I have an EMG-signal and would like to get the mean value of the amplitude in a defined frequency space. I tried making FFT, but i don't get a vector with amplitudes and frequencies. I am new to Matlab - please help.
Here is how you would get power (i.e., amplitude) and frequency from the fft function in Matlab:
fs = 1024; % sampling rate of signal
time = 1; % time in sec of simulated signal
xn = randn (fs*time,1); % creating random signal
nfft = time*fs; % size of window on which to perform FFT
Y = fft (xn, nfft);
% Convert value to obtain the power of the signal at
% each frequency
Pyy = Y .* conj(Y) / nfft;
% Create a frequency axis for ploting
fy = fs/nfft * (0:(nfft/2) -1);
plot (fy, Pyy(1:nfft/2))
ylabel ('power (AU)^2') % arbitrary units
xlabel ('frequency (Hz)')
xlim ([0 512])
However, keep in mind that EMG is not a stationary signal. When doing spectral analysis on EMG signals we are trying to approximate the true spectrum. This is why EMG is usually seperated into windows of data. FFT is performed on each of these windows and the averaged.
Rather than using the fft function, you might want to consider using the pwelch function in the Matlab Signal Processing Toolbox. It allows you to set the window size, amount of overlap of the windows, etc.
Alternatively you could use the very popular Neurospec Matlab toolbox writen by David Halliday. It has a PDF that describes all the functions and examples you can use. It has additional functionality (e.g., coherence), but you can ignore it if you like and simply extract the spectral data.
Related
I'm trying to find the maximum frequency of a periodic signal in Matlab and as i know when you convert a periodic signal to the frequency spectrum you get only delta functions however i get a few curves between the produced delta functions. Here is the code :
t=[-0.02:10^-3:0.02];
s=5.*(1+cos(2*pi*10*t)).*cos(2*pi*100*t);
figure, subplot(211), plot(t,s);
y=fft(s);
subplot(212), plot(t,y);
Here is a code-snippet to help you understand how to get the frequency-spectrum using fft in matlab.
Things to remember are:
You need to decide on a sampling frequency, which should be high enough, as per the Nyquist Criterion (You need the number of samples, at least more than twice the highest frequency or else we will have aliasing). That means, fs in this example cannot be below 2 * 110. Better to have it even higher to see a have a better appearance of the signal.
For a real signal, what you want is the power-spectrum obtained as the square of the absolute of the output of the fft() function. The imaginary part, which contains the phase should contain nothing but noise. (I didn't plot the phase here, but you can do this to check for yourself.)
Finally, we need to use fftshift to shift the signal such that we get the mirrored spectrum around the zero-frequency.
The peaks would be at the correct frequencies. Now considering only the positive frequencies, as you can see, we have the largest peak at 100Hz and two further lobs around 100Hz +- 10Hz i.e. 90Hz and 110Hz.
Apparently, 110Hz is the highest frequency, in your example.
The code:
fs = 500; % sampling frequency - Should be high enough! Remember Nyquist!
t=[-.2:1/fs:.2];
s= 5.*(1+cos(2*pi*10*t)).*cos(2*pi*100*t);
figure, subplot(311), plot(t,s);
n = length(s);
y=fft(s);
f = (0:n-1)*(fs/n); % frequency range
power = abs(y).^2/n;
subplot(312), plot(f, power);
Y = fftshift(y);
fshift = (-n/2:n/2-1)*(fs/n); % zero-centered frequency range
powershift = abs(Y).^2/n;
subplot(313), plot(fshift, powershift);
The output plots:
The first plot is the signal in the time domain
The signal in the frequency domain
The shifted fft signal
I'm having problems plotting the FFT of a wav file. I managed to plot the magnitude and phase spectrums of the signal, however I need to repeat this in range -fs/2:fs/2.
%read sound files
%'y' is the vector holding the original samples & 'fs' refers to the sampling frequency
[y,fs] = wavread('handel.wav');
ydft = fft(y); %fft to transform the original signal into frequency domain
n = length (y); %length of the original signal
% y has even length
ydft = ydft(1:length(y)/2+1);
% create a frequency vector
freq = 0:fs/length(y):fs/2;
shiftfreq = fftshift(freq);
%plot original signal in time domain;
figure;
plot ((1:n)/fs, y);
title('handel.wav in time domain');
xlabel ('second');
grid on;
% plot magnitude in frequency domain
figure;
plot(freq,abs(ydft));
title('handel.wav in frequency domain');
xlabel ('Hz');
ylabel('Magnitude');
grid on;
% plot phase in frequency domain
figure;
plot(freq,unwrap(angle(ydft)));
title ('handel.wav in frequency domain');
xlabel ('Hz');
ylabel ('Phase');
grid on;
What you are currently doing now is plotting the half spectrum, so from 0 <= f < fs/2 where fs is the sampling frequency of your signal, and so fs/2 is the Nyquist frequency. Take note that considering the half spectrum is only valid if the signal is real. This means that the negative spectra is symmetric to the positive spectra and so you don't really need to consider the negative spectra here.
However, you would like to plot the full spectrum of the magnitude and phase. Take note that when calculating the fft using MATLAB, it uses the Cooley-Tukey algorithm so when computing the N point FFT, half of result is for the frequencies from 0 Hz inclusive up to fs/2 Hz exclusive and the other half is for the frequencies from -fs/2 Hz inclusive up to 0 Hz exclusive.
As such, to plot the full spectrum, simply perform a fftshift on the full signal so that the right half and left half of the spectrum is swapped so that the 0 Hz frequency is located in the centre of the signal. Also, you must generate frequencies between -fs/2 to fs/2 to cover the full spectrum. Specifically, you need to generate N points linearly spaced between -fs/2 to fs/2. However, take note that the Nyquist frequency at fs/2 Hz is being excluded at the end, so you need to generate N+1 points between -fs/2 to fs/2 and remove the last point in order for the right step size between each frequency bin to be correct. The easiest way to generate this linear array of points is by using the linspace command where the start frequency is -fs/2, the ending frequency is fs/2 and you want N+1 points between this range and remove the last point:
freq = linspace(-fs/2, fs/2, n+1);
freq(end) = [];
As such, borrowing some parts of your code, this is what the modified code looks like to plot the full spectrum of the magnitude and phase:
%// Read in sound file
[y,fs] = wavread('handel.wav');
%// Take N-point FFT where N is the length of the signal
ydft = fft(y);
n = numel(y); %// Get N - length of signal
%// Create frequency vector - make sure you remove last point
freq = linspace(-fs/2, fs/2, n+1);
freq(end) = [];
%// Shift the spectrum
shiftSpectrum = fftshift(ydft);
%//plot original signal in time domain;
figure;
plot ((0:n-1)/fs, y); %// Note you should start from time = 0, not time = 1/fs
title('handel.wav in time domain');
xlabel ('second');
grid on;
%// plot magnitude in frequency domain
figure;
plot(freq,abs(shiftSpectrum));
title('handel.wav in frequency domain');
xlabel ('Hz');
ylabel('Magnitude');
grid on;
%// plot phase in frequency domain
figure;
plot(freq,unwrap(angle(shiftSpectrum)));
title('handel.wav in frequency domain');
xlabel('Hz');
ylabel('Phase');
grid on;
I don't have access to your handel.wav file, but I'll be using the one provided with MATLAB. You can load this in with load handel;. The sampling frequency is stored in a variable called Fs, so I had to do fs = Fs; before the code I wrote above could work. The sampling frequency for this particular file is 8192 Hz, and this is approximately a 9 second long file (numel(y) / fs = 8.9249 seconds). With that file, this is the magnitude and phase that I get:
For the discrete Fourier transform (DFT) as well as its fast implementations (FFTs), the frequencies are normalized with the sampling frequency fs, i.e., the original range -fs/2:fs/2 is changed to -pi:pi.
Besides, the DFT/FFT always starts with 0, and you can use fftshift() to shift the 0 frequency to the center. Therefore, after fftshift(), the range is -pi:pi, then, you can scale to -fs/2:fs/2.
look at the following Matlab function, it can calculate phase spectrum as well as amplitude spectrum with a perfect accuracy:
https://www.mathworks.com/matlabcentral/fileexchange/63965-amplitude-and-phase-spectra-of-a-signal--fourier-transform-
This program calculates amplitude and phase spectra of an input signal with acceptable accuracy especially in the calculation of phase spectrum.The code does three main jobs for calculation amplitude and phase spectra. First of all, it extends the input signal to infinity; because for calculation Fourier transform(FT) (fft function in Matlab), we consider our signal is periodic with an infinite wavelength, the code creates a super_signal by putting original signal next to itself until the length of super_signal is around 1000000 samples, why did I choose 1000000 samples? Actually, it is just based on try and error!! For most signals that I have tried, a supper signal with 1000000 samples has the best output.
Second, for calculating fft in Matlab you can choose different resolutions, the Mathwork document and help use NFFT=2^nextpow2(length(signal)), it definitely isn't enough for one that wants high accuracy output. Here, I choose the resolution of NFFT=100000 that works for most signals.
Third, the code filters result of FT by thresholding, it is very important step! For calculating phase spectrum, its result is very noisy because of floating rounding off error, it causes during calculation "arctan" even small rounding off error produces significant noise in the result of phase spectrum, for suppressing this kind of noise you can define a threshold value. It means if amplitude of specific frequency is less than predefined threshold value (you must define it) it put zero instead of it.
These three steps help to improve the result of amplitude and phase spectra significantly.
IF YOU USE THIS PROGRAM IN YOUR RESEARCH, PLEASE CITE THE FOLLOWING PAPER:
Afshin Aghayan, Priyank Jaiswal, and Hamid Reza Siahkoohi (2016). "Seismic denoising using the redundant lifting scheme." GEOPHYSICS, 81(3), V249-V260. https://doi.org/10.1190/geo2015-0601.1
I am new to Matlab and speech processing as well. I want to find the fundamental frequency of speech signal to determine the gender of the speaker. I removed the silence from the signal by analysing it within 10 msec periods.
After that I got the fft using this code :
abs(fft(input_signal_without_silences))
My plot of both the speech signal and the fft of it is below:
Now, I want to find the fundamental frequency but I could not understand which steps do I need to do this. Or do I misunderstand this concept?
As far as I have learnt, there are some methods like autocorrelation,
Since I am not familiar to both speech processing and matlab, any help and advice is very much appreciated.
The fft() help can solve most parts of your problem. I can give a brief overview of things based on the content of the help file.
At the moment what you are plotting is the two sided, unnormalized fft coefficients, which don't tell much. Use the following to get a more user informed spectral analysis of the voice signal. Using the single sided spectram you would be able to find the dominant frequency which might be the fundamental frequency of the speech signal.
y = []; %whatever your signal
T = 1e-2; % Sample time, 10 ms
Fs = 1/T; % Sampling frequency
L = length(y); % Length of signal
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1)))
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')
The problem is that you have a plot of Amplitude vs Sample Number instead of a plot of Amplitude vs Frequency.In order to calculate the fundamental frequency you need to find the frequency that corresponds to the highest frequency.
Matlab returns frequencies from -fs/2 to fs/2 so the frequency at index n is
f = n * (fs/N) - (fs/2)
where f = frequency, fs = sampling frequency, N = number of points in FFT.
So basically all you need to do is get the index where the plot is highest and substitute it in the equation above to get an estimate of the fundamental frequency.Make sure n > N/2 so that your fundamental frequency is positive.
I am doing the linear motion measurement with a moving audio source and a stationary observer. Described here: http://www.animations.physics.unsw.edu.au/labs/Doppler/doppler_lab.html
How to write a MATLAB script to do get the sample number of the frequency that has the greatest power in the audio file?
What you need is the Time-Frequency localization information. This can be obtained using Short-time Fourier transform. There are many other Time-Frequency analysis techniques, STFT being the simplest and hence a good starting point. Here is a simple code to help you understand the concept:
% Parameters
Fs = 44100; % Sample rate (44100 Hz)
t = 0:1/Fs:5; % Time instances
t1 = 5; % End time of signal, 5 secs
f0 = 440; % frequency swiped from 440 Hz
f1 = 880; % to 880 Hz
% Signal generation
audio = chirp(t,f0,t1,f1);
% wavplay(audio,Fs) % to play the audio
% Signal analysis
window = 2050; % Should be minimum twice the maximum frequency we want to analyze
noverlap = 1025; % 50% overlap
nfft = 44100;
[S,F,T,P] = spectrogram(audio,window,noverlap,nfft,Fs); % Spectrogram takes the STFT of the signal
% P matrix contains the power spectral density of each segment of the STFT
% Plotting results
imagesc(real(S)) % frequency-time Plot of the signal
ylim([0 1000])
xlabel('Time (secs)')
ylabel('Frequency (Hz)')
title('Time-Frequency plot of a Audio signal')
To get the sample number, you just need to find the time instance at which the frequency of your interest appears, and use sampling frequency to compute the sample number.
P is the power spectral density matrix. Along y-axis is the frequency, x-axis is time, and power contributed by each frequency at every instant is stored in this matrix. You need the element which has the highest value in the entire matrix. A code like below should work:
[maxElement, maxElementTimeIndex] = max(max(P, [], 1)); % max(P, [], 1) finds maximum power for each time instance, max(max(P,[],1)) finds maximum for the entire 2D matrix.
maxPoweredSampleInAudioSignal = (maxElementTimeIndex-1) * Fs; % This calculation is made within the limitations of STFT, so approximately here the maximum power for any frequency is present
Here is the scenario: using a spectrum analyzer i have the input values and the output values. the number of samples is 32000 and the sampling rate is 2000 samples/sec, and the input is a sine wave of 50 hz, the input is current and the output is pressure in psi.
How do i calculate the frequency response from this data using MATLAB,
using the FFT function in MATLAB.
i was able to generate a sine wave, that gives out the the magnitude and phase angles, here is the code that i used:
%FFT Analysis to calculate the frequency response for the raw data
%The FFT allows you to efficiently estimate component frequencies in data from a discrete set of values sampled at a fixed rate
% Sampling frequency(Hz)
Fs = 2000;
% Time vector of 16 second
t = 0:1/Fs:16-1;
% Create a sine wave of 50 Hz.
x = sin(2*pi*t*50);
% Use next highest power of 2 greater than or equal to length(x) to calculate FFT.
nfft = pow2(nextpow2(length(x)))
% Take fft, padding with zeros so that length(fftx) is equal to nfft
fftx = fft(x,nfft);
% Calculate the number of unique points
NumUniquePts = ceil((nfft+1)/2);
% FFT is symmetric, throw away second half
fftx = fftx(1:NumUniquePts);
% Take the magnitude of fft of x and scale the fft so that it is not a function of the length of x
mx = abs(fftx)/length(x);
% Take the square of the magnitude of fft of x.
mx = mx.^2;
% Since we dropped half the FFT, we multiply mx by 2 to keep the same energy.
% The DC component and Nyquist component, if it exists, are unique and should not be multiplied by 2.
if rem(nfft, 2) % odd nfft excludes Nyquist point
mx(2:end) = mx(2:end)*2;
else
mx(2:end -1) = mx(2:end -1)*2;
end
% This is an evenly spaced frequency vector with NumUniquePts points.
f = (0:NumUniquePts-1)*Fs/nfft;
% Generate the plot, title and labels.
subplot(211),plot(f,mx);
title('Power Spectrum of a 50Hz Sine Wave');
xlabel('Frequency (Hz)');
ylabel('Power');
% returns the phase angles, in radians, for each element of complex array fftx
phase = unwrap(angle(fftx));
PHA = phase*180/pi;
subplot(212),plot(f,PHA),title('frequency response');
xlabel('Frequency (Hz)')
ylabel('Phase (Degrees)')
grid on
i took the frequency response from the phase plot at 90 degree phase angle, is this the right way to calculate the frequency response?
how do i compare this response to the values that is obtained from the analyzer? this is a cross check to see if the analyzer logic makes sense or not.
Looks OK at first glance, but a couple of things you're missing:
you should apply a window function to the time domain data before the FFT, see e.g. http://en.wikipedia.org/wiki/Window_function for windowing in general and http://en.wikipedia.org/wiki/Hann_window for the most commonly used window function (Hann aka Hanning).
you probably want to plot log magnitude in dB rather than just raw magnitude
You should consider looking at the cpsd() function for calculating the Frequency response. The scaling and normalisation for various window functions is handled for you.
the Frequency reponse would then be
G = cpsd (output,input) / cpsd (input,input)
then take the angle() to obtain the phase difference between the input and the output.
Your code snippet does not mention what the input and output data sets are.