I have an image that I converted to a vector and plotted:
img = imread(image.png');
grayImage = rgb2gray(img);
grayImage(2:2:end,:)=fliplr(grayImage(2:2:end,:));
B = rot90(grayImage);
C = flipud(B);
[x,y]=size(C);
vector = reshape(C ,1,x*y);
plot(vector);
The problem is that although I can visually see a wave pattern, there is a lot of noise that occurs. By noise I mean the signals rapidly go up and down eventually forming a sinusoidal wave but I want to be able to just connect the crest of each spike to one another in order to create a continuous wave pattern. If anyone understands what I am trying to do, help would be appreciated.
Thank you in advance.
Not 100% sure about what you're asking, but the medfilt1 median filter function might be what you're looking for, it's a 1D smoothing filter. Example usage would be:
vector_filt = medfilt1(vector);
Check out the documentation and example at http://www.mathworks.com/help/signal/ref/medfilt1.html.
I think performing a gaussian convolution on the vector should solve your problem. Here is a link to a stack overflow question that has a very nice answer on how to do a gaussian convolution in matlab: Gaussian Filter on a vector in Matlab
Related
I have a signal 's' of voice of which you can see an extract here:
I would like to plot the zero crossing points in the same graph. I have tried with the following code:
zci = #(v) find(v(:).*circshift(v(:), [-1 0]) <= 0); % Returns Zero-Crossing Indices Of Argument Vector
zx = zci(s);
figure
set(gcf,'color','w')
plot(t,s)
hold on
plot(t(zx),s(zx),'o')
But it does not interpole the points in which the sign change, so the result is:
However, I'd like that the highlighted points were as near as possible to zero.
I hope someone can help me. Thanks you for your responses in advanced.
Try this?
w = 1;
crossPts=[];
for k=1:(length(s)-1)
if (s(k)*s(k+1)<0)
crossPts(w) = (t(k)+t(k+1))/2;
w = w + 1;
end
end
figure
set(gcf,'color','w')
plot(t,s)
hold on
plot(t, s)
plot(crossPts, zeros(length(crossPts)), 'o')
Important questions: what is the highest frequency conponent of the signal you are measuring? Can you remeasure this signal? What is your sampling rate? What is this analysis for? (Schoolwork or scholarly research). You may have quite a bit of trouble measuring the zeros of this function with any significance or accurracy because it looks like your waveform has a frequency greater than half of your sampling rate (greater than your Nyquist frequency). Upsampling/interpolating your entire waveform will allow you to find the zeros much more precisely (but with no greater degree of accurracy) but this is a huge no-no in the scientific community. While my method may not look super pretty, it's the most accurate method that doesn't make unsafe assumptions. If you just want it to look pretty, I would recommend interp1 and using the 'Spline' method. You can interpolate the whole waveform and then use the above answer to find more accurate zeros.
Also, you could calculate the zeros on the interpolated waveform and then display it on the raw data.
A remotely possible solution to improve your data;
If you're measuring a human voice, why not try filtering at the range of human speech? This should be fine mathematically and could possibly improve your waveform.
I'm just learning Matlab and the fast fourier transform algorithm.
As a first step I tried to duplicate this example: https://en.wikipedia.org/wiki/Fourier_transform#Example
I use the following code:
t = -6:0.01:6;
s = cos(2 * pi * 3 * t) .* exp(-pi * t.^2);
figure(1);
plot(t, s);
xlim([-2 2]);
r = fft(s);
figure(2);
plot(t, abs(r));
And I obtained the following picture:
Figure 2:
Figure 1 is OK, but Figure 2 is not. I see one of the problem is that in Figure 2 I should plot vector r against frequency, not against time. Another problem in Figure 2 is the scale in the Y-axis.
Thus, I have 2 questions in order to duplicate the example:
How can I obtain the frequency domain (X-axis in Figure 2)?
How should I scale vector r (Y-axis in Figure 2)?
Your issue is that you aren't actually creating a frequency vector to plot the fft against. The reason that the fft is plotted against time is because that is what you specified in your plot command.
Here is a working fft outline:
N=length(t);
index=0:N-1;
FrequencyResolution=SamplingRate/N;
Frequency=index.*FrequencyResolution;
data_fft=fft(detrend(data));
%the detrend isn't necessary but it does look nicer because it focuses the plot on changes around the mean of the data
data_FFTmagnitude=abs(data_fft);
plot(Frequency, data_FFTmagnitude)
I remember once for the first time that I wanted to use DFT and FFT for one of my study projects I used this webpage, it explains in detail with examples on how to do so. I suggest you go through it and try to replicate for your case, doing so will give you insight and better understanding of the way one can use FFt as you said you are new to Matlab. Do not hesitate to ask again if you need more detailed help.
And also keep in mind that for FFT it is better to have signal length of a power of 2, that way you will get the most exact results, and if you cannot control your signal length you can take the largest power of 2 close to that length, as everyone usually does.
I am looking at some FFT code in a matlab project and the FFT and inverse FFT is computed this way:
% Here image is a 2D image.
image_fft = fftshift(image,1);
image_fft = fftshift(image_fft,2);
image_fft = fft(image_fft,[],1);
image_fft = fft(image_fft,[],2);
image_fft = fftshift(image_fft,1);
image_fft = fftshift(image_fft,2);
% Some processing and then same sequence of fftshift, ifft and fftshift to move to
% time domain
I tried to find some information online but am having trouble wondering why the fftshift needs to be done before computing the FFT.
Another question I have is whether this is something really Matlab specific. For example, I am planning to port this code to C++ and use KISS FFT. Do I need to be vary of this?
The reason why people like to swap prior to the DFT is because it makes the center pixel of the image the one with zero-phase shift. It often makes algorithms that depend on phase easier to think about and implement. It is not matlab specific and if you want to port an exact version of the code to another language, you'll need to perform the quadswap beforehand too.
EDIT:
Let me give an example that I hope will clear things up. Let's say that our image is the sum of a bunch of sinc functions with varying locations throughout the image. In the frequency domain, each of these sinc functions is a rect function with the same amplitude but with a different linear phase component that determines the location of the sinc in the image domain. By swapping the image prior to taking the DFT, we make the linear phase component of the frequency domain representation of the center pixel be zero. Moreover, the linear phase components of the other sinc functions will now be a function of their distance from the center pixel. If we didn't swap the image beforehand, then the linear phase components of the rect functions would be a function of their distance from the pixel in the top-left of the image. This would be non-intutive and would involve the same kind of phase wrapping considerations that one sees with equating the frequencies in the range (pi,2pi) rad/sample with more the intuitive (-pi,0) rad/sample.
For images, it's better to use fft2. It's matlab's convention to arrange 2D ffts with the DC in the corners. Presumably because of the row/array conventions. fftshift allows for a more intuitive display of the FFT with the DC in the center.
I don't fully understand what the piece of code you copied is about, here is an example of fft and inverse fft of an image using matlab.
And a more detailed tutorial here.
To do a low-pass filter, I have used a Gaussian kernel, then do a convolution with this kernel to have the smoothed version of my image. Since the spline basis function tend to give a sharper cut-off, I would like to build a spline 2d kernel. Does anyone have an idea about this? Thank you in advance!
Thank you for your response. In fact I have a look on butterworth filter, but I suppose it is in frequency domain and require infinite support. My problem is very specific. I want to find the coefficients matrix that apply the filtering directly on the image.
I have use Gaussian as following:
Build the kernel
Gau2D=#(x,y) 1/(sigma*2*pi)*exp(-(x.^2+y.^2)/sigma^2/2);
[x,y] = meshgrid(-(k)/2:(k)/2);
ker = Gau2D(x,y);
ker = ker./sum(ker(:));
BLUR = convmtx2(ker,[M N]);
Apply on an image
img_filtered=BLUR*img(:);
I am thinking, for example, instead of using Gaussian kernel, I can use something like cardinal spline kernel, to increase the sharpness of the filter. But still, I can find the way to deal with it. Please help!
I was given this task, I am a noob and need some pointers to get started with centroid calculation in Matlab:
Instead of an image first I was asked to simulate a Gaussian distribution(2 dimensional), add noise(random noise) and plot the intensities, now the position of the centroid changes due to noise and I need to bring it back to its original position by
-clipping level to get rid of the noise, noise reduction by clipping or smoothing, sliding average (lpf) (averaging filter 3-5 samples ), calculating the means or using Convolution filter kernel - which does matrix operations which represent the 2-D images
Since you are a noob, even if we wrote down the answer verbatim you probably won't understand how it works. So instead I'll do what you asked, give you pointers and you'll have to read the related documentation :
a) to produce a 2-d Gaussian use meshgrid or ndgrid
b) to add noise to the image look into rand ,randn or randi, depending what exactly you need.
c) to plot the intensities use imagesc
d) to find the centroid there are several ways, try to further search SO, you'll find many discussions. Also you can check TMW File exchange for different implementations for that.