Python 音频 fftpack：过滤噪声信号并绘制图表？
Python Audio fftpack: Filter noise signal and graph it?
所以我按照教程创建信号并使用 fftpack 过滤噪声。
问题 1：我试图在图表上绘制过滤后和未过滤的信号噪声，以便我可以并排查看它们。
我收到这个错误：
Warning (from warnings module): File
"C:\Python39\lib\site-packages\numpy\core_asarray.py", line 83
return array(a, dtype, copy=False, order=order) ComplexWarning: Casting complex values to real discards the imaginary part
我认为这是导致错误的原因：
y = sig
x = time_vec
问题 2：我不确定如何在同一个图中绘制两个图形 window?
import numpy as np
from scipy import fftpack
time_step = 0.05
# Return evenly spaced time vector (0.5) between [0, 10]
time_vec = np.arange(0, 10, time_step)
print(time_vec)
period = 5
# create a signal and add some noise:
# input angle 2pi * time vector) in radians and return value ranging from -1 to +1 -- essentially mimicking a sigla wave that is goes in cycles + adding some noise to this bitch
# numpy.random.randn() - return samples from the standard normal distribution of mean 0 and variance 1
sig = (np.sin(2*np.pi*time_vec)/period) + 0.25 * np.random.randn(time_vec.size)
# Return discrete Fourier transform of real or complex sequence
sig_fft = fftpack.fft(sig) # tranform the sin function
# Get Amplitude ?
Amplitude = np.abs(sig_fft) # np.abs() - calculate absolute value from a complex number a + ib
Power = Amplitude**2 # create a power spectrum by power of 2 of amplitude
# Get the (angle) base spectrrum of these transform values i.e. sig_fft
Angle = np.angle(sig_fft) # Return the angle of the complex argument
# For each Amplitude and Power (of each element in the array?) - there is will be a corresponding difference in xxx
# This is will return the sampling frequecy or corresponding frequency of each of the (magnitude) i.e. Power
sample_freq = fftpack.fftfreq(sig.size, d=time_step)
print(Amplitude)
print(sample_freq)
# Because we would like to remove the noise we are concerned with peak freqence that contains the peak amplitude
Amp_Freq = np.array([Amplitude, sample_freq])
# Now we try to find the peak amplitude - so we try to extract
Amp_position = Amp_Freq[0,:].argmax()
peak_freq = Amp_Freq[1, Amp_position] # find the positions of max value position (Amplitude)
# print the position of max Amplitude
print("--", Amp_position)
# print the frequecies of those max amplitude
print(peak_freq)
high_freq_fft = sig_fft.copy()
# assign all the value the corresponding frequecies larger than the peak frequence - assign em 0 - cancel!! in the array (elements) (?)
high_freq_fft[np.abs(sample_freq) > peak_freq] = 0
print("yes:", high_freq_fft)
# Return discrete inverse Fourier transform of real or complex sequence
filtered_sig = fftpack.ifft(high_freq_fft)
print("filtered noise: ", filtered_sig)
# Using Fast Fourier Transform and inverse Fast Fourier Transform we can remove the noise from the frequency domain (that would be otherwise impossible to do in Time Domain) - done.
# Plotting the signal with noise (?) and filtered
import matplotlib.pyplot as plt
y = filtered_sig
x = time_vec
plt.plot(x, y)
plt.xlabel('Time')
plt.ylabel('Filtered Amplitude')
plt.show()
y = sig
x = time_vec
plt.plot(x, y)
plt.xlabel('Time')
plt.ylabel('Unfiltered Amplitude')
plt.show()
问题 1： 在绘制 filtered_sig 时出现在 matplotlib 中，因为它包含较小的虚部。您可以通过 real_if_close.
将它们砍掉
问题2：只是不要在第一个和第二个情节之间使用show
这是一张带有图例的图表中完整的工作绘图部分：
import matplotlib.pyplot as plt
x = time_vec
y = np.real_if_close(filtered_sig)
plt.plot(x, y, label='Filtered')
plt.xlabel('Time')
plt.ylabel('Amplitude')
y = sig
plt.plot(x, y, label='Unfiltered')
plt.legend()
plt.show()
所以我按照教程创建信号并使用 fftpack 过滤噪声。
问题 1：我试图在图表上绘制过滤后和未过滤的信号噪声，以便我可以并排查看它们。
我收到这个错误：
Warning (from warnings module): File "C:\Python39\lib\site-packages\numpy\core_asarray.py", line 83 return array(a, dtype, copy=False, order=order) ComplexWarning: Casting complex values to real discards the imaginary part
我认为这是导致错误的原因：
y = sig
x = time_vec
问题 2：我不确定如何在同一个图中绘制两个图形 window?
import numpy as np
from scipy import fftpack
time_step = 0.05
# Return evenly spaced time vector (0.5) between [0, 10]
time_vec = np.arange(0, 10, time_step)
print(time_vec)
period = 5
# create a signal and add some noise:
# input angle 2pi * time vector) in radians and return value ranging from -1 to +1 -- essentially mimicking a sigla wave that is goes in cycles + adding some noise to this bitch
# numpy.random.randn() - return samples from the standard normal distribution of mean 0 and variance 1
sig = (np.sin(2*np.pi*time_vec)/period) + 0.25 * np.random.randn(time_vec.size)
# Return discrete Fourier transform of real or complex sequence
sig_fft = fftpack.fft(sig) # tranform the sin function
# Get Amplitude ?
Amplitude = np.abs(sig_fft) # np.abs() - calculate absolute value from a complex number a + ib
Power = Amplitude**2 # create a power spectrum by power of 2 of amplitude
# Get the (angle) base spectrrum of these transform values i.e. sig_fft
Angle = np.angle(sig_fft) # Return the angle of the complex argument
# For each Amplitude and Power (of each element in the array?) - there is will be a corresponding difference in xxx
# This is will return the sampling frequecy or corresponding frequency of each of the (magnitude) i.e. Power
sample_freq = fftpack.fftfreq(sig.size, d=time_step)
print(Amplitude)
print(sample_freq)
# Because we would like to remove the noise we are concerned with peak freqence that contains the peak amplitude
Amp_Freq = np.array([Amplitude, sample_freq])
# Now we try to find the peak amplitude - so we try to extract
Amp_position = Amp_Freq[0,:].argmax()
peak_freq = Amp_Freq[1, Amp_position] # find the positions of max value position (Amplitude)
# print the position of max Amplitude
print("--", Amp_position)
# print the frequecies of those max amplitude
print(peak_freq)
high_freq_fft = sig_fft.copy()
# assign all the value the corresponding frequecies larger than the peak frequence - assign em 0 - cancel!! in the array (elements) (?)
high_freq_fft[np.abs(sample_freq) > peak_freq] = 0
print("yes:", high_freq_fft)
# Return discrete inverse Fourier transform of real or complex sequence
filtered_sig = fftpack.ifft(high_freq_fft)
print("filtered noise: ", filtered_sig)
# Using Fast Fourier Transform and inverse Fast Fourier Transform we can remove the noise from the frequency domain (that would be otherwise impossible to do in Time Domain) - done.
# Plotting the signal with noise (?) and filtered
import matplotlib.pyplot as plt
y = filtered_sig
x = time_vec
plt.plot(x, y)
plt.xlabel('Time')
plt.ylabel('Filtered Amplitude')
plt.show()
y = sig
x = time_vec
plt.plot(x, y)
plt.xlabel('Time')
plt.ylabel('Unfiltered Amplitude')
plt.show()
问题 1： 在绘制 filtered_sig 时出现在 matplotlib 中，因为它包含较小的虚部。您可以通过 real_if_close.
问题2：只是不要在第一个和第二个情节之间使用show
这是一张带有图例的图表中完整的工作绘图部分：
import matplotlib.pyplot as plt
x = time_vec
y = np.real_if_close(filtered_sig)
plt.plot(x, y, label='Filtered')
plt.xlabel('Time')
plt.ylabel('Amplitude')
y = sig
plt.plot(x, y, label='Unfiltered')
plt.legend()
plt.show()