I would like to know whether it is possible to customize the plot generated by MATLAB's spectrogram function in such a way that its x-axis does not represent the time but another physical signal y2captured simultaneously with the input signal y1 (used for computing the spectrogram). Therefore, it can be assumed that y1 and y2 have the same timestamps as x-axis as in the following example.
N = 1024;
n = 0:N-1;
w0 = 2*pi;
y1 = sin(w0*n);
y2 = n;
spectrogram(y1,'yaxis');
To control the scale of the axes arbitrarily, you could manually plot the spectrogram using imagesc. Here's how:
N = 1024;
n = 0:N-1;
w0 = 2*pi/10;
y1 = sin(w0*n);
y2 = n;
% compute spectrogram
[s,w,t]=spectrogram(y1,'yaxis');
% find values in y2 corresponding to spectrogram time-grid
t2 = interp1((1:N), y2, t);
% use imagesc to plot spectrogram
figure;
imagesc(t2,w/pi,10*log10(abs(s.^2)/length(w)/pi))
set(gca,'YDir','normal');
colorbar;
ylabel('Normalized Frequency (\times \pi rad/sample)');
% caxis([-160, 20]) % manually tweak the color range for best detail
Note that I have made two minor changes to your code:
Changed w0 from 2*pi to 2*pi/10, because the former results in y1 being all zeros.
Changed y2 to be something else than 1:N, which is spectrogram default.
I should also point out that the built-in spectrogram plot does let you control the axes scale in a variety of ways, including specifying the sample rate.
Related
I'm trying to add two color gradients between two curves (in this example these are lines).
This is the code for what I've done so far
% the mesh
ns=1000;
t_vec = linspace(0,100,ns);
x_vec = linspace(-120,120,ns);
[N, X] = meshgrid(t_vec, x_vec);
% the curves
x1 = linspace(0,100,ns); x2 = linspace(10,110,ns);
y1 = linspace(-50,50,ns); y2 = linspace(-20,80,ns);
X1 = repmat(x1, [size(N, 1) 1]); X2 = repmat(x2, [size(N, 1) 1]);
Y1 = repmat(y1, [size(N, 1) 1]); Y2 = repmat(y2, [size(N, 1) 1]);
% the gradient function
cc = #(x,x2,x1) ...
1./(1+(exp(-x)./(exp(-x1)-exp(-x2))));
for i=1:ns
CData1(:,i)=cc(x_vec,x2(i),x1(i));
CData2(:,i)=cc(x_vec,y2(i),y1(i));
end
CData=CData1+CData2; % here I've added the two gradients
% mask
mask = true(size(N));
mask((X > Y2 | X < Y1) & (X > X2 | X < X1)) = false;
% finalized data
Z = NaN(size(N));
Z(mask) = CData(mask);
Z = normalize(Z, 1, 'range');
% draw a figure!
figure(1); clf;
ax = axes; % create some axes
sc = imagesc(ax, t_vec, x_vec, Z); % plot the data
colormap('summer')
ax.YDir = 'normal' % set the YDir to normal again, imagesc reverses it by default;
hold on
plot(t_vec,x1,'r',t_vec,x2,'r',t_vec,y1,'k',t_vec,y2,'k')
ylim([-120 120]); xlim([0 100])
the result I get is
As you can see, the gradient stretches between the most lower line to the most upper line.
How can I separate between the two color data and present them in the same image (using imagesc) using a different colormap?
Here is a function called comat (see at the bottom of the answer) that I once made for something similar, I think you might find it useful in your case. Here's an example how to use it:
imagesc(t_vec, x_vec, comat(CData2.*mask,CData1.*mask));
colormap([summer(256).^2;flipud(bone(256).^0.5)]); % and the two colormaps
set(gca,'Ydir','normal')
The result is:
I'm not sure this is what you meant, but you can see how the data of the thin stripe is only visualized using the bone b&w colormap, while the rest is with summer. I also "abused" the colormaps with a ^ factor for emphasizing the range of the gradient.
function z = comat(z1,z2,DR)
% the function combines matrices z1 and z2 for the purpose of
% visualization with 2 different colormaps
% z1,z2 - matrices of the same size
% DR - the dynamic range for visualization (default 256)
%example
%imagesc(comat(z1,z2)); colormap([jet(256);bone(256)]);
%defaults
if (nargin < 3); DR=256; end
%normalize to dynamic range, integer values in the range 0 to DR
z1=double(uint32(DR*(z1-min(z1(:)))./(max(z1(:)-min(z1(:))))));
z2=double(uint32(DR*(z2-min(z2(:)))./(max(z2(:)-min(z2(:))))+DR+1));
thr=DR+2+10; %threshold where data is not important for z2, must be at least DR+2
z=z1.*(z2<thr)+z2.*(z2>thr);
end
I am trying to fit a 3D surface polynomial of n-degrees to some data points in 3D space. My system requires the surface to be monotonically increasing in the area of interest, that is the partial derivatives must be non-negative. This can be achieved using Matlab's built in lsqlin function.
So here's what I've done to try and achieve this:
I have a function that takes in four parameters;
x1 and x2 are my explanatory variables and y is my dependent variable. Finally, I can specify order of polynomial fit. First I build the design matrix A using data from x1 and x2 and the degree of fit I want. Next I build the matrix D that is my container for the partial derivatives of my datapoints. NOTE: the matrix D is double the length of matrix A since all datapoints must be differentiated with respect to both x1 and x2. I specify that Dx >= 0 by setting b to be zeroes.
Finally, I call lsqlin. I use "-D" since Matlab defines the function as Dx <= b.
function w_mono = monotone_surface_fit(x1, x2, y, order_fit)
% Initialize design matrix
A = zeros(length(x1), 2*order_fit+2);
% Adjusting for bias term
A(:,1) = ones(length(x1),1);
% Building design matrix
for i = 2:order_fit+1
A(:,(i-1)*2:(i-1)*2+1) = [x1.^(i-1), x2.^(i-1)];
end
% Initialize matrix containing derivative constraint.
% NOTE: Partial derivatives must be non-negative
D = zeros(2*length(y), 2*order_fit+1);
% Filling matrix that holds constraints for partial derivatives
% NOTE: Matrix D will be double length of A since all data points will have a partial derivative constraint in both x1 and x2 directions.
for i = 2:order_fit+1
D(:,(i-1)*2:(i-1)*2+1) = [(i-1)*x1.^(i-2), zeros(length(x2),1); ...
zeros(length(x1),1), (i-1)*x2.^(i-2)];
end
% Limit of derivatives
b = zeros(2*length(y), 1);
% Constrained LSQ fit
options = optimoptions('lsqlin','Algorithm','interior-point');
% Final weights of polynomial
w_mono = lsqlin(A,y,-D,b,[],[],[],[],[], options);
end
So now I get some weights out, but unfortunately they do not at all capture the structure of the data. I've attached an image so you can just how bad it looks. .
I'll give you my plotting script with some dummy data, so you can try it.
%% Plot different order polynomials to data with constraints
x1 = [-5;12;4;9;18;-1;-8;13;0;7;-5;-8;-6;14;-1;1;9;14;12;1;-5;9;-10;-2;9;7;-1;19;-7;12;-6;3;14;0;-8;6;-2;-7;10;4;-5;-7;-4;-6;-1;18;5;-3;3;10];
x2 = [81.25;61;73;61.75;54.5;72.25;80;56.75;78;64.25;85.25;86;80.5;61.5;79.25;76.75;60.75;54.5;62;75.75;80.25;67.75;86.5;81.5;62.75;66.25;78.25;49.25;82.75;56;84.5;71.25;58.5;77;82;70.5;81.5;80.75;64.5;68;78.25;79.75;81;82.5;79.25;49.5;64.75;77.75;70.25;64.5];
y = [-6.52857142857143;-1.04736842105263;-5.18750000000000;-3.33157894736842;-0.117894736842105;-3.58571428571429;-5.61428571428572;0;-4.47142857142857;-1.75438596491228;-7.30555555555556;-8.82222222222222;-5.50000000000000;-2.95438596491228;-5.78571428571429;-5.15714285714286;-1.22631578947368;-0.340350877192983;-0.142105263157895;-2.98571428571429;-4.35714285714286;-0.963157894736842;-9.06666666666667;-4.27142857142857;-3.43684210526316;-3.97894736842105;-6.61428571428572;0;-4.98571428571429;-0.573684210526316;-8.22500000000000;-3.01428571428571;-0.691228070175439;-6.30000000000000;-6.95714285714286;-2.57232142857143;-5.27142857142857;-7.64285714285714;-2.54035087719298;-3.45438596491228;-5.01428571428571;-7.47142857142857;-5.38571428571429;-4.84285714285714;-6.78571428571429;0;-0.973684210526316;-4.72857142857143;-2.84285714285714;-2.54035087719298];
% Used to plot the surface in all points in the grid
X1 = meshgrid(-10:1:20);
X2 = flipud(meshgrid(30:2:90).');
figure;
for i = 1:4
w_mono = monotone_surface_fit(x1, x2, y, i);
y_nr = w_mono(1)*ones(size(X1)) + w_mono(2)*ones(size(X2));
for j = 1:i
y_nr = w_mono(j*2)*X1.^j + w_mono(j*2+1)*X2.^j;
end
subplot(2,2,i);
scatter3(x1, x2, y); hold on;
axis tight;
mesh(X1, X2, y_nr);
set(gca, 'ZDir','reverse');
xlabel('x1'); ylabel('x2');
zlabel('y');
% zlim([-10 0])
end
I think it may have something to do with the fact that I haven't specified anything about the region of interest, but really I don't know. Thanks in advance for any help.
Alright I figured it out.
The main problem was simply an error in the plotting script. The value of y_nr should be updated and not overwritten in the loop.
Also I figured out that the second derivative should be monotonically decreasing. Here's the updated code if anybody is interested.
%% Plot different order polynomials to data with constraints
x1 = [-5;12;4;9;18;-1;-8;13;0;7;-5;-8;-6;14;-1;1;9;14;12;1;-5;9;-10;-2;9;7;-1;19;-7;12;-6;3;14;0;-8;6;-2;-7;10;4;-5;-7;-4;-6;-1;18;5;-3;3;10];
x2 = [81.25;61;73;61.75;54.5;72.25;80;56.75;78;64.25;85.25;86;80.5;61.5;79.25;76.75;60.75;54.5;62;75.75;80.25;67.75;86.5;81.5;62.75;66.25;78.25;49.25;82.75;56;84.5;71.25;58.5;77;82;70.5;81.5;80.75;64.5;68;78.25;79.75;81;82.5;79.25;49.5;64.75;77.75;70.25;64.5];
y = [-6.52857142857143;-1.04736842105263;-5.18750000000000;-3.33157894736842;-0.117894736842105;-3.58571428571429;-5.61428571428572;0;-4.47142857142857;-1.75438596491228;-7.30555555555556;-8.82222222222222;-5.50000000000000;-2.95438596491228;-5.78571428571429;-5.15714285714286;-1.22631578947368;-0.340350877192983;-0.142105263157895;-2.98571428571429;-4.35714285714286;-0.963157894736842;-9.06666666666667;-4.27142857142857;-3.43684210526316;-3.97894736842105;-6.61428571428572;0;-4.98571428571429;-0.573684210526316;-8.22500000000000;-3.01428571428571;-0.691228070175439;-6.30000000000000;-6.95714285714286;-2.57232142857143;-5.27142857142857;-7.64285714285714;-2.54035087719298;-3.45438596491228;-5.01428571428571;-7.47142857142857;-5.38571428571429;-4.84285714285714;-6.78571428571429;0;-0.973684210526316;-4.72857142857143;-2.84285714285714;-2.54035087719298];
% Used to plot the surface in all points in the grid
X1 = meshgrid(-10:1:20);
X2 = flipud(meshgrid(30:2:90).');
figure;
for i = 1:4
w_mono = monotone_surface_fit(x1, x2, y, i);
% NOTE: Should only have 1 bias term
y_nr = w_mono(1)*ones(size(X1));
for j = 1:i
y_nr = y_nr + w_mono(j*2)*X1.^j + w_mono(j*2+1)*X2.^j;
end
subplot(2,2,i);
scatter3(x1, x2, y); hold on;
axis tight;
mesh(X1, X2, y_nr);
set(gca, 'ZDir','reverse');
xlabel('x1'); ylabel('x2');
zlabel('y');
% zlim([-10 0])
end
And here's the updated function
function [w_mono, w] = monotone_surface_fit(x1, x2, y, order_fit)
% Initialize design matrix
A = zeros(length(x1), 2*order_fit+1);
% Adjusting for bias term
A(:,1) = ones(length(x1),1);
% Building design matrix
for i = 2:order_fit+1
A(:,(i-1)*2:(i-1)*2+1) = [x1.^(i-1), x2.^(i-1)];
end
% Initialize matrix containing derivative constraint.
% NOTE: Partial derivatives must be non-negative
D = zeros(2*length(y), 2*order_fit+1);
for i = 2:order_fit+1
D(:,(i-1)*2:(i-1)*2+1) = [(i-1)*x1.^(i-2), zeros(length(x2),1); ...
zeros(length(x1),1), -(i-1)*x2.^(i-2)];
end
% Limit of derivatives
b = zeros(2*length(y), 1);
% Constrained LSQ fit
options = optimoptions('lsqlin','Algorithm','active-set');
w_mono = lsqlin(A,y,-D,b,[],[],[],[],[], options);
w = lsqlin(A,y);
end
Finally a plot of the fitting (Have used a new simulation, but fit also works on given dummy data).
Here I am plotting a spectrogram twice, once using imagesc and once using the spectrogram automatic plotting. I don't know why I get different scaling results, probably some filtering by the automatic plotting function but I would like to know what exactly and how to transform it so that it matches.
fs = 44100;
% Frequency sweep signal
sw = logspace(log10(500),log10(5000),fs*5);
x = 0.95 * sin(cumsum((2*pi*sw)/fs));
N = 128;
win_size = N;
noverlap = N/2;
win = window(#blackman,win_size);
[s,f,t] = spectrogram(x,win,noverlap,N,fs,'yaxis');
%% IMAGESC --- FIGURE 1
figure(1)
imagesc(t,f/1000,20*log(abs(s)));
title('Spectrogram');
set(gca,'Ydir','Normal');
xlabel('Time (secs)');
ylabel('Frequency (kHz)');
hcb=colorbar;
title(hcb,'Spectral Magnitude (dB)');
%% test with automatic spectrogram plot ---FIGURE2
figure(2)
spectrogram(x,win,noverlap,N,fs,'yaxis');
end
Help is appreciated :)
Change your code "imagesc(t,f/1000,20*log(abs(s)))" as imagesc(t,f/1000,20*log10(abs(s))).
log() is natural logarithm.
When you calculate dB scale, you should use log10(), not log().
I have two classes(normally distributed), C1 and C2, each defined by their mean and standard deviation. I want to be able to visualize the pdf plot of a normal distributions and the classification boundary between the two. Currently I have the code to plot the distributions but I'm not sure how to go about plotting the decision boundary. Any ideas would be appreciated. I have included a sample of what I want to plot. 1
Many thanks!
This is what I came up with:
% Generate some example data
mu1 = -0.5; sigma1 = 0.7; mu2 = 0.8; sigma2 = 0.5;
x = linspace(-8, 8, 500);
y1 = normpdf(x, mu1, sigma1);
y2 = normpdf(x, mu2, sigma2);
% Plot it
figure; plot(x, [y1; y2])
hold on
% Detect intersection between curves; choose threshold so you get the whole
% intersection (0.0001 should do unless your sigmas are very large)
ind = y1 .* y2 > 0.0001;
% Find the minimum values in range
minVals = min([y1(ind); y2(ind)]);
if ~isempty(minVals)
area(x(ind), minVals)
end
I don't know if this is the best way to do what you want, but it seems to work.
Question: is it possible to illustrate an image on non-uniform axis?
Details:
I need to illustrate a multidimensional timeseries as an image. But the time grid of this timeseries is very non-uniform. Here is an example:
m = 10;
n = 3;
t = sort(rand(m, 1)); % non-uniform time
values = randn(m, n); % some random values
The figure, plot(t, values); handles it well.
But imagesc() converts t into uniform time between t(1) and t(end) according to documentation:
imagesc(x,y,C) displays C as an image and specifies the bounds of the
x- and y-axis with vectors x and y.
Therefore, the command:
figure, imagesc(t, 1 : n, values'); colorbar;
illustrates the image on uniform time grid.
Edit: It's possible to re-sample the timeseries with higher uniform resolution. But my timeseries is already very large.
There is pcolor function in MATLAB. This function does exactly what you're asking.
m = 10;
n = 3;
t = sort(rand(m, 1)); % non-uniform time
values = randn(m, n); % some random values
figure
plot(t, values);
figure
pcolor(t, 1 : n, values');
colorbar;
try uimagesc from the file exchange.
Solution
Try using surface for non-uniform spacing.
First, create a 3D xyz surface of the same size as your input data:
m = 10;
n = 3;
t = sort(rand(m, 1)); % non-uniform time
values = randn(m, n); % some random values
x = repmat(t,1,n);
y = repmat(1:n,m,1);
z = zeros(size(y));
Then, colormap your values. There is a nice tool posted to the mathworks file exchange, real2rgb, that can do this for you:
cdata = real2rgb(values); % Where size(cdata) = [m n 3]
Lastly, plot the surface. You can even get fancy and set the transparency.
surface(x,y,z,cdata,'EdgeColor','none','FaceColor','texturemap',...
'CDataMapping','direct');
alpha(0.3)