2 outcome will be filtered again for further decomposition.

15
**PyWavelets decomposition reconstruction**

pywt pywt.wavelist pywt.wavelet pywt.wavedec pywt.waverec import pywt myw=pywt.wavelet(‘db4’) dec = myw.wavedec(data,’db4’,’zpd’,5)

16
**PyWavelets decomposition reconstruction**

pywt pywt.wavelist pywt.wavelet pywt.wavedec pywt.waverec import pywt myw=pywt.wavelet(‘sym20’) dec = myw.wavedec(data,’sym20’,’zpd’,5)

17
pywt : Denoising import pywt … set high order “difference” coeffs to zero. … among “diff” coeffs, clip small coeffs < 0.2*sigma … then, reconstruct dec = myw.wavedec(data,’db4’,’zpd’,5)

18
Wavelet: Denoising

19
Wavelet: Denoise in 2D

20
Wavelet: Denoise in 2D

Similar presentations

Presentation is loading. Please wait....

OK

Wavelet Transforms ( WT ) -Introduction and Applications

Wavelet Transforms ( WT ) -Introduction and Applications

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on centring tattoo Ppt on carbon arc welding Class 11 ppt on conic section maths Ppt on bond length Ppt on sound navigation and ranging systematic Download ppt on role of chemistry in our daily life Ppt on trade fair circular Ppt on area of parallelogram and triangles for class 9 Ppt on earth movements and major landforms in china Ppt on standing orders