Can anyone help me on this?
I have a file with 8 wave signals that belong to the same wave gauge S1:
The idea is to adjust the phase of the signals so that they start with the same wave phase and height.
If I do this manually (as I did in the figure) I have to shift each signal in time until I find a proper overlap for the 8 signals.
Is there any function/routine available for this purpose?
Many thanks!
I would like to use Matlab. The plot was made in Tecplot.
The idea is to overlap the signals and then do the average wave of the 8 signals.
Here is the file:
https://www.dropbox.com/s/bc9imi5frhakgxz/time_phases1.csv
to align the signals you can use a zero crossing method, basically you find the zero crossings point of each signal then shift the signals until the zero crossing position is the same.
if you have a noisy signal, pass the signals through a low pass filter first,
and if you have a dc component pass the signals through a high pass filter.
for similar height you can factor the waveform peak or the rms-which will be more accurate,
example: divide factor = rms1/rms2 and then multiply factor by signal 2.
Related
I created a sinusoid with frequency 550Hz that goes for 1 second
fs=44100;
Duration=1; %second
Len=Duration * fs; %length of sinusoid
t=(0:Len-1)/fs;
x=sin(2*pi*550*t);
for the purpose of exploring and learning, I have decided to take the short time Fourier transform of this signal. I did it as below:
window_len=0.02*fs; %length of the window
hop=window_len/3; %hop size
nfft=2^nextpow2(window_len);
window=hamming(window_len,'periodic');
[S,f,t]=spectrogram(x,window,hop,nfft,fs);
Now I want to plot the real versus imaginary value of S for the frequency equal to 550 and see what happens. First of all, in the frequency vector I didn’t have the exact 550. There was one 516.5 and 559.6. So, I just looked at the spectrogram and chose whichever that was close to it and picked that. When I tried to plot real vs imaginary of S for the frequency I chose (over all time frames), the values all fall in 3 points as it shows in the attached plot. Why three points?
Each STFT window can have a different complex phase depending on how the start (or middle) of the window is synchronized (or not) with the sinusoids period. So the real-complex IQ plot for the peak magnitude DFT result bin can be a circular scatter plot, depending on the number of DFT windows and the ratio between the stepping distance (or length - overlap) and the period of the sinusoid.
The phase of the STFT coefficients for the different windows depends on which data exactly the window "sees". So for your particular choice of window length and hop, it so happens that as you slide through your single-frequency sinusoid, there only three different data chunks that you window "sees". To see what I mean, just plot:
plot(x(1:window_len),'x')
plot(x(1+hop:window_len+hop),'x')
plot(x(1+2*hop:window_len+2*hop),'x')
plot(x(1+3*hop:window_len+3*hop),'x')
.. and if you continue you will see that the pattern repeats itself, i.e., the first plot for instance is the same as the fourth, the second as the fifth etc. Therefore you only have three different real-imaginary part combinations.
Of course, this will change if you change the window length and the hopsize, and you will get more points. For instance, try
window_len =nfft;
hop=ceil(window_len/4)
I hope that helps.
I am trying to plot the spectrogram of my time domain signal given:
N=5000;
phi = (rand(1,N)-0.5)*pi;
a = tan((0.5.*phi));
i = 2.*a./(1-a.^2);
plot(i);
spectrogram(i,100,1,100,1e3);
The problem is I don't understand the parameters and what values should be given. These values that I am using, I referred to MATLAB's online documentation of spectrogram. I am new to MATLAB, and I am just not getting the idea. Any help will be greatly appreciated!
Before we actually go into what that MATLAB command does, you probably want to know what a spectrogram is. That way you'll get more meaning into how each parameter works.
A spectrogram is a visual representation of the Short-Time Fourier Transform. Think of this as taking chunks of an input signal and applying a local Fourier Transform on each chunk. Each chunk has a specified width and you apply a Fourier Transform to this chunk. You should take note that each chunk has an associated frequency distribution. For each chunk that is centred at a specific time point in your time signal, you get a bunch of frequency components. The collection of all of these frequency components at each chunk and plotted all together is what is essentially a spectrogram.
The spectrogram is a 2D visual heat map where the horizontal axis represents the time of the signal and the vertical axis represents the frequency axis. What is visualized is an image where darker colours means that for a particular time point and a particular frequency, the lower in magnitude the frequency component is, the darker the colour. Similarly, the higher in magnitude the frequency component is, the lighter the colour.
Here's one perfect example of a spectrogram:
Source: Wikipedia
Therefore, for each time point, we see a distribution of frequency components. Think of each column as the frequency decomposition of a chunk centred at this time point. For each column, we see a varying spectrum of colours. The darker the colour is, the lower the magnitude component at that frequency is and vice-versa.
So!... now you're armed with that, let's go into how MATLAB works in terms of the function and its parameters. The way you are calling spectrogram conforms to this version of the function:
spectrogram(x,window,noverlap,nfft,fs)
Let's go through each parameter one by one so you can get a greater understanding of what each does:
x - This is the input time-domain signal you wish to find the spectrogram of. It can't get much simpler than that. In your case, the signal you want to find the spectrogram of is defined in the following code:
N=5000;
phi = (rand(1,N)-0.5)*pi;
a = tan((0.5.*phi));
i = 2.*a./(1-a.^2);
Here, i is the signal you want to find the spectrogram of.
window - If you recall, we decompose the image into chunks, and each chunk has a specified width. window defines the width of each chunk in terms of samples. As this is a discrete-time signal, you know that this signal was sampled with a particular sampling frequency and sampling period. You can determine how large the window is in terms of samples by:
window_samples = window_time/Ts
Ts is the sampling time of your signal. Setting the window size is actually very empirical and requires a lot of experimentation. Basically, the larger the window size, the better frequency resolution you get as you're capturing more of the frequencies, but the time localization is poor. Similarly, the smaller the window size, the better localization you have in time, but you don't get that great of a frequency decomposition. I don't have any suggestions here on what the most optimal size is... which is why wavelets are preferred when it comes to time-frequency decomposition. For each "chunk", the chunks get decomposed into smaller chunks of a dynamic width so you get a mixture of good time and frequency localization.
noverlap - Another way to ensure good frequency localization is that the chunks are overlapping. A proper spectrogram ensures that each chunk has a certain number of samples that are overlapping for each chunk and noverlap defines how many samples are overlapped in each window. The default is 50% of the width of each chunk.
nfft - You are essentially taking the FFT of each chunk. nfft tells you how many FFT points are desired to be computed per chunk. The default number of points is the largest of either 256, or floor(log2(N)) where N is the length of the signal. nfft also gives a measure of how fine-grained the frequency resolution will be. A higher number of FFT points would give higher frequency resolution and thus showing fine-grained details along the frequency axis of the spectrogram if visualised.
fs - The sampling frequency of your signal. The default is 1 Hz, but you can override this to whatever the sampling frequency your signal is at.
Therefore, what you should probably take out of this is that I can't really tell you how to set the parameters. It all depends on what signal you have, but hopefully the above explanation will give you a better idea of how to set the parameters.
Good luck!
I need to generate a white noise signal with Matlab that has a maximum frequency of 5, 10 and 20 Hz. I know one way is to create the signal, then do a fourier transform, adjust the signal frequency and then inverse transform the signal back to the time domain. I can't really figure out how to do that in Matlab. Any help at all would be great
I need to generate a white noise signal with Matlab that has a maximum frequency of 5, 10 and 20 Hz.
That's the same as saying "I need a perfect circle, but it has to have exactly three edges". White noise doesn't have maximum frequencies; it's white because it spans all your bandwidth with the same expected noise energy.
Now, I presume you want to say "I want to have noise that is shaped a bit like signals that center around 5, 10 and 20 Hz". You'd still have to define the spectral shape -- but for the sake of argument, I assume you want to have gaussian shaped frequency response around these frequencies with a bandwidth of 2 Hz, with a sampling frequency of 50 Hz (has to be twice the highest frequency your signal has[in the real signal case], or else you'll get aliasing).
You can simply do that by using matlabs filter design toolbox, and applying the resulting filter to your signal. Usually, you'd just design one filter and shift it in frequency, but that doesn't seem to be your level of expertise yet -- which indicates that experimenting is an extremely good approach to becoming accustomed to DSP. Go wild!
I recently visited this page in order to determine the frequency from signal data in MATLAB:
Determine frequency from signal data in MATLAB
And in this page, an answerer responded with the following code:
[maxValue,indexMax] = max(abs(fft(signal-mean(signal))));
From what I can see, a Fast Fourier Transform is taken on a signal named signal, its magnitude is kept by using 'abs', and the max value is computed. The max value will be in maxValue, and the indexMax will contain the position of the maxValue. However, can someone explain what is meant by signal-mean, and what the purpose of it?
It basically normalize the vector signal so it has mean zero (subtracts the mean from signal). So signal - mean(signal) looks like signal except that is shifted on the y axis so it has a zero mean. Hope it is clear.
In the example you posted in the link, the mean of the signal is around -2, so by subtracting the mean you end up with a the signal shifted up around the y=0 axis.
As stated in vsoftco's answer, signal-mean(signal) subtracts the mean of the signal.
However, the key point is: why is this is done? If you don't subtract the mean, it's very likely that the maximum peak in the FFT appears at frequency 0 (DC component). But you don't want to detect that as the "frequency" of your signal, even if it truly is the highest spectral component. So you remove that zero-frequency component by subtracting the mean. That way, the max operation will detect the maximum non-zero frequency component, which is probably what you want.
I'm working on a control system that measures the movement of a vibrating robot arm. Because there is some deadtime, I need to look into the future of the somewhat noisy signal.
My idea was to use the frequencies in the sampled signal and produce a fourier function that could be used for extrapolation.
My question: I already have the FFT of the signal vector (containing 60-100 values e.g.) and can see the main frequencies in the amplitude spectrum. Now I want to have a function f(t) which fits to the signal, removes some noise, and can be used to predict the near future of the signal. How do I calculate the coefficients for the sine/cosine functions out of the complex FFT data?
Thank you so much!
AFAIR FFT essentially produces output as a sum of sine functions with different frequencies. The importance of each frequency is the height of each peak. So what you really want to do here is filter out some frequencies (ie. high frequencies for the arm to move gently) and then come back to the time domain.
In matlab this should be like going through the vector of what you got from fft, setting some values to 0 (or doing something more complex to it) and then use ifft to come back to time domain and make the prediction based on what you get.
There's also one thing you should consider while doing this - Nyquist frequency - this means that the highest frequency that you get on your fft is half of the sampling frequency.
If you use an FFT for data that isn't periodic within the FFT aperture length, then you may need to use a window to reduce spurious frequencies due to "spectral leakage". Frequency estimation techniques to better estimate "between bin" frequency content may also be appropriate. The phase of each cosine sinusoid, relative to the edge of the window, is usually atan2(imag[i], real[i]). The frequency depends on the sample rate and bin number versus the length of the FFT.
You might also want to look into using a Kalman filter instead of an FFT.
Added: If your signal isn't exactly integer periodic in the FFT length, then you may want to do an fftshift before the FFT to move the resulting phase measurement reference point to the center of your data vector, instead of a possibly discontinuous circular edge.