I am trying to plot a fourier transform of a sign wave based on the scipy documentation
import numpy as np
import matplotlib.pyplot as plt
import scipy.fft
def sinWav(amp, freq, time, phase=0):
return amp * np.sin(2 * np.pi * (freq * time - phase))
def plotFFT(f, speriod, time):
"""Plots a fast fourier transform
Args:
f (np.arr): A signal wave
speriod (int): Number of samples per second
time ([type]): total seconds in wave
"""
N = speriod * time
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N*T, N, endpoint=False)
yf = scipy.fft.fft(f)
xf = scipy.fft.fftfreq(N, T)[:N//2]
plt.plot(xf, 2.0/N * np.abs(yf[0:N//2]))
plt.grid()
plt.xlim([1,3])
plt.show()
speriod = 1000
time = {
0: np.arange(0, 4, 1/speriod),
1: np.arange(4, 8, 1/speriod),
2: np.arange(8, 12, 1/speriod)
}
signal = np.concatenate([
sinWav(amp=0.25, freq=2, time=time[0]),
sinWav(amp=1, freq=2, time=time[1]),
sinWav(amp=0.5, freq=2, time=time[2])
]) # generate signal
plotFFT(signal, speriod, 12)
Desired output
I want to be getting a fourier transform graph which looks like this
Current output
But instead it looks like this
Extra
This is the sin wave I am working with
import numpy as np
import matplotlib.pyplot as plt
import scipy.fft
def sinWav(amp, freq, time, phase=0):
return amp * np.sin(2 * np.pi * (freq * time - phase))
def plotFFT(f, speriod, time):
"""Plots a fast fourier transform
Args:
f (np.arr): A signal wave
speriod (int): Number of samples per second
time ([type]): total seconds in wave
"""
N = speriod * time
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N*T, N, endpoint=False)
yf = scipy.fft.fft(f)
xf = scipy.fft.fftfreq(N, T)[:N//2]
amplitudes = 1/speriod* np.abs(yf[:N//2])
plt.plot(xf, amplitudes)
plt.grid()
plt.xlim([1,3])
plt.show()
speriod = 800
time = {
0: np.arange(0, 4, 1/speriod),
1: np.arange(4, 8, 1/speriod),
2: np.arange(8, 12, 1/speriod)
}
signal = np.concatenate([
sinWav(amp=0.25, freq=2, time=time[0]),
sinWav(amp=1, freq=2, time=time[1]),
sinWav(amp=0.5, freq=2, time=time[2])
]) # generate signal
plotFFT(signal, speriod, 12)
You should have what you want. Your amplitudes were not properly computed, as your resolution and speriod were inconsistent.
Longer data acquisition:
import numpy as np
import matplotlib.pyplot as plt
import scipy.fft
def sinWav(amp, freq, time, phase=0):
return amp * np.sin(2 * np.pi * (freq * time - phase))
def plotFFT(f, speriod, time):
"""Plots a fast fourier transform
Args:
f (np.arr): A signal wave
speriod (int): Number of samples per second
time ([type]): total seconds in wave
"""
N = speriod * time
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N*T, N, endpoint=False)
yf = scipy.fft.fft(f)
xf = scipy.fft.fftfreq(N, T)[:N//2]
amplitudes = 1/(speriod*4)* np.abs(yf[:N//2])
plt.plot(xf, amplitudes)
plt.grid()
plt.xlim([1,3])
plt.show()
speriod = 800
time = {
0: np.arange(0, 4*4, 1/speriod),
1: np.arange(4*4, 8*4, 1/speriod),
2: np.arange(8*4, 12*4, 1/speriod)
}
signal = np.concatenate([
sinWav(amp=0.25, freq=2, time=time[0]),
sinWav(amp=1, freq=2, time=time[1]),
sinWav(amp=0.5, freq=2, time=time[2])
]) # generate signal
plotFFT(signal, speriod, 48)
You can also interactively plot this. You may need to install the pip install scikit-dsp-comm
# !pip install scikit-dsp-comm
# Make an interactive version of the above
from ipywidgets import interact, interactive
import numpy as np
import matplotlib.pyplot as plt
from scipy import fftpack
plt.rcParams['figure.figsize'] = [10, 8]
font = {'weight' : 'bold',
'size' : 14}
plt.rc('font', **font)
def pulse_plot(fm = 1000, Fs = 2010):
tlen = 1.0 # length in seconds
# generate time axis
tt = np.arange(np.round(tlen*Fs))/float(Fs)
# generate sine
xt = np.sin(2*np.pi*fm*tt)
plt.subplot(211)
plt.plot(tt[:500], xt[:500], '-b')
plt.plot(tt[:500], xt[:500], 'or', label='xt values')
plt.ylabel('$x(t)$')
plt.xlabel('t [sec]')
strt2 = 'Sinusoidal Waveform $x(t)$'
strt2 = strt2 + ', $f_m={}$ Hz, $F_s={}$ Hz'.format(fm, Fs)
plt.title(strt2)
plt.legend()
plt.grid()
X = fftpack.fft(xt)
freqs = fftpack.fftfreq(len(xt)) * Fs
plt.subplot(212)
N = xt.size
# DFT
X = np.fft.fft(xt)
X_db = 20*np.log10(2*np.abs(X)/N)
#f = np.fft.fftfreq(N, 1/Fs)
f = np.arange(0, N)*Fs/N
plt.plot(f, X_db, 'b')
plt.xlabel('Frequency in Hertz [Hz]')
plt.ylabel('Frequency Domain\n (Spectrum) Magnitude')
plt.grid()
plt.tight_layout()
interactive_plot = interactive(pulse_plot,fm = (1000,20000,1000), Fs = (1000,40000,10));
output = interactive_plot.children[-1]
# output.layout.height = '350px'
interactive_plot
Related
I am using FFT do find the frequencies of a signal. I am only interested in a certain range of frequencies, between 1 and 4 Hz.
I have this code to compute frequencies:
from scipy.fft import rfft, rfftfreq, irfft
plt.plot(d)
plt.show()
N = len(d)
yf = rfft(d)
xf = rfftfreq(N, 1 / sample_rate) # 29
plt.plot(xf, np.abs(yf))
plt.show()
Which results in :
How do I modify my code so that xf and yf only correspond to frequencies in my desired range of 1-4 Hz, instead of the 0-15 seen in the plot?
You can use xlim feature of matplotlib to modify x axis.
Here is the example code that you can refer.
from scipy.fft import fft, fftfreq
import numpy as np
# Number of sample points
N = 600
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N*T, N, endpoint=False)
y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)
yf = fft(y)
xf = fftfreq(N, T)[:N//2]
import matplotlib.pyplot as plt
plt.plot(xf, 2.0/N * np.abs(yf[0:N//2]),'b')
plt.plot()
plt.grid()
plt.show()
plt.plot(xf, 2.0/N * np.abs(yf[0:N//2]),'b')
plt.xlim(0,100) # you need this
plt.grid()
plt.show()
I have code that looks like this:
import matplotlib.pyplot as plt
import numpy as np
from nfft import nfft
# number of sample points
N = 400
# Simulated non-uniform data
x = np.linspace(0.0, 1 / 2, N) + np.random.random((N)) * 0.001
y = np.sin(50.0 * 2.0 * np.pi * x) + 0.5 * np.sin(80.0 * 2.0 * np.pi * x)
yf = np.abs(nfft(x, y))
fig, axs = plt.subplots(1)
fig_f, axs_f = plt.subplots(1)
axs.plot(x, y, '.', color='red')
axs_f.plot(x, yf, color='red')
How do I convert the values on the second graph to represent frequency?
The use of the nfft module is not required, answers using pynfft or scipy will be greatly appreciated.
See also:
How do I obtain the frequencies of each value in an FFT?
The following seems to work. Notice the line inserted before graphing the Fourier transform, to generate the frequencies, and that we graph N/2 of the data.
import matplotlib.pyplot as plt
import numpy as np
from nfft import nfft
# number of sample points
N = 400
# Simulated non-uniform data
x = np.linspace(0.0,0.5-0.02, N) + np.random.random((N)) * 0.001
print(x)
print( 'random' )
print( np.random.random((N)) * 0.001 )
y = np.sin(50.0 * 2.0 * np.pi * x) + 0.5 * np.sin(80.0 * 2.0 * np.pi * x)
yf = np.abs(nfft(x, y))
fig, axs = plt.subplots(1)
fig_f, axs_f = plt.subplots(1)
axs.plot(x, y, '.', color='red')
xf = np.fft.fftfreq(N,1./N)
axs_f.plot(xf[:int(N/2)], yf[:int(N/2)], color='red')
plt.show()
Output:
I can plot a spectrogram (in a Jupyter notebook) thus:
fs = 48000
noverlap = (fftFrameSamps*3) // 4
spectrum2d, freqs, timePoints, image = \
plt.specgram( wav, NFFT=fftFrameSamps, Fs=fs, noverlap=noverlap )
plt.show()
However, I am only interested in the 15-20 kHz range.
How can I plot only this range?
I can see that the function returns image, so maybe I could convert the image to a matrix and take an appropriate slice from the matrix...?
I can see that the function accepts vmin and vmax but these appear to be undocumented and playing with them doesn't yield a valid result.
You can modify the limits of the axis as you would normally with set_ylim() and set_xlim(). In this case
plt.ylim([15000, 20000])
should restrict your plot to the 15-20 kHz range. For a complete example drawing from the Spectrogram Demo:
import matplotlib.pyplot as plt
import numpy as np
np.random.seed(19680801)
dt = 0.0005
t = np.arange(0.0, 20.0, dt)
s1 = np.sin(2 * np.pi * 100 * t)
s2 = 2 * np.sin(2 * np.pi * 400 * t)
# create a transient "chirp"
s2[t <= 10] = s2[12 <= t] = 0
# add some noise into the mix
nse = 0.01 * np.random.random(size=len(t))
x = s1 + s2 + nse # the signal
NFFT = 1024 # the length of the windowing segments
Fs = int(1.0 / dt) # the sampling frequency
fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(14, 7))
ax1.specgram(x, NFFT=NFFT, Fs=Fs, noverlap=900)
ax2.specgram(x, NFFT=NFFT, Fs=Fs, noverlap=900)
ax2.set_ylim([50, 500])
plt.show()
Supposing that I have following signal:
y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(100.0 * 2.0*np.pi*x) + 0.2*np.sin(200 * 2.0*np.pi*x)
how can I filter out in example 100Hz using Band-stop filter in Python? In this signal there are peaks at 50Hz, 100Hz and 200Hz. It would be helpful it it could be visualized using FFT in order to confirm that this frequency has been filtered correctly.
Basing on answers from:
Plotting a Fast Fourier Transform in Python
and:
Bandstop filter
I wrote following code:
import pandas as pd
import time
from scipy.signal import lfilter
import matplotlib.pyplot as plt
import scipy
import numpy as np
# In the below lines data are being filtered using Bandstop filter
print("Filtering using Bandstop filter...")
start_filtering_bandstop = time.time()
# Define filtering parameters:
order = 2
fs = 800.0 # sample rate, Hz
lowcut = 90 # desired cutoff frequency of the filter, Hz
highcut = 110
# Define plots
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 7))
# Number of samplepoints
N = 600
# sample spacing
T = 1.0 / fs
x = np.linspace(0.0, N*T, N)
y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(100.0 * 2.0*np.pi*x) + 0.2*np.sin(200 * 2.0*np.pi*x) # You can put there pandas series too...
ax1.plot(x, y, label='Signal before filtering')
print("Calculating FFT, please wait...")
yf = scipy.fftpack.fft(y)
xf = np.linspace(0.0, 1.0/(2.0*T), N/2)
ax1.set_title('Signal')
ax2.set_title('FFT')
ax2.plot(xf, 2.0/N * np.abs(yf[:N//2]), label='Before filtering')
def butter_bandstop_filter(data, lowcut, highcut, fs, order):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
b, a = scipy.signal.butter(order, [low, high], btype='bandstop')#, fs, )
y = lfilter(b, a, data)
return y
print("Filtering signal, please wait...")
signal_filtered = butter_bandstop_filter(y, lowcut, highcut, fs, order)
ax1.plot(x, signal_filtered, label='Signal after filtering')
ax1.set(xlabel='X', ylabel='Signal values')
ax1.legend() # Don't forget to show the legend
ax1.set_xlim([0,0.8])
ax1.set_ylim([-1.5,2])
# Number of samplepoints
N = len(signal_filtered)
# sample spacing
T = 1.0 / fs
x = np.linspace(0.0, N*T, N)
y = signal_filtered
print("Calculating FFT after filtering, please wait...")
yf = scipy.fftpack.fft(y)
xf = np.linspace(0.0, 1.0/(2.0*T), N/2)
# Plot axes...
ax2.plot(xf, 2.0/N * np.abs(yf[:N//2]), label='After filtering')
ax2.set(xlabel='Frequency [Hz]', ylabel='Magnitude')
ax2.legend() # Don't forget to show the legend
plt.savefig('FFT_after_bandstop_filtering.png', bbox_inches='tight', dpi=300) # If dpi isn't set, the script execution will be faster
# Alternatively for immediate showing of plot:
# plt.show()
plt.close()
end_filtering_bandstop = time.time()
print("Data filtered using Bandstop filter in",round(end_filtering_bandstop - start_filtering_bandstop,2),"seconds!")
and obtained following plots:
As we can see, the 100Hz has been filtered out using band-stop filter.
Why magnitude for frequency 50 Hz decreased from 1 to 0.7 after Fast Fourier Transform?
I want to remove one frequency (one peak) from signal and plot my function without it. After fft I found frequency and amplitude and I am not sure what I need to do now. For example I want to remove my highest peak (marked with red dot on plot).
import numpy as np
import matplotlib.pyplot as plt
# create data
N = 4097
T = 100.0
t = np.linspace(-T/2,T/2,N)
f = np.sin(50.0 * 2.0*np.pi*t) + 0.5*np.sin(80.0 * 2.0*np.pi*t)
#plot function
plt.plot(t,f,'r')
plt.show()
# perform FT and multiply by dt
dt = t[1]-t[0]
ft = np.fft.fft(f) * dt
freq = np.fft.fftfreq(N, dt)
freq = freq[:N/2+1]
amplitude = np.abs(ft[:N/2+1])
# plot results
plt.plot(freq, amplitude,'o-')
plt.legend(('numpy fft * dt'), loc='upper right')
plt.xlabel('f')
plt.ylabel('amplitude')
#plt.xlim([0, 1.4])
plt.plot(freq[np.argmax(amplitude)], max(amplitude), 'ro')
print "Amplitude: " + str(max(amplitude)) + " Frequency: " + str(freq[np.argmax(amplitude)])
plt.show()
One option is to transform the signal to the frequency domain then remove the selected frequency.
import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import rfft, irfft, fftfreq, fft
# Number of samplepoints
N = 500
# sample spacing
T = 0.1
x = np.linspace(0.0, (N-1)*T, N)
# x = np.arange(0.0, N*T, T) # alternate way to define x
y = 5*np.sin(x) + np.cos(2*np.pi*x)
yf = fft(y)
xf = np.linspace(0.0, 1.0/(2.0*T), N//2)
#fft end
f_signal = rfft(y)
W = fftfreq(y.size, d=x[1]-x[0])
cut_f_signal = f_signal.copy()
cut_f_signal[(W>0.6)] = 0 # filter all frequencies above 0.6
cut_signal = irfft(cut_f_signal)
# plot results
f, axarr = plt.subplots(1, 3, figsize=(9, 3))
axarr[0].plot(x, y)
axarr[0].plot(x,5*np.sin(x),'g')
axarr[1].plot(xf, 2.0/N * np.abs(yf[:N//2]))
axarr[1].legend(('numpy fft * dt'), loc='upper right')
axarr[1].set_xlabel("f")
axarr[1].set_ylabel("amplitude")
axarr[2].plot(x,cut_signal)
axarr[2].plot(x,5*np.sin(x),'g')
plt.show()
You can design a bandstop filter:
from scipy import signal
wc = freq[np.argmax(amplitude)] / (0.5 / dt)
wp = [wc * 0.9, wc / 0.9]
ws = [wc * 0.95, wc / 0.95]
b, a = signal.iirdesign(wp, ws, 1, 40)
f = signal.filtfilt(b, a, f)