I'm trying to calculate Frequency Modulation (radio context) for a given audio file (12 seconds), I managed to do it on a sine wave with the following formula:
fm = np.sin(TWO_PI * (fc + b * data) * t)
Where fc is the Carrier Frequency, b is the Modulation index, data is the audio file and t is the time vector.
But I can't seem to get it to work on the audio file,
this is what I have so far:
As you can see, you can't really understand when the frequency changes, I can zoom in but that's not really reliable and confusing I would be happy to hear other ways.
Here is my full code:
import scipy.io.wavfile
import matplotlib.pyplot as plt
import numpy as np
def generateSignalFM(t,data):
TWO_PI = 2 * np.pi
fc = 10000
b = 5
fm = np.sin(TWO_PI * (fc + b * np.array(data)) * t) # calculaying frequency modulation
fig, axs = plt.subplots(nrows=2, ncols=1)
fig.tight_layout()
axs[1].plot(t,fm)
axs[1].set_xlabel("Time(s)")
axs[1].set_ylabel("Amplitude")
axs[1].set_title("Modulated Signal (FM)")
axs[0].plot(t,data)
axs[0].set_xlabel("Time(s)")
axs[0].set_ylabel("Amplitude")
axs[0].set_title("Original Signal")
plt.show()
samplerate, data = scipy.io.wavfile.read("musicSample.wav")
sample_for = 12
start_time = 30*samplerate # start from 30 seconds
end_time = start_time + (samplerate * sample_for) # sample for 1 second
split_data= data[start_time:end_time]
time = np.arange(0,sample_for,1/samplerate) #sample 1 second
You can see your signal's PSD after modulation by using "welch" algorithm. You can do it by scipy.signal.welch and something like this will be shown:
This is the example for fc = 100 and sampleRate=1000
To see this, you should use the following context in your code:
import scipy.signal as ss
FM = ss.welch(fm, fs=sampleRate, nperseg=2048, noverlap=1024, nfft=2048)
axs[0].plot(FM[0],FM[1])
Related
I need to process a periodic signal and obtain its frequency.
This can be easily done with scipy.fft and it works fine.
However, I have a particular signal that is not strictly periodic. The period changes slightly but randomly.
Applying the fft to this signal is quite hard. Many peaks are obtained and I cannot extrapolate only the range of frequencies that are near the (1/period) I am interested in.
How can I do this?
This is a simple code snippet of what I am doing:
df = pd.read_csv('data.txt', header=None)
x = np.asarray(df.iloc[:, 0])
y = np.asarray(df.iloc[:, 1])
yf = fft(y)
xf = fftfreq(len(y))
plt.plot(xf, abs(yf))
You can find an example of such signal at the following GitHub repository, inside the README file: https://github.com/crazydecibel/Stack-Overflow-question
What about taking the weighted average of frequency of top energy bins?
import numpy as np
import matplotlib.pyplot as plt
your_data = '15.042,...' # your github data
t, y = np.array([list(map(float, row.split(','))) for row in your_data.split()]).T
# here is the solution in terms of t and y.
Y = np.fft.fftshift(np.fft.fft(y))
Ts = (t[-1] - t[0]) / (len(t) + 1) # sampling period
Fs = 1 / Ts # sampling frequency
f = np.fft.fftshift(np.fft.fftfreq(len(y))) * Fs
# get top 5%
top = np.argsort(abs(Y))[-10:]
plt.subplot(211)
plt.stem(f, abs(Y), 'o')
plt.stem(f[top], abs(Y[top]), '+r')
plt.xlim(-0.05 * Fs, 0.05 * Fs)
fc = np.sum(abs(f[top]*Y[top]**2))/np.sum(abs(Y[top])**2)
plt.subplot(212)
plt.plot(t, y)
plt.plot(t, np.sin(t*(2*np.pi*fc)))
i'm trying to get the frequency of a signal via fourier transform but it's not able to recognize it (sets the peak to f=0). Maybe something is wrong in my code (FULL reprudible code at the end of the page):
PF = fft.fft(Y[0,:])/Npoints #/Npoints to get the true amplitudes
ZF = fft.fft(Y[1,:])/Npoints
freq = fft.fftfreq(Npoints,deltaT)
PF = fft.fftshift(PF) #change of ordering so that the frequencies are increasing
ZF = fft.fftshift(ZF)
freq = fft.fftshift(freq)
plt.plot(freq, np.abs(PF))
plt.show()
plt.plot(T,Y[0,:])
plt.show()
where Npoints is the number of intervals (points) and deltaT is the time spacing of the intervals. You can see that the peak is at f=0
I show also a plot of Y[0,:] (my signal) over time where it's clear that the signal has a characteristic frequency
FULL REPRUDICIBLE CODE
import numpy as np
import matplotlib.pyplot as plt
#numerical integration
from scipy.integrate import solve_ivp
import scipy.fft as fft
r=0.5
g=0.4
e=0.6
H=0.6
m=0.15
#define a vector of K between 0 and 4 with 50 componets
K=np.arange(0.1,4,0.4)
tsteps=np.arange(7200,10000,5)
Npoints=len(tsteps)
deltaT=2800/Npoints #sample spacing
for k in K :
i=0
def RmAmodel(t,y):
return [r*y[0]*(1-y[0]/k)-g*y[0]/(y[0]+H)*y[1], e*g*y[0]/(y[1]+H)*y[1]-m*y[1]]
sol = solve_ivp(RmAmodel, [0,10000], [3,3], t_eval=tsteps) #t_eval specify the points where the solution is desired
T=sol.t
Y=sol.y
vk=[]
for i in range(Npoints):
vk.append(k)
XYZ=[vk,Y[0,:],Y[1,:]]
#check periodicity over P and Z with fourier transform
#try Fourier analysis just for the last value of K
PF = fft.fft(Y[0,:])/Npoints #/Npoints to get the true amplitudes
ZF = fft.fft(Y[1,:])/Npoints
freq = fft.fftfreq(Npoints,deltaT)
PF = fft.fftshift(PF) #change of ordering so that the frequencies are increasing
ZF = fft.fftshift(ZF)
freq = fft.fftshift(freq)
plt.plot(T,Y[0,:])
plt.show()
plt.plot(freq, np.abs(PF))
plt.show()
I can't pinpoint where the problem is. It looks like there is some problem in the fft code. Anyway, I have little time so I will just put a sample code I made before. You can use it as reference or copy-paste it. It should work.
import numpy as np
import matplotlib.pyplot as plt
from scipy.fft import fft, fftfreq
fs = 1000 #sampling frequency
T = 1/fs #sampling period
N = int((1 / T) + 1) #number of sample points for 1 second
t = np.linspace(0, 1, N) #time array
pi = np.pi
sig1 = 1 * np.sin(2*pi*10*t)
sig2 = 2 * np.sin(2*pi*30*t)
sig3 = 3 * np.sin(2*pi*50*t)
#generate signal
signal = sig1 + sig2 + sig3
#plot signal
plt.plot(t, signal)
plt.show()
signal_fft = fft(signal) #getting fft
f2 = np.abs(signal_fft / N) #full spectrum
f1 = f2[:N//2] #half spectrum
f1[1:] = 2*f1[1:] #actual amplitude
freq = fs * np.linspace(0,N/2,int(N/2)) / N #frequency array
#plot fft result
plt.plot(freq, f1)
plt.xlim(0,100)
plt.show()
I want to read data from the file and plot the fft of it.
I have used the scipy's fft function to plot the fft of the synthetically generated signal data however while I am trying to save the generated signal data and plot the fft I am getting the peaks as I was getting but the value of the amplitude and frequency is off as compared to the Original plotting.I found problem with the second fft function. Can anyone help me with the same.
import numpy as np
import pandas as pd
import scipy
from scipy.fftpack import fft,fftfreq
import matplotlib.pyplot as plt
import csv
#Function to plot the raw data
def raw_plot(signals,time):
'''Plot the raw values in the time domain '''
plt.figure(0)
plt.plot(time,signals)
plt.xlabel("Time(s)")
plt.ylabel("Amplitude(g)")
plt.show()
#Function to plot the fft of the data
def fft_signal(signal, sampling_frequency, timestart, timeend):
T = 1 / sampling_frequency
N = (timeend - timestart) * sampling_frequency
x = np.linspace(0.0, 1.0 / (2.0 * T), int(N / 2))
# print("Values of X are :",x)
# print(len(x))
yr2 = fft(signal)
y2 = 2 / N * np.abs(yr2[0:int(N / 2)])
# amp_spec = abs(fft(signal))/N
# freq = np.linspace(0,2,num=N)
plt.figure(2)
plt.plot(x, y2)
plt.xlabel("Frequency")
plt.ylabel("Amplitude")
plt.show()
def fftsignal2(data, sampling_freq = 100, timestep = 1 ):
N = len(data)
FS = 1000
T= 1/FS
timestep = timestep
yr2 = fft(data)
y2 = 2 / N * np.abs(yr2[0:int(N / 2)])
# f= np.arange(0,N)*FS/N
# f= np.linspace(0,1.0/T,N)
frq = np.fft.fftfreq(N,d=timestep)
# f= np.linspace(0.0,int(N/2)*sampling_freq)
frq= frq[0:len(frq)//2]
print("Frequencies Length :",len(frq))
print("DATA LENGTH :",len(y2))
plt.figure(3)
plt.plot(frq,y2)
plt.xlabel("Frequency")
plt.ylabel("Amplitude")
plt.show()
Mag1_Hz = 70
Mag1_AMP = 10
Mag4_AMP = 60
Mag4_Hz= 50
Mag2_Hz = 20
Mag2_AMP = 8
time_start = 0
time_end = 4
Sampling_frequency = 100
No_of_samples = (time_end-time_start) * Sampling_frequency
time = np.linspace(time_start,time_end,No_of_samples)
#Generate the signals values
data_signal = Mag1_AMP * np.sin(2* np.pi * Mag1_Hz * time ) + Mag2_AMP * np.cos(2* np.pi * Mag2_Hz * time)
raw_plot(signals=data_signal[:800],time=time[:800])
fft_signal(data_signal,sampling_frequency=Sampling_frequency,timestart=time_start,timeend=time_end)
# for (time, datavalues) in zip(time,data_signal):
# with open("data_signals_27.csv","a",newline="") as file:
# writefile = csv.writer(file)
# print("Time%f,Data %f"%(time,datavalues))
# print(time,datavalues)
# writefile.writerow([time,datavalues])
fftsignal2(data= data_signal, sampling_freq= Sampling_frequency,timestep=2)
The peaks are coming right in the fft_signal function no 1 while I am trying to construct the fftsignal2 to plot the fft of the data so the peaks which I am getting is correct but the magnitude and frequency is off.I don't understand why ? Can anyone help me with that.
I tried to filter some signal with fft.
The signal I am working on is quite complicated and im not really experienced in this topic.
That's why I created a simple sin wave 3Hz and tried to cut off the 3 Hz.
and so far, so good
import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import fftfreq, irfft, rfft
t = np.linspace(0, 2*np.pi, 1000, endpoint=True)
f = 3.0 # Frequency in Hz
A = 100.0 # Amplitude in Unit
s = A * np.sin(2*np.pi*f*t) # Signal
dt = t[1] - t[0] # Sample Time
W = fftfreq(s.size, d=dt)
f_signal = rfft(s)
cut_f_signal = f_signal.copy()
cut_f_signal[(np.abs(W)>3)] = 0 # cut signal above 3Hz
cs = irfft(cut_f_signal)
fig = plt.figure(figsize=(10,5))
plt.plot(s)
plt.plot(cs)
What i expected
What i got
I don't really know where the noise is coming from.
I think it is some basic stuff, but i dont get it.
Can someone explain to to me?
Edit
Just further information
Frequency
yf = fft(s)
N = s.size
xf = np.linspace(0, fa/2, N/2, endpoint=True)
fig, ax = plt.subplots()
ax.plot(xf,(2.0/N * np.abs(yf[:N//2])))
plt.xlabel('Frequency ($Hz$)')
plt.ylabel('Amplitude ($Unit$)')
plt.show()
You could change the way you create your signal and use a sample frequency:
fs = 1000
t = np.linspace(0, 1000 / fs, 1000, endpoint=False) # 1000 samples
f = 3.0 # Frequency in Hz
A = 100.0 # Amplitude in Unit
s = A * np.sin(2*np.pi*f*t) # Signal
dt = 1/fs
And here the whole code:
import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import fftfreq, irfft, rfft
fs = 1000
t = np.linspace(0, 1000 / fs, 1000, endpoint=False)
f = 3.0 # Frequency in Hz
A = 100.0 # Amplitude in Unit
s = A * np.sin(2*np.pi*f*t) # Signal
dt = 1/fs
W = fftfreq(s.size, d=dt)
f_signal = rfft(s)
cut_f_signal = f_signal.copy()
cut_f_signal[(np.abs(W)>3)] = 0 # cut signal above 3Hz
cs = irfft(cut_f_signal)
fig = plt.figure(figsize=(10,5))
plt.plot(s)
plt.plot(cs)
And with f = 3.0 Hz and (np.abs(W) >= 3):
And with f = 1.0 Hz:
Just some additional information about why A. As solution works better than yours:
A. A's model doesn't include any non-integer frequencies in its Solution and after filtering out the higher frequencies the result looks like:
1.8691714842589136e-12 * exp(2*pi*n*t*0.0)
1.033507502555532e-12 * exp(2*pi*n*t*1.0)
2.439774536202658e-12 * exp(2*pi*n*t*2.0)
-8.346741339115191e-13 * exp(2*pi*n*t*3.0)
-5.817427588021649e-15 * exp(2*pi*n*t*-3.0)
4.476938066992472e-14 * exp(2*pi*n*t*-2.0)
-3.8680170177940454e-13 * exp(2*pi*n*t*-1.0)
while your solution includes components like:
...
177.05936105690256 * exp(2*pi*n*t*1.5899578814880346)
339.28717376420747 * exp(2*pi*n*t*1.7489536696368382)
219.76658524130005 * exp(2*pi*n*t*1.9079494577856417)
352.1094590251063 * exp(2*pi*n*t*2.0669452459344453)
267.23939871205346 * exp(2*pi*n*t*2.2259410340832484)
368.3230130593005 * exp(2*pi*n*t*2.384936822232052)
321.0888818355804 * exp(2*pi*n*t*2.5439326103808555)
...
Please refer to this question regarding possible side effects of zeroing FFT bins out.
I'm trying to understand how fft in python works (or in general).
When I have a signal that is recorded for a few seconds I can only display one second of that FFT.
Is there a way to take all of the data and averaged this out?
I did this before in LabView.
Can any one help?
Here is an example code that I'm using.
from numpy import linspace, sin, pi, log10, average, arange
from matplotlib.pyplot import plot, show, figure
from numpy.fft import fft, fftfreq
N = 1000 * 60 * 4
dt = 1 / 1000
x = linspace(0, N*dt, N)
freq = linspace(10, 200, N)
sinsweep = sin(x*freq)
mavg = [average(sinsweep[i*60:(i+1)*60]) for i in range(int(N/60))]
plot(freq, sinsweep, '.')
plot(linspace(10, 200, int(N/60)), mavg, '.')
f = figure()
t = arange(60)
sp = fft(mavg, n=60)
freq = fftfreq(t.shape[-1])
plot(sp.imag)
show()
I give some modification to your code, to obtain a beautiful spectrum. First I increase the number of points to verify Shannon criterion. And some tricks to
improve speed.
from numpy import linspace, sin, pi, log10, average, arange
from matplotlib.pyplot import plot, show, figure
from numpy.fft import fft, fftfreq
close()
N = 10000 * 60 * 4
dt = 1 / 10000
t = arange(0, N*dt, dt)
freq = linspace(10, 200, N)
sinsweep = sin(t*freq)
mavg = sinsweep.reshape(-1,60).mean(1)
tm=t[::60]
figure('signal')
plot(tm, mavg)
sp = fft(mavg)
freq = fftfreq(tm.size,dt*60)
valid=freq>0
figure('spectrum')
plot(freq[valid],abs(sp[valid]))
show()
for
Is it what you expected ?