[NEW] Wiener Filter Example — astroML 0.2 documentation | wiener filter – Pickpeup

wiener filter: นี่คือโพสต์ที่เกี่ยวข้องกับหัวข้อนี้

# Author: Jake VanderPlas

# License: BSD

# The figure produced by this code is published in the textbook

# "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)

# For more information, see http://astroML.github.com

# To report a bug or issue, use the following forum:

# https://groups.google.com/forum/#!forum/astroml-general

import

numpy

as

np

from

matplotlib

import

pyplot

as

plt

from

scipy

import

optimize

,

fftpack

from

astroML.filters

import

savitzky_golay

,

wiener_filter

#----------------------------------------------------------------------

# This function adjusts matplotlib settings for a uniform feel in the textbook.

# Note that with usetex=True, fonts are rendered with LaTeX. This may

# result in an error if LaTeX is not installed on your system. In that case,

# you can set usetex to False.

from

astroML.plotting

import

setup_text_plots

setup_text_plots

(

fontsize

=

8

,

usetex

=

True

)

#------------------------------------------------------------

# Create the noisy data

np

.

random

.

seed

(

5

)

N

=

2000

dt

=

0.05

t

=

dt

*

np

.

arange

(

N

)

h

=

np

.

exp

(

-

0.5

*

((

t

-

20.

)

/

1.0

)

**

2

)

hN

=

h

+

np

.

random

.

normal

(

,

0.5

,

size

=

h

.

shape

)

Df

=

1.

/

N

/

dt

f

=

fftpack

.

ifftshift

(

Df

*

(

np

.

arange

(

N

)

-

N

/

2

))

HN

=

fftpack

.

fft

(

hN

)

#------------------------------------------------------------

# Set up the Wiener filter:

# fit a model to the PSD consisting of the sum of a

# gaussian and white noise

h_smooth

,

PSD

,

P_S

,

P_N

,

Phi

=

wiener_filter

(

t

,

hN

,

return_PSDs

=

True

)

#------------------------------------------------------------

# Use the Savitzky-Golay filter to filter the values

h_sg

=

savitzky_golay

(

hN

,

window_size

=

201

,

order

=

4

,

use_fft

=

False

)

#------------------------------------------------------------

# Plot the results

N

=

len

(

t

)

Df

=

1.

/

N

/

(

t

[

1

]

-

t

[

])

f

=

fftpack

.

ifftshift

(

Df

*

(

np

.

arange

(

N

)

-

N

/

2

))

HN

=

fftpack

.

fft

(

hN

)

fig

=

plt

.

figure

(

figsize

=

(

5

,

3.75

))

fig

.

subplots_adjust

(

wspace

=

0.05

,

hspace

=

0.25

,

bottom

=

0.1

,

top

=

0.95

,

left

=

0.12

,

right

=

0.95

)

# First plot: noisy signal

ax

=

fig

.

add_subplot

(

221

)

ax

.

plot

(

t

,

hN

,

'-'

,

c

=

'gray'

)

ax

.

plot

(

t

,

np

.

zeros_like

(

t

),

':k'

)

ax

.

text

(

0.98

,

0.95

,

"Input Signal"

,

ha

=

'right'

,

va

=

'top'

,

transform

=

ax

.

transAxes

,

bbox

=

dict

(

fc

=

'w'

,

ec

=

'none'

))

ax

.

set_xlim

(

,

90

)

ax

.

set_ylim

(

-

0.5

,

1.5

)

ax

.

xaxis

.

set_major_locator

(

plt

.

MultipleLocator

(

20

))

ax

.

set_xlabel

(

r'$\lambda$'

)

ax

.

set_ylabel

(

'flux'

)

# Second plot: filtered signal

ax

=

plt

.

subplot

(

222

)

ax

.

plot

(

t

,

np

.

zeros_like

(

t

),

':k'

,

lw

=

1

)

ax

.

plot

(

t

,

h_smooth

,

'-k'

,

lw

=

1.5

,

label

=

'Wiener'

)

ax

.

plot

(

t

,

h_sg

,

'-'

,

c

=

'gray'

,

lw

=

1

,

label

=

'Savitzky-Golay'

)

ax

.

text

(

0.98

,

0.95

,

"Filtered Signal"

,

ha

=

'right'

,

va

=

'top'

,

transform

=

ax

.

transAxes

)

ax

.

legend

(

loc

=

'upper right'

,

bbox_to_anchor

=

(

0.98

,

0.9

),

frameon

=

False

)

ax

.

set_xlim

(

,

90

)

ax

.

set_ylim

(

-

0.5

,

1.5

)

ax

.

yaxis

.

set_major_formatter

(

plt

.

NullFormatter

())

ax

.

xaxis

.

set_major_locator

(

plt

.

MultipleLocator

(

20

))

ax

.

set_xlabel

(

r'$\lambda$'

)

# Third plot: Input PSD

ax

=

fig

.

add_subplot

(

223

)

ax

.

scatter

(

f

[:

N

/

2

],

PSD

[:

N

/

2

],

s

=

9

,

c

=

'k'

,

lw

=

)

ax

.

plot

(

f

[:

N

/

2

],

P_S

[:

N

/

2

],

'-k'

)

ax

.

plot

(

f

[:

N

/

2

],

P_N

[:

N

/

2

],

'-k'

)

ax

.

text

(

0.98

,

0.95

,

"Input PSD"

,

ha

=

'right'

,

va

=

'top'

,

transform

=

ax

.

transAxes

)

ax

.

set_ylim

(

-

100

,

3500

)

ax

.

set_xlim

(

,

0.9

)

ax

.

yaxis

.

set_major_locator

(

plt

.

MultipleLocator

(

1000

))

ax

.

xaxis

.

set_major_locator

(

plt

.

MultipleLocator

(

0.2

))

ax

.

set_xlabel

(

'$f$'

)

ax

.

set_ylabel

(

'$PSD(f)$'

)

# Fourth plot: Filtered PSD

ax

=

fig

.

add_subplot

(

224

)

filtered_PSD

=

(

Phi

*

abs

(

HN

))

**

2

ax

.

scatter

(

f

[:

N

/

2

],

filtered_PSD

[:

N

/

2

],

s

=

9

,

c

=

'k'

,

lw

=

)

ax

.

text

(

0.98

,

0.95

,

"Filtered PSD"

,

ha

=

'right'

,

va

=

'top'

,

transform

=

ax

.

transAxes

)

ax

.

set_ylim

(

-

100

,

3500

)

ax

.

set_xlim

(

,

0.9

)

ax

.

yaxis

.

set_major_locator

(

plt

.

MultipleLocator

(

1000

))

ax

.

yaxis

.

set_major_formatter

(

plt

.

NullFormatter

())

ax

.

xaxis

.

set_major_locator

(

plt

.

MultipleLocator

(

0.2

))

ax

.

set_xlabel

(

'$f$'

)

plt

.

show

()


DSP Lecture 20: The Wiener filter


ECSE4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 20: The Wiener filter (11/10/14)
0:00:03 Review of autoregressive (AR) processes and parameter estimation
0:06:06 Optimal linear discretetime filters (Wiener filters)
0:10:03 Problem setup and cost function
0:12:37 Taking the derivative of the cost function
0:16:41 The orthogonality property
0:19:38 The WienerHopf equations
0:22:27 The WienerHopf linear system for an FIR filter
0:26:21 Computing the error for the optimal filter
0:30:05 The result
0:31:45 Proof that the Wiener filter is optimal and unique
0:34:38 Linear prediction
0:38:19 Onestepahead linear prediction equations
0:44:17 Error for onestepahead predictor
0:45:55 The augmented system for the optimal predictor and error
0:49:22 Goal: find an optimal longer filter from a shorter one
0:53:12 Backward prediction
0:55:37 The relationship between forward and backward prediction
0:59:22 The LevinsonDurbin algorithm
1:01:15 Reflection coefficients
1:02:36 Deriving the LevinsonDurbin equations
1:11:15 The final result
Follows Section 12.7 of the textbook (Proakis and Manolakis, 4th ed.).

READ  [Update] 絢香 10周年ライブツアー2016 セトリ・感想レポ・グッズ画像まとめ | 絢香 大阪 城 ホール - Pickpeup

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DSP Lecture 20: The Wiener filter

Lec 17 : Optimal linear filters: Wiener Filter


Statistical Signal Processing
Course URL: https://swayam.gov.in/nd1_noc20_ee53/preview
Prof. Prabin Kumar Bora
Dept. of Electronics and Electrical Engineering
IIT Guwahati

Lec 17 : Optimal linear filters: Wiener Filter

wiener filter


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wiener filter

#6 Noise Reduction by wiener filter by MATLAB


Audio Processing by MATLAB 6
1. Speech enhancement / Noise cancellation and suppression
2. A convex combination of two DD approaches
3. Minimum mean squared error (MMSE) to estimate desired speech signal
音訊處理 6
使用基本Wiener filter 進行噪音消除
Introduction \u0026 Download
https://medium.com/audioprocessingbymatlab/noisereductionbywienerfilterbymatlab44438af83f96
Tutorial \u0026 Contact Jarvus
https://medium.com/audioprocessingbymatlab
MATLAB Audio Tutorial Jarvus

#6 Noise Reduction by wiener filter by MATLAB

Lecture 34 – Digital Image Processing – Wiener Filters


This lecture describes about the Wiener Filters. Wiener Filter is a used for Image Restoration where partial knowledge of the blurring function H is available. (AKTU)
Please share, subscribe and comment if you like the video.

Lecture 34 - Digital Image Processing - Wiener Filters

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