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How do I find, plot, and output the peaks of a live plotted Fast Fourier Transform (FFT) in Python?

I am working with the pyaudio and matplotlib packages for the first time and I am attempting to plot live audio data from microphone input, transform it to frequency domain information, and then output peaks with an input distance. This project is a modification of the three-part guide to build a spectrum analyzer found here.
Currently the code is formatted in a class as I have alternative methods that I am applying to the audio but I am only posting the class with the relevant methods as they don't make reference to each and are self-contained. Another quirk of the program is that it calls upon a local file though it only uses input from the user microphone; this is a leftover from the original functionality of plotting a sound file's intensity while it played and is no longer integral to the code.
import pyaudio
import wave
import struct
import pandas as pd
from scipy.fftpack import fft
from scipy.signal import find_peaks
import matplotlib.pyplot as plt
import numpy as np
class Wave:
def __init__(self, file) -> None:
self.CHUNK = 1024 * 4
self.obj = wave.open(file, "r")
self.callback_output = []
self.data = self.obj.readframes(self.CHUNK)
self.rate = 44100
# Initiate an instance of PyAudio
self.p = pyaudio.PyAudio()
# Open a stream with the file specifications
self.stream = self.p.open(format = pyaudio.paInt16,
channels = self.obj.getnchannels(),
rate = self.rate,
output = True,
input = True,
frames_per_buffer = self.CHUNK)
def fft_plot(self, distance: float):
x_fft = np.linspace(0, self.rate, self.CHUNK)
fig, ax = plt.subplots()
line_fft, = ax.semilogx(x_fft, np.random.rand(self.CHUNK), "-", lw = 2)
# Bind plot window sizes
ax.set_xlim(20, self.rate / 2)
plot_data = self.stream.read(self.CHUNK)
self.data_int = pd.DataFrame(struct.unpack(\
str(self.CHUNK * 2) + 'h', plot_data)).astype(dtype = "b")[::2]
y_fft = fft(self.data_int)
line_fft.set_ydata(np.abs(y_fft[0:self.CHUNK]) / (256 * self.CHUNK))
plt.show(block = False)
while True:
# Read incoming audio data
data = self.stream.read(self.CHUNK)
# Convert data to bits then to array
self.data_int = struct.unpack(str(4 * self.CHUNK) + 'B', data)
# Recompute FFT and update line
yf = fft(self.data_int)
line_data = np.abs(yf[0:self.CHUNK]) / (128 * self.CHUNK)
line_fft.set_ydata(line_data)
# Find all values above threshold
peaks, _ = find_peaks(line_data, distance = distance)
# Update the plot
plt.plot(peaks, line_data[peaks], "x")
fig.canvas.draw()
fig.canvas.flush_events()
# Exit program when plot window is closed
fig.canvas.mpl_connect('close_event', exit)
test_file = "C:/Users/Tam/Documents/VScode/Final Project/PrismGuitars.wav"
audio_test = Wave(test_file)
audio_test.fft_plot(2000)
The code does not throw any errors and runs fine with an okay framerate and only terminates when the plot window is closed, all of which is good. The issue I'm encountering is with the determination and plotting of the peaks of line_data as when I run this code the output over time looks like this matplotlib graph instance.
It seems that the peaks (or peak) are being found but at a lower frequency than the x of line_data and as such are shifted comparatively. The other, more minor, issue is that since this is a live plot I would like to clear the previous instance of the peak marker so that it only shows the current instance and not all of the ones plotted prior.
I have attempted in prior fixes to use the line_fft in the peak detection but as it is cast to a Line2D format the peak detection algorithm isn't able to deal with the data type. I have also tried implementing a list comprehension as seen in this post but the time to cast to list is prohibitively slow and did not return any peak markers when I ran it.
EDIT: Following Jody's input the program now returns the proper values as I was only printing an index for the x-coordinate of the peak marker. Nevertheless I would still appreciate some insight as to whether it is possible to update per marker rather than having all the previous ones constantly displayed.
As for the marker updating I have attempted to clear the plot in the while loop both before and after drawing the markers (in different tests of course) but I only ever end up with a completely blank graph.
Please let me know if there is anything I should clarify and thank you for your time.

As Jody pointed out the peaks variable contains indexes for the detected peaks that then need to be retrieved from x_fft and line_data in order to match up with the displayed data.
First we create a scatter plot:
scat = ax.scatter([], [], c = "purple", marker = "x")
This data can then be stacked using a container variable in the while loop as such:
array_peaks = np.c_[x_fft[peaks], line_data[peaks]]
and update the data in the while loop with:
scat.set_offsets(array_peaks)

How can I smooth out noise from a bluetooth accelerometer dynamically?

I have a program that connects to a bluetooth accelerometer and reads that data to determine motion in real time and I'm trying to figure out how to smooth out the noise so I can better represent the motion. I found a scipy function for a butterworth filter (pardon my ignorance on filters) but it seems like it only works when you have the whole plot as it looks at the points before and after to smooth noise. How can I smooth out noise dynamically? Here's my code:
def animator():
global xyz
fig = plt.figure()
xyz_mot = fig.add_subplot(111, projection = "3d")
xyz_mot.set_title("Motion")
xyz_mot.set_xlim3d(-100, 100)
xyz_mot.set_ylim3d(-100, 100)
xyz_mot.set_zlim3d(-100, 100)
xyz = xyz_mot.scatter(0,0,0)
ani = FuncAnimation(fig, updateAni, frames=2, interval=50)
fig.show()
def updateAni(i):
t = float(time_data[-1] / 1000)**2
xmot[0] = .5 * acceleration_data[-1].x * t
ymot[0] = .5 * acceleration_data[-1].y * t
zmot[0] = .5 * acceleration_data[-1].z * t
xyz._offsets3d = (xmot, ymot, zmot)
#print("X Motion: " + str(xmot) + ", Y Motion: " + str(ymot))
#print(time_data[-1])
The accelerometer data and time data are being added to the arrays acceleration_data and time_data from another thread. Is there a matplotlib/some other library function to smooth noise? Any help is appreciated

Look at running data through an exponential averaging or moving average filter. The exponential average allows you to trade off averaging verse speed with alpha parameter. Filter the raw data from the accelerometer before adding to the output array.
The following snippet implements simple exponential avererager
avg = alpha * x + (1 - alpha) * x_prev
x_prev = x
buffer.append(avg)

Instead of adding the raw acceleration data to acceleration_data from your secondary thread, I'd filter the data there by using a buffer to constantly take the average of the last several measurements. Without your code for the thread, I can only give you some pseudo-code, but this should give you an idea of how it would work.:
import collections
def thread_func():
buf = collections.deque(maxlen=10) #take the average of up to the last 10 samples
while True:
accel = bluetooth_device.read()
buf.append(accel)
if buf: #may want to make sure the buffer isn't empty first to prevent devide by 0
acceleration_data.append(sum(buf)/len(buf))

FFT spectrogram in python

I have python 3.4.
I transmitted a 2MHz (for example) frequency and received the cavitation over the time (until I stopped the measurement).
I want to get a spectrogram (cavitation vs frequency) and more interesting is a spectrogram of cavitation over the time of the sub-harmonic (1MHz) frequency.
The data is saved in sdataA (=cavitation), and t (=measurement time)
I tried to save fft in FFTA
FFTA = np.array([])
FFTA = np.fft.fft(dataA)
FFTA = np.append(FFTA, dataA)
I got real and complex numbers
Then I took only half (from 0 to 1MHz) and save the real and complex data.
nA = int(len(FFTA)/2)
yAre = FFTA[range(nA)].real
yAim = FFTA[range(nA)].imag
I tried to get the frequencies by:
FFTAfreqs = np.fft.fftfreq(len(yAre))
But it is totally wrong (I printed the data by print (FFTAfreqs))
I also plotted the data and again it's wrong:
plt.plot(t, FFTA[range(n)].real, 'b-', t, FFTA[range(n)].imag, 'r--')
plt.legend(('real', 'imaginary'))
plt.show()
How can I output a spectrogram of cavitation over the time of the sub-harmonic (1MHz) frequency?
EDIT:
Data example:
see a sample of 'dataA' and 'time':
dataA = [6.08E-04,2.78E-04,3.64E-04,3.64E-04,4.37E-04,4.09E-04,4.49E-04,4.09E-04,3.52E-04,3.24E-04,3.92E-04,3.24E-04,2.67E-04,3.24E-04,2.95E-04,2.95E-04,4.94E-04,4.09E-04,3.64E-04,3.07E-04]
time = [0.00E+00,4.96E-07,9.92E-07,1.49E-06,1.98E-06,2.48E-06,2.98E-06,3.47E-06,3.97E-06,4.46E-06,4.96E-06,5.46E-06,5.95E-06,6.45E-06,6.94E-06,7.44E-06,7.94E-06,8.43E-06,8.93E-06,9.42E-06]
EDIT II:
From #Martin example I tried the following code, please let me know if I did it right.
In the case that dataA and Time are saved as h5 files (or the data that I posted already)
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
dfdata = pd.read_hdf("C:\\data_python\\DataA.h5")
dft = pd.read_hdf("C:\\data_python\\time.h5")
dft_cor = int((len(dft)-2)*4.96E-6) # calculating the measured time
fs = 2000000 #sampling frequency 2MHz
CHUNK = 10000
signal_time = dft_cor # seconds
def sine(freq,fs,secs):
data=dfdata
wave = np.sin(freq*2*np.pi*data)
return wave
a1 = sine(fs,fs,120)
a2 = sine(fs/2,fs,120)
signal = a1+a2
afft = np.abs(np.fft.fft(signal[0:CHUNK]))
freqs = np.linspace(0,fs,CHUNK)[0:int(fs/2)]
spectrogram_chunk = freqs/np.amax(freqs*1.0)
# Plot spectral analysis
plt.plot(freqs[0:1000000],afft[0:1000000]) # 0-1MHz
plt.show()
number_of_chunks = 1000
# Empty spectrogram
Spectrogram = np.zeros(shape = [CHUNK,number_of_chunks])
for i in range(number_of_chunks):
afft = np.abs(np.fft.fft(signal[i*CHUNK:(1+i)*CHUNK]))
freqs = np.linspace(0,fs,CHUNK)[0:int(fs/2)]
spectrogram_chunk = afft/np.amax(afft*1.0)
try:
Spectrogram[:,i]=spectrogram_chunk
except:
break
import cv2
Spectrogram = Spectrogram[0:1000000,:]
cv2.imshow('spectrogram',np.uint8(255*Spectrogram/np.amax(Spectrogram)))
cv2.waitKey()
cv2.destroyAllWindows()

It seems your problem is not in Python but in understanding what is Spectrogram.
Spectrogram is sequences of spectral analysis of a signal.
1) You need to cut your signal in CHUNKS.
2) Do spectral analysis of these CHUNKS and stick it together.
Example:
You have 1 second of audio recoding (44100 HZ sampling). That means the recording will have 1s * 44100 -> 44100 samples. You define CHUNK size = 1024 (for example).
For each chunk you will do FFT, and stick it together into 2D matrix (X axis - FFT of the CHUNK, Y axis - CHUNK number,). 44100 samples / CHUNK ~ 44 FFTs, each of the FFT covers 1024/44100~0.023 seconds of the signal
The bigger the CHUNK, the more accurate Spectrogram is, but less 'realtime'.
The smaller the CHUNK is, the less acurate is the Spectrogram, but you have more measurements as you measure frequencies 'more often'.
If you need 1MHZ - actually you cannot use anything higher than 1MHZ, you just take half of the resulting FFT array - and it doesnt matter which half, because 1MHZ is just the half of your sampling frequency, and the FFT is mirroring anything that is higher than 1/2 of sampling frequency.
About FFT, you dont want complex numbers. You want to do
FFT = np.abs(FFT) # Edit - I just noticed you use '.real', but I will keep it here
because you want real numbers.
Preparation for Spectrogram - example of Spectrogram
Audio Signal with 150HZ wave and 300HZ Wave
import numpy as np
import matplotlib.pyplot as plt
fs = 44100#sampling frequency
CHUNK = 10000
signal_time = 20 # seconds
def sine(freq,fs,secs):
data=np.arange(fs*secs)/(fs*1.0)
wave = np.sin(freq*2*np.pi*data)
return wave
a1 = sine(150,fs,120)
a2 = sine(300,fs,120)
signal = a1+a2
afft = np.abs(np.fft.fft(signal[0:CHUNK]))
freqs = np.linspace(0,fs,CHUNK)[0:int(fs/2)]
spectrogram_chunk = freqs/np.amax(freqs*1.0)
# Plot spectral analysis
plt.plot(freqs[0:250],afft[0:250])
plt.show()
number_of_chunks = 1000
# Empty spectrogram
Spectrogram = np.zeros(shape = [CHUNK,number_of_chunks])
for i in range(number_of_chunks):
afft = np.abs(np.fft.fft(signal[i*CHUNK:(1+i)*CHUNK]))
freqs = np.linspace(0,fs,CHUNK)[0:int(fs/2)]
#plt.plot(spectrogram_chunk[0:250],afft[0:250])
#plt.show()
spectrogram_chunk = afft/np.amax(afft*1.0)
#print(signal[i*CHUNK:(1+i)*CHUNK].shape)
try:
Spectrogram[:,i]=spectrogram_chunk
except:
break
import cv2
Spectrogram = Spectrogram[0:250,:]
cv2.imshow('spectrogram',np.uint8(255*Spectrogram/np.amax(Spectrogram)))
cv2.waitKey()
cv2.destroyAllWindows()
Spectral analysis of single CHUNK
Spectrogram

FFT of data received from PyAudio gives wrong frequency

My main task is to recognize a human humming from a microphone in real time. As the first step to recognizing signals in general, I have made a 5 seconds recording of a 440 Hz signal generated from an app on my phone and tried to detect the same frequency.
I used Audacity to plot and verify the spectrum from the same 440Hz wav file and I got this, which shows that 440Hz is indeed the dominant frequency :
(https://i.imgur.com/2UImEkR.png)
To do this with python, I use the PyAudio library and refer this blog. The code I have so far which I run with the wav file is this :
"""PyAudio Example: Play a WAVE file."""
import pyaudio
import wave
import sys
import struct
import numpy as np
import matplotlib.pyplot as plt
CHUNK = 1024
if len(sys.argv) < 2:
print("Plays a wave file.\n\nUsage: %s filename.wav" % sys.argv[0])
sys.exit(-1)
wf = wave.open(sys.argv[1], 'rb')
p = pyaudio.PyAudio()
stream = p.open(format=p.get_format_from_width(wf.getsampwidth()),
channels=wf.getnchannels(),
rate=wf.getframerate(),
output=True)
data = wf.readframes(CHUNK)
i = 0
while data != '':
i += 1
data_unpacked = struct.unpack('{n}h'.format(n= len(data)/2 ), data)
data_np = np.array(data_unpacked)
data_fft = np.fft.fft(data_np)
data_freq = np.abs(data_fft)/len(data_fft) # Dividing by length to normalize the amplitude as per https://www.mathworks.com/matlabcentral/answers/162846-amplitude-of-signal-after-fft-operation
print("Chunk: {} max_freq: {}".format(i,np.argmax(data_freq)))
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.plot(data_freq)
ax.set_xscale('log')
plt.show()
stream.write(data)
data = wf.readframes(CHUNK)
stream.stop_stream()
stream.close()
p.terminate()
In the output, I get that the max frequency is 10 for all the chunks and an example of one of the plots is :
(https://i.imgur.com/zsAXME5.png)
I had expected this value to be 440 instead of 10 for all the chunks. I admit I know very little about the theory of FFTs and I appreciate any help in letting my solve this.
EDIT:
The sampling rate is 44100. no. of channels is 2 and sample width is also 2.

Forewords
As xdurch0 pointed out, you are reading a kind of index instead of a frequency. If you are about to make all computation by yourself you need to compute you own frequency vector before plotting if you want to get consistent result. Reading this answer may help you towards the solution.
The frequency vector for FFT (half plane) is:
f = np.linspace(0, rate/2, N_fft/2)
Or (full plane):
f = np.linspace(-rate/2, rate/2, N_fft)
On the other hand we can delegate most of the work to the excellent scipy.signal toolbox which aims to cope with this kind of problems (and many more).
MCVE
Using scipy package it is straight forward to get the desired result for a simple WAV file with a single frequency (source):
import numpy as np
from scipy import signal
from scipy.io import wavfile
import matplotlib.pyplot as plt
# Read the file (rate and data):
rate, data = wavfile.read('tone.wav') # See source
# Compute PSD:
f, P = signal.periodogram(data, rate) # Frequencies and PSD
# Display PSD:
fig, axe = plt.subplots()
axe.semilogy(f, P)
axe.set_xlim([0,500])
axe.set_ylim([1e-8, 1e10])
axe.set_xlabel(r'Frequency, $\nu$ $[\mathrm{Hz}]$')
axe.set_ylabel(r'PSD, $P$ $[\mathrm{AU^2Hz}^{-1}]$')
axe.set_title('Periodogram')
axe.grid(which='both')
Basically:
Read the wav file and get the sample rate (here 44.1kHz);
Compute the Power Spectrum Density and frequencies;
Then display it with matplotlib.
This outputs:
Find Peak
Then we can find the frequency of the first highest peak (P>1e-2, this criterion is subject to tuning) using find_peaks:
idx = signal.find_peaks(P, height=1e-2)[0][0]
f[idx] # 440.0 Hz
Putting all together it merely boils down to:
def freq(filename, setup={'height': 1e-2}):
rate, data = wavfile.read(filename)
f, P = signal.periodogram(data, rate)
return f[signal.find_peaks(P, **setup)[0][0]]
Handling multiple channels
I tried this code with my wav file, and got the error for the line
axe.semilogy(f, Pxx_den) as follows : ValueError: x and y must have
same first dimension. I checked the shapes and f has (2,) while
Pxx_den has (220160,2). Also, the Pxx_den array seems to have all
zeros only.
Wav file can hold multiple channels, mainly there are mono or stereo files (max. 2**16 - 1 channels). The problem you underlined occurs because of multiple channels file (stereo sample).
rate, data = wavfile.read('aaaah.wav') # Shape: (46447, 2), Rate: 48 kHz
It is not well documented, but the method signal.periodogram also performs on matrix and its input is not directly consistent with wavfile.read output (they perform on different axis by default). So we need to carefully orient dimensions (using axis switch) when performing PSD:
f, P = signal.periodogram(data, rate, axis=0, detrend='linear')
It also works with Transposition data.T but then we need to back transpose the result.
Specifying the axis solve the issue: frequency vector is correct and PSD is not null everywhere (before it performed on the axis=1 which is of length 2, in your case it performed 220160 PSD on 2-samples signals we wanted the converse).
The detrend switch ensure the signal has zero mean and its linear trend is removed.
Real application
This approach should work for real chunked samples, provided chunks hold enough data (see Nyquist-Shannon sampling theorem). Then data are sub-samples of the signal (chunks) and rate is kept constant since it does not change during the process.
Having chunks of size 2**10 seems to work, we can identify specific frequencies from them:
f, P = signal.periodogram(data[:2**10,:], rate, axis=0, detrend='linear') # Shapes: (513,) (513, 2)
idx0 = signal.find_peaks(P[:,0], threshold=0.01, distance=50)[0] # Peaks: [46.875, 2625., 13312.5, 16921.875] Hz
fig, axe = plt.subplots(2, 1, sharex=True, sharey=True)
axe[0].loglog(f, P[:,0])
axe[0].loglog(f[idx0], P[idx0,0], '.')
# [...]
At this point, the trickiest part is the fine tuning of find-peaks method to catch desired frequencies. You may need to consider to pre-filter your signal or post-process the PSD in order to make the identification easier.

How do I get the values of a specific frequency range

I have a .wav file, I load it and I get the next spectrogram showing the spectrum in dB
http://i.stack.imgur.com/22TjY.png
Now I would like to know these values exactly because I want to compare with other wav file, for recognizing if these 4 values are there.
http://i.stack.imgur.com/Jun25.png
The source to generate that pictures (taken from other stackoverflow example)
## some stuff here
for i in range(0, int(RATE / CHUNK_SIZE * RECORD_SECONDS)):
# little endian, signed shortdata_chunk
data_chunk = array('h', stream.read(CHUNK_SIZE))
if byteorder == 'big':
data_chunk.byteswap()
data_all.extend(data_chunk)
## some stuff here
Fs = 16000
f = np.arange(1, 9) * 2000
t = np.arange(RECORD_SECONDS * Fs) / Fs
x = np.empty(t.shape)
for i in range(8):
x[i*Fs:(i+1)*Fs] = np.cos(2*np.pi * f[i] * t[i*Fs:(i+1)*Fs])
w = np.hamming(512)
Pxx, freqs, bins = mlab.specgram(data_all, NFFT=512, Fs=Fs, window=w,
noverlap=464)
#plot the spectrogram in dB
Pxx_dB = np.log10(Pxx)
pyplot.subplots_adjust(hspace=0.4)
pyplot.subplot(211)
ex1 = bins[0], bins[-1], freqs[0], freqs[-1]
pyplot.imshow(np.flipud(Pxx_dB), extent=ex1)
pyplot.axis('auto')
pyplot.axis(ex1)
pyplot.xlabel('time (s)')
pyplot.ylabel('freq (Hz)')
I "think" that the information is in Pxx but I don't know how to get it.

From the documentation, I gather that Pxx is a simple 2D numpy array.
You're interested in periodograms around 1s. Considering Pxx should have 512 columns and your sample is about 5s long, I'd take a slice somewhere around column 100:
periodogram_of_interest = Pxx[:, 100]
Then find the 4 maxima. Unfortunately, each of those 4 frequencies has a finite width, so simply looking for the top 4 maxima will nog be as easy. However, assuming your signal is quite clean, there's a function in scipy.signal that will list all local extrema: argrelmax. You could play with the order argument of that function to reduce your search space.
With the values returned from that function, you could get the frequencies like this: freqs[those_4_indices].