I am plotting some data I collected at 10000 Hz, I attached a snip of some of the data in the form of an FFT and time. I am getting a repeating frequency around 10Hz that seems to be pretty obviously some sort of noise from the system i am testing. The signal shows up in the time domain and also the frequency domain.
I am looking to use MATLAB to remove these spikes.
Has anyone dealt with a similar issue and can provide any advice.
To filter out specific frequency components of a signal, you would normally use either a notch filter or a comb filter, for which MATLAB already has some commands in the DSP System Toolbox:
https://www.mathworks.com/help/dsp/ref/iirnotch.html
https://www.mathworks.com/help/dsp/ref/fdesign.comb.html
Alternatively, if you have the Signal Processing Toolbox, you can use the band-stop Butterworth filter to remove individual frequency components (ranges) using
https://www.mathworks.com/help/signal/ref/butter.html
Review for removing periodicsI have a dataset that contains hourly wind speed data for 7 seven. I am trying to implement a forecasting model to the data and the review paper states that trimming of diurnal, weekly, monthly, and annual patterns in data significantly enhances estimation accuracy. They then follow along by using the fourier series to remove the periodic components as seen in the image. Any ideas on how i model this in matlab?
I am afraid this topic is not explained "urgently". What you need is a filter for the respective frequencies and a certain number of their harmonics. You can implement such a filter with an fft or directly with a IIR/FIR-formula.
FFT is faster than a IIR/FIR-implementation, but requires some care with respect to window function. Even if you do a "continuous" DFT, you will have a window function (like exponential or gaussian). The window function determines the bandwidth. The wider the window, the smaller the bandwidth. With an IIR/FIR-filter the bandwidth is encoded in the recursive parameters.
For suppressing single frequencies (like the 24hr weather signal) you need a notch-filter. This also requires you to specify a bandwidth, as you can see in the linked article. The smaller the bandwidth, the longer it will take (in time) until the filter has evolved to the frequency to suppress it. If you want the filter to recognize the amplitude of the 24hr-signal fast, then you need a wider bandwidth. But then however you are going to suppress also more frequencies slightly lower and slightly higher than 1/24hrs. It's a tradeoff.
If you also want to suppress several harmonics (like described in the paper) you have to combine several notch-filters in series. If you want to do it with FFT, you have to model the desired transfer function in the frequency space and since you can do this for all frequencies at once, so it's more efficient.
An easy but approximate way to get something similar to a notch-filter including all harmonics is with a Comb-filter. But it's an approximation, you have no control over the details of the transfer function. You could do that in Matlab by adding to the original a signal that is shifted by 12hrs. This is because a sinusoidal signal will cancel with one that is shifted by pi.
So you see, there's lots of possibilities for what you want.
I have audio record.
I want to detect sinusoidal pattern.
If i do regular fft i have result with bad SNR.
for example
my signal contents 4 high frequencies:
fft result:
To reduce noise i want to do Coherent integration as described in this article: http://flylib.com/books/en/2.729.1.109/1/
but i cant find any MATLAB examples how to do it. Sorry for bad english. Please help )
I look at spectra almost every day, but I never heard of 'coherent integration' as a method to calculate one. As also mentioned by Jason, coherent integration would only work when your signal has a fixed phase during every FFT you average over.
It is more likely that you want to do what the article calls 'incoherent integration'. This is more commonly known as calculating a periodogram (or Welch's method, a slightly better variant), in which you average the squared absolute value of the individual FFTs to obtain a power-spectral-density. To calculate a PSD in the correct way, you need to pay attention to some details, like applying a suitable Fourier window before doing each FFT, doing the proper normalization (so that the result is properly calibrated in i.e. Volt^2/Hz) and using half-overlapping windows to make use of all your data. All of this is implemented in Matlab's pwelch function, which is part of the signal-processing toolbox. See my answer to a similar question about how to use pwelch.
Integration or averaging of FFT frames just amounts to adding the frames up element-wise and dividing by the number of frames. Since MATLAB provides vector operations, you can just add the frames with the + operator.
coh_avg = (frame1 + frame2 + ...) / Nframes
Where frameX are the complex FFT output frames.
If you want to do non-coherent averaging, you just need to take the magnitude of the complex elements before adding the frames together.
noncoh_avg = (abs(frame1) + abs(frame2) + ...) / Nframes
Also note that in order for coherent averaging to work the best, the starting phase of the signal of interest needs to be the same for each FFT frame. Otherwise, the FFT bin with the signal may add in such a way that the amplitudes cancel out. This is usually a tough requirement to ensure without some knowledge of the signal or some external triggering so it is more common to use non-coherent averaging.
Non-coherent integration will not reduce the noise power, but it will increase signal to noise ratio (how the signal power compares to the noise power), which is probably what you really want anyway.
I think what you are looking for is the "spectrogram" function in Matlab, which computes the short time Fourier transform(STFT) of an input signal.
STFT
Spectrogram
For a homework assignment I have to design a simple bandpass filter in Matlab that filters out everything between 250Hz and 1000 Hz. What I did so far:
- using the 'enframe' function to create half overlapping windows with 512 samples each. On the windows I apply the hann window function.
- On each window I apply an fft. After this I reconstruct the original signal with the function ifft, that all goes well.
But the problem is how I have to interpret the result of the fft function and how to filter out a frequency band.
Unless I'm mistaken, it sounds like you're taking the wrong approach to this.
If your assignment is to manipulate a signal specifically by manipulating its FFT then ignore me. Otherwise.. read on.
The FFT is normally used to analyse a signal in the frequency domain. If you start fiddling with the complex coefficients that an FFT returns then you're getting into a complicated mathematical situation. This is particularly the case since your cut-off frequencies aren't going to lie nicely on FFT bin frequencies. Also, remember that the FFT is not a perfect transform of the signal you're analysing. It will always introduce artefacts of its own due to scalloping error, and convolution with your hann window.
So.. let's leave the FFT for analysis, and build a filter.
If you're doing band-pass design in your class I'm going to assume you understand what they do. There's a number of functions in Matlab to generate the coefficients for different types of filter i.e. butter, kaiser cheby1. Look up their help pages in Matlab for loads more info. The values you plug in to these functions will be dependent on your filter specification, i.e. you want "X"dB rolloff and "Y"dB passband ripple. You'll need some idea of the how these filters work, and knowledge of their transfer functions to understand how their filter order relates to your specification.
Once you have your coefficients, it's just a case of running them through the filter function (again.. check the help page if you're not sure how this works).
The mighty JOS has a great walkthrough of bandpass filter design here.
One other little niggle.. in your question you mentioned that you want your filter to "filter out" everything between 250Hz and 1000Hz. This is a bit ambiguous. If you're designing a bandpass filter you would want to "pass" everything between 250Hz and 1000Hz. If you do in fact want to "filter out" everything in this range you want a band-stop filter instead.
It all depends on the sampling rate you use.
If you sample right according to the Nyquist-Shannon sampling theorem then you can try and interpret the samples of your fft using the definition of the DFT.
For understanding which frequencies correspond with which samples in the dft results, I think it's best to look at the inverse transformation. You multiply coefficient k with
exp(i*2*pi*k/N*n)
which can be interpreted to be a cosine with Euler's Formula. So each coefficient gets multiplied by a sine of a certain frequency.
Good luck ;)
Does anyone know how to use filters in MATLAB?
I am not an aficionado, so I'm not concerned with roll-off characteristics etc — I have a 1 dimensional signal vector x sampled at 100 kHz, and I want to perform a high pass filtering on it (say, rejecting anything below 10Hz) to remove the baseline drift.
There are Butterworth, Elliptical, and Chebychev filters described in the help, but no simple explanation as to how to implement.
There are several filters that can be used, and the actual choice of the filter will depend on what you're trying to achieve. Since you mentioned Butterworth, Chebyschev and Elliptical filters, I'm assuming you're looking for IIR filters in general.
Wikipedia is a good place to start reading up on the different filters and what they do. For example, Butterworth is maximally flat in the passband and the response rolls off in the stop band. In Chebyschev, you have a smooth response in either the passband (type 2) or the stop band (type 1) and larger, irregular ripples in the other and lastly, in Elliptical filters, there's ripples in both the bands. The following image is taken from wikipedia.
So in all three cases, you have to trade something for something else. In Butterworth, you get no ripples, but the frequency response roll off is slower. In the above figure, it takes from 0.4 to about 0.55 to get to half power. In Chebyschev, you get steeper roll off, but you have to allow for irregular and larger ripples in one of the bands, and in Elliptical, you get near-instant cut off, but you have ripples in both bands.
The choice of filter will depend entirely on your application. Are you trying to get a clean signal with little to no losses? Then you need something that gives you a smooth response in the passband (Butterworth/Cheby2). Are you trying to kill frequencies in the stopband, and you won't mind a minor loss in the response in the passband? Then you will need something that's smooth in the stop band (Cheby1). Do you need extremely sharp cut-off corners, i.e., anything a little beyond the passband is detrimental to your analysis? If so, you should use Elliptical filters.
The thing to remember about IIR filters is that they've got poles. Unlike FIR filters where you can increase the order of the filter with the only ramification being the filter delay, increasing the order of IIR filters will make the filter unstable. By unstable, I mean you will have poles that lie outside the unit circle. To see why this is so, you can read the wiki articles on IIR filters, especially the part on stability.
To further illustrate my point, consider the following band pass filter.
fpass=[0.05 0.2];%# passband
fstop=[0.045 0.205]; %# frequency where it rolls off to half power
Rpass=1;%# max permissible ripples in stopband (dB)
Astop=40;%# min 40dB attenuation
n=cheb2ord(fpass,fstop,Rpass,Astop);%# calculate minimum filter order to achieve these design requirements
[b,a]=cheby2(n,Astop,fstop);
Now if you look at the zero-pole diagram using zplane(b,a), you'll see that there are several poles (x) lying outside the unit circle, which makes this approach unstable.
and this is evident from the fact that the frequency response is all haywire. Use freqz(b,a) to get the following
To get a more stable filter with your exact design requirements, you'll need to use second order filters using the z-p-k method instead of b-a, in MATLAB. Here's how for the same filter as above:
[z,p,k]=cheby2(n,Astop,fstop);
[s,g]=zp2sos(z,p,k);%# create second order sections
Hd=dfilt.df2sos(s,g);%# create a dfilt object.
Now if you look at the characteristics of this filter, you'll see that all the poles lie inside the unit circle (hence stable) and matches the design requirements
The approach is similar for butter and ellip, with equivalent buttord and ellipord. The MATLAB documentation also has good examples on designing filters. You can build upon these examples and mine to design a filter according to what you want.
To use the filter on your data, you can either do filter(b,a,data) or filter(Hd,data) depending on what filter you eventually use. If you want zero phase distortion, use filtfilt. However, this does not accept dfilt objects. So to zero-phase filter with Hd, use the filtfilthd file available on the Mathworks file exchange site
EDIT
This is in response to #DarenW's comment. Smoothing and filtering are two different operations, and although they're similar in some regards (moving average is a low pass filter), you can't simply substitute one for the other unless it you can be sure that it won't be of concern in the specific application.
For example, implementing Daren's suggestion on a linear chirp signal from 0-25kHz, sampled at 100kHz, this the frequency spectrum after smoothing with a Gaussian filter
Sure, the drift close to 10Hz is almost nil. However, the operation has completely changed the nature of the frequency components in the original signal. This discrepancy comes about because they completely ignored the roll-off of the smoothing operation (see red line), and assumed that it would be flat zero. If that were true, then the subtraction would've worked. But alas, that is not the case, which is why an entire field on designing filters exists.
Create your filter - for example using [B,A] = butter(N,Wn,'high') where N is the order of the filter - if you are unsure what this is, just set it to 10. Wn is the cutoff frequency normalized between 0 and 1, with 1 corresponding to half the sample rate of the signal. If your sample rate is fs, and you want a cutoff frequency of 10 Hz, you need to set Wn = (10/(fs/2)).
You can then apply the filter by using Y = filter(B,A,X) where X is your signal. You can also look into the filtfilt function.
A cheapo way to do this kind of filtering that doesn't involve straining brain cells on design, zeros and poles and ripple and all that, is:
* Make a copy of the signal
* Smooth it. For a 100KHz signal and wanting to eliminate about 10Hz on down, you'll need to smooth over about 10,000 points. Use a Gaussian smoother, or a box smoother maybe 1/2 that width twice, or whatever is handy. (A simple box smoother of total width 10,000 used once may produce unwanted edge effects)
* Subtract the smoothed version from the original. Baseline drift will be gone.
If the original signal is spikey, you may want to use a short median filter before the big smoother.
This generalizes easily to 2D images, 3D volume data, whatever.