I have 2 FFT spectrums on a plot. I want to get the top 5 maximum points of the overall plot. I get the maximum points separately for each spectrum. How can i combine these spectrums into one and get the overall maximum 5 points?
You have two separate maximum matrix: lets Max1 and Max2
Now combine both of them to form third matrix
Max3 = [Matx1 Max2]
Sort the Max3 in descending order
Max3 = sort(Max3,'descend');
Extract the first 5 element
peaks = Max3(1:5)
Put the spectra in one vector and sort them in descending order.
spec1 = fft(x1); % a spectrum (column vector)
spec2 = fft(x2); % another spectrum (column vector)
dummy = abs([spec1; spec2]); % concatenate absolute values
sorted = sort(dummy, 'descending');
five_greatest = sorted(1:5);
Related
In Matlab, given a vector A (please, find it here: https://www.dropbox.com/s/otropedwxj0lki7/A.mat?dl=0 ), how could I find the n-samples vector subset with the smallest range (or standard deviation)?
I am trying a potential solution: reshaping the vector in columns, performing range of each column and selecting the smallest. However, reshape does not always works well when applied to other examples with different lengths. How could this be worked around in an easier and more efficient way?
Fs = 1000; % sampling frequency
time = round(length(A)/Fs)-1; % calculate approximated rounded total length in time
A_reshaped = reshape(A(1:time*Fs), [], time/2); % reshape A (deleting some samples at the end) in time/2 columns
D(1,:) = mean(A_reshaped);
D(2,:) = range(A_reshaped);
[~,idx] = min(D(2,:));
Value = D(1,idx);
Any help is much appreciated.
To find the n-sample with minimum range you can sort the vector and subtract the first section of the sorted vector from the last section. Then use index of the minimum to find the n-sample:
n=4
a= rand(1,10);
s= sort(a);
[~,I]=min(s(n:end)-s(1:end-n+1))
result = s(I:I+n-1)
I have two matrices A and B. The size of A is 200*1000 double (here: 1000 represents 1000 different features). Matrix A belongs to group 1, where I use ones(200,1) as the label vector. The size of B is also 200*1000 double (here: 1000 also represents 1000 different features). Matrix B belongs to group 2, where I use -1*ones(200,1) as the label vector.
My question is how do I visualize matrices A and B so that I can clearly distinguish them based on the given groups?
I'm assuming each sample in your matrices A and B is determined by a row in either matrix. If I understand you correctly, you want to draw a series of 1000-dimensional vectors, which is impossible. We can't physically visualize anything beyond three dimensions.
As such, what I suggest you do is perform a dimensionality reduction to reduce your data so that each input is reduced to either 2 or 3 dimensions. Once you reduce your data, you can plot them normally and assign a different marker to each point, depending on what group they belonged to.
If you want to achieve this in MATLAB, use Principal Components Analysis, specifically the pca function in MATLAB, that calculates the residuals and the reprojected samples if you were to reproject them onto a lower dimensionality. I'm assuming you have the Statistics Toolbox... if you don't, then sorry this won't work.
Specifically, given your matrices A and B, you would do this:
[coeffA, scoreA] = pca(A);
[coeffB, scoreB] = pca(B);
numDimensions = 2;
scoreAred = scoreA(:,1:numDimensions);
scoreBred = scoreB(:,1:numDimensions);
The second output of pca gives you reprojected values and so you simply have to determine how many dimensions you want by extracting the first N columns, where N is the desired number of dimensions you want.
I chose 2 for now, and we can see what it looks like in 3 dimensions after. Once we have what we need for 2 dimensions, it's just a matter of plotting:
plot(scoreAred(:,1), scoreAred(:,2), 'rx', scoreBred(:,1), scoreBred(:,2), 'bo');
This will produce a plot where the samples from matrix A are with red crosses while the samples from matrix B are with blue circles.
Here's a sample run given completely random data:
rng(123); %// Set seed for reproducibility
A = rand(200,1000); B = rand(200,1000); %// Generate random data
%// Code as before
[coeffA, scoreA] = pca(A);
[coeffB, scoreB] = pca(B);
numDimensions = 2;
scoreAred = scoreA(:,1:numDimensions);
scoreBred = scoreB(:,1:numDimensions);
%// Plot the data
plot(scoreAred(:,1), scoreAred(:,2), 'rx', scoreBred(:,1), scoreBred(:,2), 'bo');
We get this:
If you want three dimensions, simply change numDimensions = 3, then change the plot code to use plot3:
plot3(scoreAred(:,1), scoreAred(:,2), scoreAred(:,3), 'rx', scoreBred(:,1), scoreBred(:,2), scoreBred(:,3), 'bo');
grid;
With those changes, this is what we get:
I have some travel time data stored as column vectors. I want to write a script that will allow me run a linear interpolation from specified initial and final values, to make a column of distances, so I can calculate velocity.
example: Column 1: t1,t2,t3......tn; Column 2: (using the linear interpolation we create) d1, d2, d3....dn
So here we have generated a distance for each travel time based on an initial distance and a final distance.
then it should be simple to generate a new column that is simply the interpolated distances / travel times. Thanks for your help. Cheers
interp1 is your friend here:
% from zero to one hour
measuredTime = [0 1];
% from 0 to 100 km
measuredDistance = [0 100];
% 10 minute intervals
intermediateTimes = measuredTime(1):10/60:measuredTime(end);
% interpolated distances
intermediateDistances = interp1(measuredTime,measuredDistance,intermediateTimes);
I have a matrix of multiple particle trajectories that I would like to analyze separately The trajectory number is one of the columns of the matrix, so I am trying to sort based on that number. I am using some of the code from this answer: MSD with matlab (which was very helpful, thank you!) to calculate MSD, but I am having difficulty parsing out the individual trajectories. To explain in more detail what I am trying to do: I have trajectory outputs that are in matrix format, with one column for trajectory number, one column for x-position, one column for y-position, etc. I want to be able to take this information and calculate the mean-squared displacement for each trajectory. In order to do this, I have to create a way to distinguish data points based on trajectory number (which is listed in row 7 of mymatrix). This seems to be where I am having trouble. The important columns in this matrix are 1: x-position, 2: y-position and 7: trajectory number. So far I have
total_rows=size(mymatrix,1);
max_trajectory_number=mymatrix(total_rows,7);
nData=0;
msd=zeros(total_rows, 4)
for i=0:max_trajectory_number
trajectornumber= mymatrix(i,7);
if trajectorynumber.equals(i)
nData=nData+1; %counts the number of instances of this trajectory number, which is the number of data points in the trajectory
for dt = 1:nData
deltaCoords = mymatrix(1+dt:end,1:2) - traj0mat(1:end-dt,1:2); %calculates time-averaged MSD based on y and y positions in colums 1 and 2 respectively
squaredDisplacement = sum(deltaCoords.^2,2); %# dx^2+dy^2+dz^2
msd(dt,1) = trajectorynumber; %trajectory number
msd(dt,2) = mean(squaredDisplacement); %# average
msd(dt,3) = std(squaredDisplacement); %# std
msd(dt,4) = length(squaredDisplacement); %# n
end
end
Unfortunately when I run this on mymatrix, the resulting msd matrix remains all zeros. I think this is likely due to an error in sorting based on the trajectory number. I do not get an error just not the results I was looking for
If anyone has any suggestions on how to fix this, it would be greatly appreciated.
It looks like you want to bundle all rows identified by the same trajectory number. I assume that they show up in chronological order as you continue down a column. Then try something like
tnumbs = unique(mymatrix(:,7)); % identify unique trajectory numbers
for i=1:length(tnumbs) % loop through trajectories
icurr = find(mymatrix(:,7)==tnumbs(i)); % find indices to entries for current trajectory
% perform your averaging
deltaCoords = mymatrix(icurr(1+dt:end),1:2) - traj0mat(icurr(1:end-dt),1:2); %calculates time-averaged MSD based on y and y positions in colums 1 and 2 respectively
squaredDisplacement = sum(deltaCoords.^2,2); %# dx^2+dy^2+dz^2
msd(i,1) = tnumbs(i); %trajectory number
msd(i,2) = mean(squaredDisplacement); %# average
msd(i,3) = std(squaredDisplacement); %# std
msd(i,4) = length(squaredDisplacement); %# n
end
I have channel measurements which has values > 20,000, which has to be divided into discrete levels, as in my case K=8 and which has to be mapped to channel measurements with states. I have to find state-transition probability matrix for this in Matlab.
My question is, I need to know how to divide these values into 8 states and to find the state-transition probability matrix for these 8 states in Matlab.
Here is a made-up example:
%# some random vector (load your data here instead)
x = randn(1000,1);
%# discretization/quantization into 8 levels
edges = linspace(min(x),max(x),8+1);
[counts,bins] = histc(x, edges);
%# fix last level of histc output
last = numel(counts);
bins(bins==last) = last - 1;
counts(last-1) = counts(last-1) + counts(last);
counts(last) = [];
%# show histogram
bar(edges(1:end-1), counts, 'histc')
%# transition matrix
trans = full(sparse(bins(1:end-1), bins(2:end), 1));
trans = bsxfun(#rdivide, trans, sum(trans,2));
A few things to note:
Discretization is performed simply by dividing the whole range of data into 8 bins. This is done using histc. Note that due to the way the function works, we had to combine the last two counts and fix the bins accordingly.
the transition matrix is computed by first counting the co-occurrences using a less-known call form of the sparse function. The accumarray could have also been used. The count matrix is then normalized to obtain probabilities that sum to one.
You mentioned that your MC model should only allow transitions between adjacent states (1 to 2 or 8 to 7, but not between 2 and 5). I did not enforce this fact since this should be a property of the data itself, which is not applicable in this example with random data.