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

wiener filter: นี่คือโพสต์ที่เกี่ยวข้องกับหัวข้อนี้

# Author: Jake VanderPlas
#   The figure produced by this code is published in the textbook
#   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
#   To report a bug or issue, use the following forum:
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))
bottom=0.1, top=0.95,
left=0.12, right=0.95)

# First plot: noisy signal
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.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
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()


เนื้อหา

## DSP Lecture 20: The Wiener filter

ECSE4530 Digital Signal Processing
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
0:45:55 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

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## #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

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

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