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.).
นอกจากการดูบทความนี้แล้ว คุณยังสามารถดูข้อมูลที่เป็นประโยชน์อื่นๆ อีกมากมายที่เราให้ไว้ที่นี่: ดูเพิ่มเติม
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
wiener filter
explanation Created using PowToon Free sign up at http://www.powtoon.com/youtube/ Create animated videos and animated presentations for free. PowToon is a free tool that allows you to develop cool animated clips and animated presentations for your website, office meeting, sales pitch, nonprofit fundraiser, product launch, video resume, or anything else you could use an animated explainer video. PowToon’s animation templates help you create animated presentations and animated explainer videos from scratch. Anyone can produce awesome animations quickly with PowToon, without the cost or hassle other professional animation services require.
#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
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.
นอกจากการดูบทความนี้แล้ว คุณยังสามารถดูข้อมูลที่เป็นประโยชน์อื่นๆ อีกมากมายที่เราให้ไว้ที่นี่: ดูวิธีอื่นๆMusic of Turkey
ขอบคุณที่รับชมกระทู้ครับ wiener filter
