I'm new to analysing EMG data and would appreciate some carefully explained help.
I would like to generate a smooth, linear enevelope signal of my EMG data (50kHz sampling rate) like the one published in this paper: https://openi.nlm.nih.gov/detailedresult.php?img=PMC3480942_1743-0003-9-29-3&req=4
My end goal is to be able to analyze the relationship between EMG activity (output) and action potentials fired from upstream neurons (putative input) recorded at the same time.
Even though this paper lists the filtering methods out quite clearly, I do not understand what they mean or how to perform them in matlab, which is the analysis tool I have available to me.
In the code I have written so far, I can dc offset as well as rectify my data:
x = EMGtime_data
y = EMGvoltage_data
%dc offset
y2=detrend(y)
% Rectification of the EMG signal
rec_y=abs(y2);
plot(x, rec_y)
But then I am not sure how to proceed.
I have tried the envelope function, but it is not as smooth as I would like:
For instance, if I used the following:
envelope(y_rec,2000,'rms')
I get this (which also doesn't seem to care that the data is rectified):
Even if I were to accept the envelope function, I'm not sure how to access just the processed envelope data to adjust the plot (i.e. change the y-range), or analyse the data further for on-set and off-set of the signal since the results of this function seem to be coupled with the original trace.
I have also come across fastrms.m, which seems promising. Unfortunately, I do not understand how to implement this function since the general explanation is over my head and the example code is lacking any defined variable (so I don't know where to integrate my own data!)
The example code from fastrms.m file exchange is here
Fs = 200; T = 5; N = T*Fs; t = linspace(0,T,N);
noise = randn(N,1);
[a,b] = butter(5, [9 12]/(Fs/2));
x = filtfilt(a,b,noise);
window = gausswin(0.25*Fs);
rms = fastrms(x,window,[],1);
plot(t,x,t,rms*[1 -1],'LineWidth',2);
xlabel('Time (sec)'); ylabel('Signal')
title('Instantaneous amplitude via RMS')
I will be eternally grateful for help in understanding how to filter and smooth EMG data!
In order to analysis EMG signals in time domain, researcher use The combination of rectification and low pass filtering which is also called finding the “linear envelope” of the signal.
And as mentioned in both the above sentence and your attached article image's explanation, in order to plot overlaid signal, you could simply low pass filter your signal at specific frequency.
In your attached article the said signal was filtered at 8 HZ.
For better understanding the art of EMG signal analysis , i think this document could help you a lot (link)
Related
I have some accelerometer data in MATLAB and I was told to try FFT and try to use FFT features on classification. However, I am confused about the plot after FFT. It seems that there is a large spike only in the beginning of the plot and I am not sure what to make of it. I tried using some code from other posts such as this one: Accelerometer with FFT - strange output, and also some examples on the Mathworks website, but it did not help.
data = acc_data_x(1:300);
fs = 1/(1/12);
m = length(data);
nfft = 2^nextpow2(m);
y = fft(data,nfft)/m;
f = fs/2 * linspace(0,1,nfft/2+1);
power = abs(y);
plot(f,power(1:nfft/2+1))
t = (0 : m-1)/fs;
figure
plot(t,data);
I attached the plot of the accelerometer data in x and the result of the FFT. Is there some other step I am missing? I apologize for any ignorance since this is my first time trying FFT and working with this type of data.
Accelerometer Data in X plot:
After FFT:
Edit: I have tried Gareth's suggestion and used detrend function in MATLAB
After Detrend and FFT:
Also here is the full data with FFT (in the first example I only used up to 300 data points).
I'm now confused if this tells me any information?
You should first detrend your data. FFT inputs that have an uncorrected DC bias (ie, sits positive or negative) have a strong 0 Hz component.
Try data = detrend(data) after your first line. It'll skew some of the other things you do, but might help with showing the issue in the FFT. You can more carefully manage your data so that you can both clean it for FFT and also plot the original raw data once you feel happy with the issue being mostly fixed.
The amplitude of the first "zero-frequency" component in FFT is exactly the mean value of your data. If you fft(x-mean(x)), the first component will be zero. Other components nearby can be related with slow trend.
I have two data sets that I want to analyze using a cross power spectral density plot in MATLAB with the function cpsd. With the complex output of cpsd, I was wondering how I can get amplitude information out of it. I know I can get phase info by angle(Pxy) but I don't know how to pull the amplitude information. Thanks
I think what you are looking for is abs(Pxy). According to the documentation, if Pxy = x + i*y, then:
abs(Pxy) = sqrt(x^2 + y^2) = sqrt(real(Pxy)^2 + imag(Pxy)^2)
Edit:
In light of your comment though, you are looking for the time-domain magnitude (not frequency domain, as the above will give you). This thread from the signal processing stack exchange may be of some help. It kind of looks like the averaging that cpsd performs eliminates the time-domain data from the signal.
I'm very much a novice at signal processing techniques, but I am trying to apply the fast fourier transform to a daily time series to remove the seasonality present in the data. The example I am working with is from here:
http://www.mathworks.com/help/signal/ug/frequency-domain-linear-regression.html
While I understand how to implement the code as it is written in the example, I am having a hard time adapting it to my specific application. What I am trying to do is create a preprocessing function which deseasonalizes the training data using similar code to the above example. Then, using the same estimated coefficients from the in-sample data, deseasonalize the out-of-sample data to preserve its independence from the in-sample data. Basically, once the coefficients are estimated, I will normalize each new data point using the same coefficients. I suspect this is akin to estimating a linear trend, then removing it from the in-sample data, and then using the same linear model on unseen data to detrend it i the same manner.
Obviously, when I estimate the fourier coefficients, the vector I get out is equal to the length of the in-sample data. The out-of-sample data is comprised of much fewer observations, so directly applying them is impossible.
Is this sort of analysis possible using this technique or am I going down a dead end road? How should I approach that using the code in the example above?
What you want to do is certainly possible, you are on the right track, but you seem to misunderstand a few points in the example. First, it is shown in the example that the technique is the equivalent of linear regression in the time domain, exploiting the FFT to perform in the frequency domain an operation with the same effect. Second, the trend that is removed is not linear, it is equal to a sum of sinusoids, which is why FFT is used to identify particular frequency components in a relatively tidy way.
In your case it seems you are interested in the residuals. The initial approach is therefore to proceed as in the example as follows:
(1) Perform a rough "detrending" by removing the DC component (the mean of the time-domain data)
(2) FFT and inspect the data, choose frequency channels that contain most of the signal.
You can then use those channels to generate a trend in the time domain and subtract that from the original data to obtain the residuals. You need not proceed by using IFFT, however. Instead you can explicitly sum over the cosine and sine components. You do this in a way similar to the last step of the example, which explains how to find the amplitudes via time-domain regression, but substituting the amplitudes obtained from the FFT.
The following code shows how you can do this:
tim = (time - time0)/timestep; % <-- acquisition times for your *new* data, normalized
NFpick = [2 7 13]; % <-- channels you picked to build the detrending baseline
% Compute the trend
mu = mean(ts);
tsdft = fft(ts-mu);
Nchannels = length(ts); % <-- size of time domain data
Mpick = 2*length(NFpick);
X(:,1:2:Mpick) = cos(2*pi*(NFpick-1)'/Nchannels*tim)';
X(:,2:2:Mpick) = sin(-2*pi*(NFpick-1)'/Nchannels*tim)';
% Generate beta vector "bet" containing scaled amplitudes from the spectrum
bet = 2*tsdft(NFpick)/Nchannels;
bet = reshape([real(bet) imag(bet)].', numel(bet)*2,1)
trend = X*bet + mu;
To remove the trend just do
detrended = dat - trend;
where dat is your new data acquired at times tim. Make sure you define the time origin consistently. In addition this assumes the data is real (not complex), as in the example linked to. You'll have to examine the code to make it work for complex data.
I want to estimate the time of arrival of GPR echo signals using Music algorithm in matlab, I am using the duality property of Fourier transform.
I am first applying FFT on the obtained signal and then passing these as parameters to pmusic function, i am still getting the result in frequency domain.?
Short Answer: You're using the wrong function here.
As far as I can tell Matlab's pmusic function returns the pseudospectrum of an input signal.
If you click on the pseudospectrum link, you'll see that the pseudospectrum of a signal lives in the frequency domain. In particular, look at the plot:
(from Matlab's documentation: Plotting Pseudospectrum Data)
Notice that the result is in the frequency domain.
Assuming that by GPR you mean Ground Penetrating Radar, then try radar or sonar echo detection approach to estimate the two way transit time.
This can be done and the theory has been published in several papers. See, for example, here:
STAR Channel Estimation in DS-CDMA Systems
That paper describes spatiotemporal estimation (i.e. estimation of both time and direction of arrival), but you can ignore the spatial part and just do temporal estimation if you have a single-antenna receiver.
You probably won't want to use Matlab's pmusic function directly. It's always quicker and easier to write these sorts of functions for yourself, so you know what is actually going on. In the case of MUSIC:
% Get noise subspace (where M is number of signals)
[E, D] = eig(Rxx);
[lambda, idx] = sort(diag(D), 'descend');
E = E(:, idx);
En = E(:,M+1:end);
% [Construct matrix S, whose columns are the vectors to search]
% Calculate MUSIC null spectrum and convert to dB
Z = 10*log10(sum(abs(S'*En).^2, 2));
You can use the Phased array system toolbox of MATLAB if you want to estimate the DOA using different algorithms using a single command. Such as for Root MUSIC it is phased.RootMUSICEstimator phased.ESPRITEstimator.
However as Harry mentioned its easy to write your own function, once you define the signal subspace and receive vector, you can directly apply it in the MUSIC function to find its peaks.
This is another good reference.
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1143830
We're trying to analyse flow around circular cylinder and we have a set of Cp values that we got from wind tunnel experiment. Initially, we started off with a sample frequency of 20 Hz and tried to find the frequency of vortex shedding using FFT in matlab. We got a frequency of around 7 Hz. Next, we did the same experiment, but the only thing we changed was the sampling frequency- from 20 Hz to 200 Hz. We got the frequency of the vortex shedding to be around 70 Hz (this is where the peak is located in the graph). The graph doesn't change regardless of the Cp data that we enter. The only time the peak differs is when we change the sample frequency. It seems like the increase in the frequency of vortex shedding is proportional to the sample frequency and this doesn't seem to make sense at all. Any help regarding establishing a relation between sample frequency and vortex shedding frequency would be greatly appreaciated.
The problem you are seeing is related to "data aliasing" due to limitations of the FFT being able to detect frequencies higher than the Nyquist Frequency (half-the sampling frequency).
With data aliasing, a peak in real frequency will be centered around (real frequency modulo Nyquist frequency). In your 20 Hz sampling (assuming 70 Hz is the true frequency, that results in zero frequency which means you're not seeing the real information. One thing that can help you with this is to use FFT "windowing".
Another problem that you may be experiencing is related to noisy data generation via single-FFT measurement. It's better to take lots of data, use windowing with overlap, and make sure you have at least 5 FFTs which you average to find your result. As Steven Lowe mentioned, you should also sample at faster rates if possible. I would recommend sampling at the fastest rate your instruments can sample.
Lastly, I would recommend that you read some excerpts from Numerical Recipes in C (<-- link):
Section 12.0 -- Introduction to FFT
Section 12.1 (Discusses data aliasing)
Section 13.4 (Discusses FFT windowing)
You don't need to read the C source code -- just the explanations. Numerical Recipes for C has excellent condensed information on the subject.
If you have any more questions, leave them in the comments. I'll try to do my best in answering them.
Good luck!
this is probably not a programming problem, it sounds like an experiment-measurement problem
i think the sampling frequency has to be at least twice the rate of the oscillation frequency, otherwise you get artifacts; this might explain the difference. Note that the ratio of the FFT frequency to the sampling frequency is 0.35 in both cases. Can you repeat the experiment with higher sampling rates? I'm thinking that if this is a narrow cylinder in a strong wind, it may be vibrating/oscillating faster than the sampling rate can detect..
i hope this helps - there's a 97.6% probability that i don't know what i'm talking about ;-)
If it's not an aliasing problem, it sounds like you could be plotting the frequency response on a normalised frequency scale, which will change with sample frequency. Here's an example of a reasonably good way to plot a frequency response of a signal in Matlab:
Fs = 100;
Tmax = 10;
time = 0:1/Fs:Tmax;
omega = 2*pi*10; % 10 Hz
signal = 10*sin(omega*time) + rand(1,Tmax*Fs+1);
Nfft = 2^8;
[Pxx,freq] = pwelch(signal,Nfft,[],[],Fs)
plot(freq,Pxx)
Note that the sample frequency must be explicitly passed to the pwelch command in order to output the “real” frequency data. Otherwise, when you change the sample frequency the bin where the resonance occurs will seem to shift, which is similar to the problem you describe.
Methinks you need to do some serious reading on digital signal processing before you can even begin to understand all the nuances of the DFT (FFT). If I was you, I'd get grounded in it first with this great book:
Discrete-Time Signal Processing
If you want more of a mathematical treatment that will really expand your abilities,
Fourier Analysis by Körner
Take a look at this related question. While it was originally asked about asked about VB the responses are generically about FFTs
I tried using the frequency response code as above but it seems that I dont have the appropriate toolbox in Matlab. Is there any way to do the same thing without using fft command? So far, this is what I have:
% FFT Algorithm
Fs = 200; % Sampling frequency
T = 1/Fs; % Sample time
L = 65536; % Length of signal
t = (0:L-1)*T; % Time vector
y = data1; % Your CP values go in this vector
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);
% Plot single-sided amplitude spectrum.
loglog(f,2*abs(Y(1:NFFT/2)))
title(' y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')
I think there might be something wrong with the code I am using. I'm not sure what though.
A colleague of mine has written some nice GPL-licenced functions for spectral analysis:
http://www.mecheng.adelaide.edu.au/~pvl/octave/
(Update: this code is now part of one of the Octave modules:
http://octave.svn.sourceforge.net/viewvc/octave/trunk/octave-forge/main/signal/inst/.
But it might be tricky to extract just the pieces you need from there.)
They're written for both Matlab and Octave and serve mostly as a drop-in replacement for the analogous functions in the Signal Processing Toolbox. (So the code above should still work fine.)
It may help with your data analysis; better than rolling your own with fft and the like.