I have a (very) long signal in the form of vector, and I would like to apply a non-linear frequency response on that vector. For example:
v=rand(1000000,1);
nonlinFreqResponse = #(f,v) sqrt(v).*1/f;
V=wfft(v); %windowed FFt, cant do FFT on the entire signal
....?
Note that since the signal is long, running FFT on the entire signal is computationally complex and not feasible.
I believe the best solution is to apply the FFT as usual. Then apply a correction factor, or a transfer function, to your vector that is gain dependent. I'm not sure what's going on with your code, so can't help you there. Good luck!
Related
I have a signal that is both noisy and drifts. I want to calculate the noise of the signal, but I think for this drift should not be taken into account as "noise". using the snr() funciontion in matlab will give me a really high noise value, I think because it takes into account the drift, right?
How can I calculate it? is there any function available for this?
In this picture, for instance, the noise should be around 2% right? ((22.45-22.36)/2)/22.38. (although what I really want is the SNR value)
Thank you!
Filtered signal with low pass filter with a really low frequency:
I would approach this by identifying the drift of the signal with a low pass filter. Just subtract the filtered signal from the original signal. This will lead to noise signal with low drift.
Filtering the signal might be the most difficult task, but by playing around with the filter parameters this will work
I have a set of experimental data s(t) which consists of a vector (with 81 points as a function of time t).
From the physics, this is the result of the convolution of the system response e(t) with a probe p(t), which is a Gaussian (actually a laser pulse). In terms of vector, its FWHM covers approximately 15 points in time.
I want to deconvolve this data in Matlab using the convolution theorem: FT{e(t)*p(t)}=FT{e(t)}xFT{p(t)} (where * is the convolution, x the product and FT the Fourier transform).
The procedure itself is no problem, if I suppose a Dirac function as my probe, I recover exactly the initial signal (which makes sense, measuring a system with a Dirac gives its impulse response)
However, the Gaussian case as a probe, as far as I understood turns out to be a critical one. When I divide the signal in the Fourier space by the FT of the probe, the wings of the Gaussian highly amplifies those frequencies and I completely loose my initial signal instead of having a deconvolved one.
From your experience, which method could be used here (like Hamming windows or any windowing technique, or...) ? This looks rather pretty simple but I did not find any easy way to follow in signal processing and this is not my field.
You have noise in your experimental data, do you? The problem is ill-posed then (non-uniquely solvable) and you need regularization.
If the noise is Gaussian the keywords are Tikhonov regularization or Wiener filtering.
Basically, add a positive regularization factor that acts as a lowpass filter. In your notation the estimation of the true curve o(t) then becomes:
o(t) = FT^-1(FT(e)*conj(FT(p))/(abs(FT(p))^2+l))
with a suitable l>0.
You're trying to do Deconvolution process by assuming the Filter Model is Gaussian Blur.
Few notes for doing Deconvolution:
Since your data is real (Not synthetic) data it includes some kind of Noise.
Hence it is better to use the Wiener Filter (Even with the assumption of low variance noise). Otherwise, the "Deconvolution Filter" will increase the noise significantly (As it is an High Pass basically).
When doing the division in the Fourier Domain zero pad the signals to the correct size or better yet create the Gaussian Filter in the time domain with the same number of samples as the signal.
Boundaries will create artifact, Windowing might be useful.
There are many more sophisticated methods for Deconvolution by defining a more sophisticated model on the signal and the noise. If you have more prior data about them, you should look for this kind of framework.
You can always set a threshold on the amplification level for certain frequencies, do that if needed.
Use as much samples as you can.
I hope this will assist you.
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
Imagine I have a rectangular reference value for the position/displacement x and I need to smooth it.
The math for translatoric movements is quite simple:
speed: v = x'
acceleration: a = v' = x''
jerk. j = a' = v'' = x'''
I need to limit all these values. So I thought about using rate limiters in Simulink:
This approach works perfect for ramp signals, as you can see in the following output:
BUT, my reference signals for x are no ramps, they are rectangles/steps. Hence the rate limiters are not working, because the derivatives they get to limit are already infinite and Simulink throws an error. How can I resolve this problem? Is there actually a more elegant way to implement the high order rate-limiters? I guess this approach could be unstable in some cases.
continue reading: related question
Even though it seems absurd, the following approach is working: integration and instant derivation does the trick:
leading to:
More elegant, faster and simpler solutions for the whole smoothing problem are highly appreciated!
It's generally not a good idea to differentiate signals in Simulink because of numerical issues, I would advise to start with the higher order derivatives (e.g. acceleration) and integrate, much more robust numerically. This is what the doc about the derivative block says:
The Derivative block output might be very sensitive to the dynamics of
the entire model. The accuracy of the output signal depends on the
size of the time steps taken in the simulation. Smaller steps allow a
smoother and more accurate output curve from this block. However,
unlike with blocks that have continuous states, the solver does not
take smaller steps when the input to this block changes rapidly.
Depending on the dynamics of the driving signal and model, the output
signal of this block might contain unexpected fluctuations. These
fluctuations are primarily due to the driving signal output and solver
step size.
Because of these sensitivities, structure your models to use
integrators (such as Integrator blocks) instead of Derivative blocks.
Integrator blocks have states that allow solvers to adjust step size
and improve accuracy of the simulation. See Circuit Model for an
example of choosing the best-form mathematical model to avoid using
Derivative blocks in your models.
See also Best-Form Mathematical Models for more details.
I was trying to do something similar. I was looking for a "Smooth Ramp". Here is what I found:
A simpler approach is to combine ramp with a second order lag. Then the signal approachs s-shape. And your derivatives will exist and be smooth as well. Only thing to remember is that the 2nd or lag must be critically damped.
Y(s) = H(s)*X(s) where H(s) = K*wo^2/(s^2 + 2*zeta*wo*s + wo^2). Here you define zeta = 1.0. Then the s-shape is retained for any K and wo value. Note that X(s) has already been hit by a ramp. In matlab or any other tools, linear ramp and 2nd lag are standard blocks.
Good luck!
I think the 'Transfer Fcn' block is what you're looking for.
If you leave the equation in the default form 1/(s+1) you have a low-pass filter which can be tuned to what you need by changing the numerator and denominator coefficients.
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 ;)