I am trying to do a spectrogram analysis on a song. Currently I have about a 10 second clip from a song and am attempting to find the local peaks.
All I really want is to have a scatter plot showing local maxima within some NxN neighborhood worth of amplitudes
[y,fs] = audioread('audio_file.wav');
window = hamming(512);
num_overlap = 256;
nfft = 1024;
[S,F,T,P] = spectrogram(y(:,1), window, num_overlap, nfft, fs, 'yaxis');
surf(T,F,10*log10(P), 'edgecolor', 'none'); axis tight; view(0, 90); colormap hot;
This results in the below image:
Where the x-axis is of course time [0,~10], y-axis is frequency [0,22.5 KHz] and the z-axis is the amplitude
Now What I would like to do is create a 3D scatter plot over this surf to show where the peaks are. The dimensions of S, F, T, P are
S: 513 x 1770 complex double
F: 513 x 1 double
T: 1 x 1770 double
P: 513 x 1770 double
Now this is where I am pretty sure I am doing something wrong or not understanding MATLAB entirely.
msk = true(3,3,3);
msk(2,2,2) = false;
dil = imdilate(10*log10(P), msk);
M = 10*log10(P) > dil;
My understanding is that will get me a 1 wherever my local peak is
Now let's just say that amp = 10*log10(P), I would like to just be able to call scatter3 the same way I called surf, like so:
scatter3(T, F, amp(M))
but of course I get X, Y and Z must be vectors of the same length. I suppose that makes sense to me so I decided to repeat the values as many times as they needed to be to get the axes equal.
Tr = repelem(T, 513)';
Fr = repelem(F, 1770);
Zr = reshape(amp, [908010, 1]);
[pks, locs] = findpeaks(Zr);
scatter3(Tr(locs), Fr(locs), Zr(locs));
This results in a 3D scatter plot like so:
And that is definitely not right because there should be many local peaks throughout the amplitude shown. I'm not really sure what I'm doing wrong, but I'm also almost positive that there's an easier way to achieve what I want. All I really want is to have a scatter plot showing local maxima within some NxN neighborhood worth of amplitudes
If I understand want you want, you have a matrix M with local peaks and your want to draw scatter in the locations of the peaks. You can get the row\col of each peak using find and the linear index using sub2ind:
[Fi,Ti] = find(10*log10(P) > dil);
Pi = sub2ind(size(P),Fi,Ti);
scatter3(T(Ti),F(Fi),amp(Pi));
Related
MATLAB's surf command allows you to pass it optional X and Y data that specify non-cartesian x-y components. (they essentially change the basis vectors). I desire to pass similar arguments to a function that will draw a line.
How do I plot a line using a non-cartesian coordinate system?
My apologies if my terminology is a little off. This still might technically be a cartesian space but it wouldn't be square in the sense that one unit in the x-direction is orthogonal to one unit in the y-direction. If you can correct my terminology, I would really appreciate it!
EDIT:
Below better demonstrates what I mean:
The commands:
datA=1:10;
datB=1:10;
X=cosd(8*datA)'*datB;
Y=datA'*log10(datB*3);
Z=ones(size(datA'))*cosd(datB);
XX=X./(1+Z);
YY=Y./(1+Z);
surf(XX,YY,eye(10)); view([0 0 1])
produces the following graph:
Here, the X and Y dimensions are not orthogonal nor equi-spaced. One unit in x could correspond to 5 cm in the x direction but the next one unit in x could correspond to 2 cm in the x direction + 1 cm in the y direction. I desire to replicate this functionality but drawing a line instead of a surf For instance, I'm looking for a function where:
straightLine=[(1:10)' (1:10)'];
my_line(XX,YY,straightLine(:,1),straightLine(:,2))
would produce a line that traced the red squares on the surf graph.
I'm still not certain of what your input data are about, and what you want to plot. However, from how you want to plot it, I can help.
When you call
surf(XX,YY,eye(10)); view([0 0 1]);
and want to get only the "red parts", i.e. the maxima of the function, you are essentially selecting a subset of the XX, YY matrices using the diagonal matrix as indicator. So you could select those points manually, and use plot to plot them as a line:
Xplot = diag(XX);
Yplot = diag(YY);
plot(Xplot,Yplot,'r.-');
The call to diag(XX) will take the diagonal elements of the matrix XX, which is exactly where you'll get the red patches when you use surf with the z data according to eye().
Result:
Also, if you're just trying to do what your example states, then there's no need to use matrices just to take out the diagonal eventually. Here's the same result, using elementwise operations on your input vectors:
datA = 1:10;
datB = 1:10;
X2 = cosd(8*datA).*datB;
Y2 = datA.*log10(datB*3);
Z2 = cosd(datB);
XX2 = X2./(1+Z2);
YY2 = Y2./(1+Z2);
plot(Xplot,Yplot,'rs-',XX2,YY2,'bo--','linewidth',2,'markersize',10);
legend('original','vector')
Result:
Matlab has many built-in function to assist you.
In 2D the easiest way to do this is polar that allows you to make a graph using theta and rho vectors:
theta = linspace(0,2*pi,100);
r = sin(2*theta);
figure(1)
polar(theta, r), grid on
So, you would get this.
There also is pol2cart function that would convert your data into x and y format:
[x,y] = pol2cart(theta,r);
figure(2)
plot(x, y), grid on
This would look slightly different
Then, if we extend this to 3D, you are only left with plot3. So, If you have data like:
theta = linspace(0,10*pi,500);
r = ones(size(theta));
z = linspace(-10,10,500);
you need to use pol2cart with 3 arguments to produce this:
[x,y,z] = pol2cart(theta,r,z);
figure(3)
plot3(x,y,z),grid on
Finally, if you have spherical data, you have sph2cart:
theta = linspace(0,2*pi,100);
phi = linspace(-pi/2,pi/2,100);
rho = sin(2*theta - phi);
[x,y,z] = sph2cart(theta, phi, rho);
figure(4)
plot3(x,y,z),grid on
view([-150 70])
That would look this way
I have a set of data with over 4000 points. I want to exclude grooves from them, ideally from the point from which they start. The data look for example like this:
The problem with this is the noise I get at the top of the plateaus. I have an idea, in which I would take an average value of the most common within some boundaries (again, ideally sth like the red line here:
and then I would construct a temporary matrix, which would fill up one by one with Y if they are less than this average. If the Y(i) would rise above average, the matrix would find its minima and compare it with the global minima. If the temporary matrix's minima wouldn't be sth like 80% of the global minima, it would be discarded as noise.
I've tried using mean(Y), interpolating and fitting it in a polynomial (the green line) - none of those method would cut it to the point I would be satisfied.
I need this to be extremely robust and it doesn't need to be quick. The top and bottom values can vary a lot, as well as the shape of the plateaus. The groove width is more or less the same.
Do you have any ideas? Again, the point is to extract the values that would make the groove.
How about a median filter?
Let's define some noisy data similar to yours, and plot it in blue:
x = .2*sin((0:9999)/1000); %// signal
x(1000:1099) = x(1000:1099) + sin((0:99)/50*pi); %// noise: spike
x(5000:5199) = x(5000:5199) - sin((0:199)/100*pi); %// noise: wider spike
x = x + .05*sin((0:9999)/10); %// noise: high-freq ripple
plot(x)
Now apply the median filter (using medfilt2 from the Image Processing Toolbox) and plot in red. The parameter k controls the filter memory. It should chosen to be large compared to noise variations, and small compared to signal variations:
k = 500; %// filter memory. Choose as needed
y = medfilt2(x,[1 k]);
hold on
plot(y, 'r', 'linewidth', 2)
In case you don't have the image processing toolbox and can't use medfilt2 a method that's more manual. Skip the extreme values, and do a curve fit with sin1 as curve type. Note that this will only work if the signal is in fact a sine wave!
x = linspace(0,3*pi,1000);
y1 = sin(x) + rand()*sin(100*x).*(mod(round(10*x),5)<3);
y2 = 20*(mod(round(5*x),5) == 0).*sin(20*x);
y = y1 + y2; %// A messy sine-wave
yy = y; %// Store the messy sine-wave
[~, idx] = sort(y);
y(idx(1:round(0.15*end))) = y(idx(round(0.15*end))); %// Flatten out the smallest values
y(idx(round(0.85*end):end)) = y(idx(round(0.85*end)));%// Flatten out the largest values
[foo goodness output] = fit(x.',y.', 'sin1'); %// Do a curve fit
plot(foo,x,y) %// Plot it
hold on
plot(x,yy,'black')
Might not be perfect, but it's a step in the right direction.
i just started with my master thesis and i already am in trouble with my capability/understanding of matlab.
The thing is, i have a trajectory on a surface of a planet/moon whatever (a .mat with the time, and the coordinates. Then i have some .mat with time and the measurement at that time.
I am able to plot this as a color coded trajectory (using the measurement and the coordinates) in scatter(). This works awesomely nice.
However my problem is that i need something more sophisticated.
I now need to take the trajectory and instead of color-coding it, i am supposed to add the graph (value) of the measurement (which is given for each point) to the trajectory (which is not always a straight line). I will added a little sketch to explain what i want. The red arrow shows what i want to add to my plot and the green shows what i have.
You can always transform your data yourself: (using the same notation as #Shai)
x = 0:0.1:10;
y = x;
m = 10*sin(x);
So what you need is the vector normal to the curve at each datapoint:
dx = diff(x); % backward finite differences for 2:end points
dx = [dx(1) dx]; % forward finite difference for 1th point
dy = diff(y);
dy = [dy(1) dy];
curve_tang = [dx ; dy];
% rotate tangential vectors 90° counterclockwise
curve_norm = [-dy; dx];
% normalize the vectors:
nrm_cn = sqrt(sum(abs(curve_norm).^2,1));
curve_norm = curve_norm ./ repmat(sqrt(sum(abs(curve_norm).^2,1)),2,1);
Multiply that vector with the measurement (m), offset it with the datapoint coordinates and you're done:
mx = x + curve_norm(1,:).*m;
my = y + curve_norm(2,:).*m;
plot it with:
figure; hold on
axis equal;
scatter(x,y,[],m);
plot(mx,my)
which is imo exactly what you want. This example has just a straight line as coordinates, but this code can handle any curve just fine:
x=0:0.1:10;y=x.^2;m=sin(x);
t=0:pi/50:2*pi;x=5*cos(t);y=5*sin(t);m=sin(5*t);
If I understand your question correctly, what you need is to rotate your actual data around an origin point at a certain angle. This is pretty simple, as you only need to multiply the coordinates by a rotation matrix. You can then use hold on and plot to overlay your plot with the rotated points, as suggested in the comments.
Example
First, let's generate some data that resembles yours and create a scatter plot:
% # Generate some data
t = -20:0.1:20;
idx = (t ~= 0);
y = ones(size(t));
y(idx) = abs(sin(t(idx)) ./ t(idx)) .^ 0.25;
% # Create a scatter plot
x = 1:numel(y);
figure
scatter(x, x, 10, y, 'filled')
Now let's rotate the points (specified by the values of x and y) around (0, 0) at a 45° angle:
P = [x(:) * sqrt(2), y(:) * 100] * [1, 1; -1, 1] / sqrt(2);
and then plot them on top of the scatter plot:
hold on
axis square
plot(P(:, 1), P(:, 2))
Note the additional things have been done here for visualization purposes:
The final x-coordinates have been stretched (by sqrt(2)) to the appropriate length.
The final y-coordinates have been magnified (by 100) so that the rotated plot stands out.
The axes have been squared to avoid distortion.
This is what you should get:
It seems like you are interested in 3D plotting.
If I understand your question correctly, you have a 2D curve represented as [x(t), y(t)].
Additionally, you have some value m(t) for each point.
Thus we are looking at the plot of a 3D curve [x(t) y(t) m(t)].
you can easily achieve this using
plot3( x, y, m ); % assuming x,y, and m are sorted w.r.t t
alternatively, you can use the 3D version of scatter
scatter3( x, y, m );
pick your choice.
Nice plot BTW.
Good luck with your thesis.
I apologize for the ambiguous title, but I am not entirely sure how to phrase this one. So bear with me.
I have a matrix of data. Each column and row represents a certain vector (column 1 = row 1, column 2 = row 2, etc.), and every cell value is the cosine similarity between the corresponding vectors. So every value in the matrix is a cosine.
There are a couple of things I want to do with this. First, I want to create a figure that shows all of the vectors on it. I know the cosine of the angle between every vector, and I know the magnitude of each vector, but that is the only information I have - is there some algorithm I can implement that will run through all of the various pair-wise angles and display it graphically? That is, I don't know where all the vectors are in relation to each other, and there are too many data points to do this by hand (e.g. if I only had three vectors, and the angles between them all were 45, 12, and 72 degrees it would be trivial). So how do I go about doing this? I don't even have the slightest idea what sort of mathematical function I would need to do this. (I have 83 vectors, so that's thousands of cosine values). So basically this figure (it could be either 2D or multidimensional, and to be honest I would like to do both) would show all of the vectors and how they relate to each other in space (so I could compare both angles and relative magnitudes).
The other thing I would like to do is simpler but I am having a hard time figuring it out. I can convert the cosine values into Cartesian coordinates and display them in a scatter plot. Is there a way to connect each of the points of a scatter plot to (0,0) on the plot?
Finally, in trying to figure out how to do some of the above on my own I have run into some inconsistencies. I calculated the mean angles and Cartesian coordinates for each of the 83 vectors. The math for this is easy, and I have checked and double-checked it. However, when I try to plot it, different plotting methods give me radically different things. So, if I plot the Cartesian coordinates as a scatter plot I get this:
If I plot the mean angles in a compass plot I get this:
And if I use a quiver plot I get something like this (I transformed this a little by shifting the origin up and to the right just so you can see it better):
Am I doing something wrong, or am I misunderstanding the plotting functions I am using? Because these results all seem pretty inconsistent. The mean angles on the compass plot are all <30 degrees or so, but on the quiver plot some seem to exceed 90 degrees, and on the scatter plot they extend above 30 as well. What's going on here?
(Here is my code:)
cosine = load('LSA.txt');
[rows,columns]=size(cosine);
p = cosine.^2;
pp = bsxfun(#minus, 1, p);
sine = sqrt(pp);
tangent = sine./cosine;
Xx = zeros(rows,1);
Yy = zeros(rows,1);
for i = 1:columns
x = cosine(:,i);
y = sine(:,i);
Xx(i,1) = sum(x) * (1/columns);
Yy(i,1) = sum(y) * (1/columns);
end
scatter(Xx,Yy);
Rr = zeros(rows,1);
Uu = zeros(rows,1);
for j = 1:rows
Rr(j,1) = sqrt(Xx(j,1).^2 + Yy(j,1).^2);
Uu(j,1) = atan2(Xx(j,1),Yy(j,2));
end
%COMPASS PLOT
[theta,rho] = pol2cart(Uu,1);
compass(theta,rho);
%QUIVER PLOT
r = 7;
sx = ones(size(cosine))*2; sy = ones(size(cosine))*2;
pu = r * cosine;
pv = r * sine;
h = quiver(sx,sy,pu,pv);
set(gca, 'XLim', [1 10], 'YLim', [1 10]);
You can exactly solve this problem. The dot product calculates the cosine. This means your matrix is actually M=V'*V
This should be solvable through eigenvalues. And you said you also have the length.
Your only problem - as your original matrix the vectors will be 83 dimensional. Not easy to plot in 2 or 3 dimensions. I think you are over simplifying by just using the average angle. There are some techniques called dimensionality reduction - here's a toolbox. I would suggest a sammon projection on 1-cosine (as this would be the distance of points on the unit ball) to calculate the vectors for such a plot.
In the quiver plot, you are plotting all of the data in the cosine and sine matrices. In the other plots, you are only plotting the means. The first two plots appear to match up, so no problem there.
A few other things. I notice that in
Uu(j,1) = atan2(Xx(j,1),Yy(j,2));
Yy(j,2) is not actually defined, so it seems like this code should fail.
Furthermore, you could define Yy and Xx as:
Xx = mean(cosine,2);
Yy = mean(sine,2);
And also get rid of the other for loop:
Rr = sqrt(Xx.^2 + Yy.^2)
Uu = atan2(Xx,Yy)
I still have to think about your first question, but I hope this was helpful.
I have a problem dealing with 3rd dimension plot for three variables.
I have three matrices: Temperature, Humidity and Power. During one year, at every hour, each one of the above were measured. So, we have for each matrix 365*24 = 8760 points. Then, one average point is taken every day. So,
Tavg = 365 X 1
Havg = 365 X 1
Pavg = 365 X 1
In electrical point of veiw, the power depends on the temperature and humidity. I want to discover this relation using a three dimensional plot.
I tried using mesh, meshz, surf, plot3, and many other commands in MATLAB but unfortunately I couldn't get what I want. For example, let us take first 10 days. Here, every day is represented by average temperature, average humidity and average power.
Tavg = [18.6275
17.7386
15.4330
15.4404
16.4487
17.4735
19.4582
20.6670
19.8246
16.4810];
Havg = [75.7105
65.0892
40.7025
45.5119
47.9225
62.8814
48.1127
62.1248
73.0119
60.4168];
Pavg = [13.0921
13.7083
13.4703
13.7500
13.7023
10.6311
13.5000
12.6250
13.7083
12.9286];
How do I represent these matrices by three dimension plot?
The challenge is that the 3-D surface plotting functions (mesh, surf, etc.) are looking for a 2-D matrix of z values. So to use them you need to construct such a matrix from the data.
Currently the data is sea of points in 3-D space, so, you have to map these points to a surface. A simple approach to this is to divide up the X-Y (temperature-humidity) plane into bins and then take the average of all of the Z (power) data. Here is some sample code for this that uses accumarray() to compute the averages for each bin:
% Specify bin sizes
Tbin = 3;
Hbin = 20;
% Create binned average array
% First create a two column array of bin indexes to use as subscripts
subs = [round(Havg/Hbin)+1, round(Tavg/Tbin)+1];
% Now create the Z (power) estimate as the average value in each bin
Pest = accumarray(subs,Pavg,[],#mean);
% And the corresponding X (temp) & Y (humidity) vectors
Tval = Tbin/2:Tbin:size(Pest,2)*Tbin;
Hval = Hbin/2:Hbin:size(Pest,1)*Hbin;
% And create the plot
figure(1)
surf(Tval, Hval, Pest)
xlabel('Temperature')
ylabel('Humidity')
zlabel('Power')
title('Simple binned average')
xlim([14 24])
ylim([40 80])
The graph is a bit coarse (can't post image yet, since I am new) because we only have a few data points. We can enhance the visualization by removing any empty bins by setting their value to NaN. Also the binning approach hides any variation in the Z (power) data so we can also overlay the orgional point cloud using plot3 without drawing connecting lines. (Again no image b/c I am new)
Additional code for the final plot:
%% Expanded Plot
% Remove zeros (useful with enough valid data)
%Pest(Pest == 0) = NaN;
% First the original points
figure(2)
plot3(Tavg, Havg, Pavg, '.')
hold on
% And now our estimate
% The use of 'FaceColor' 'Interp' uses colors that "bleed" down the face
% rather than only coloring the faces away from the origin
surfc(Tval, Hval, Pest, 'FaceColor', 'Interp')
% Make this plot semi-transparent to see the original dots anb back side
alpha(0.5)
xlabel('Temperature')
ylabel('Humidity')
zlabel('Power')
grid on
title('Nicer binned average')
xlim([14 24])
ylim([40 80])
I think you're asking for a surface fit for your data. The Curve Fitting Toolbox handles this nicely:
% Fit model to data.
ft = fittype( 'poly11' );
fitresult = fit( [Tavg, Havg], Pavg, ft);
% Plot fit with data.
plot( fitresult, [xData, yData], zData );
legend( 'fit 1', 'Pavg vs. Tavg, Havg', 'Location', 'NorthEast' );
xlabel( 'Tavg' );
ylabel( 'Havg' );
zlabel( 'Pavg' );
grid on
If you don't have the Curve Fitting Toolbox, you can use the backslash operator:
% Find the coefficients.
const = ones(size(Tavg));
coeff = [Tavg Havg const] \ Pavg;
% Plot the original data points
clf
plot3(Tavg,Havg,Pavg,'r.','MarkerSize',20);
hold on
% Plot the surface.
[xx, yy] = meshgrid( ...
linspace(min(Tavg),max(Tavg)) , ...
linspace(min(Havg),max(Havg)) );
zz = coeff(1) * xx + coeff(2) * yy + coeff(3);
surf(xx,yy,zz)
title(sprintf('z=(%f)*x+(%f)*y+(%f)',coeff))
grid on
axis tight
Both of these fit a linear polynomial surface, i.e. a plane, but you'll probably want to use something more complicated. Both of these techniques can be adapted to this situation. There's more information on this subject at mathworks.com: How can I determine the equation of the best-fit line, plane, or N-D surface using MATLAB?.
You might want to look at Delaunay triangulation:
tri = delaunay(Tavg, Havg);
trisurf(tri, Tavg, Havg, Pavg);
Using your example data, this code generates an interesting 'surface'. But I believe this is another way of doing what you want.
You might also try the GridFit tool by John D'Errico from MATLAB Central. This tool produces a surface similar to interpolating between the data points (as is done by MATLAB's griddata) but with cleaner results because it smooths the resulting surface. Conceptually multiple datapoints for nearby or overlapping X,Y coordinates are averaged to produce a smooth result rather than noisy "ripples." The tool also allows for some extrapolation beyond the data points. Here is a code example (assuming the GridFit Tool has already been installed):
%Establish points for surface
num_points = 20;
Tval = linspace(min(Tavg),max(Tavg),num_points);
Hval = linspace(min(Havg),max(Havg),num_points);
%Do the fancy fitting with smoothing
Pest = gridfit(Tavg, Havg, Pavg, Tval, Hval);
%Plot results
figure(5)
surfc(XI,YI,Pest, 'FaceColor', 'Interp')
To produce an even nicer plot, you can add labels, some transparancy and overlay the original points:
alpha(0.5)
hold on
plot3(Tavg,Havg,Pavg,'.')
xlabel('Temperature')
ylabel('Humidity')
zlabel('Power')
grid on
title('GridFit')
PS: #upperBound: Thanks for the Delaunay triangulation tip. That seems like the way to go if you want to go through each of the points. I am a newbie so can't comment yet.
Below is your solution:
Save/write the Myplot3D function
function [x,y,V]=Myplot3D(X,Y,Z)
x=linspace(X(1),X(end),100);
y=linspace(Y(1),Y(end),100);
[Xt,Yt]=meshgrid(x,y);
V=griddata(X,Y,Z,Xt,Yt);
Call the following from your command line (or script)
[Tavg_new,Pavg_new,V]=Myplot3D(Tavg,Pavg,Havg);
surf(Tavg_new,Pavg_new,V)
colormap jet;
xlabel('Temperature')
ylabel('Power/Pressure')
zlabel('Humidity')