matlab - How to plot a 3d graph of 2d fft transformations with a changing parameter -

i want make 3d plot of 2d plots of function y y dft of function z having axis k(x) w0(y) , amplitude(y)(z), k dft variable in frequency domain , w0 changing parameter between 0 , 4*pi/45.

n=(0:255); x1 = exp(n.*(w1*1j)); x2 = 0.8.*exp(n*((w2-w0)).*1j); z =hamming(256)*(x1+x2); y = fft(abs(z)) 

if i'm interpreting question properly, wish have this:

the x axis dft number, y axis parameter changes time-domain signal , z magnitude of fft each signal.

what need define 2d grid of points x number of fft points have... in case, that'll 256 points, , y axis defines varying w0 term 0 4*pi/45. structure grid such each row defines 1 dft result.

for this, use ndgrid that, , following way:

max_dft_number = 256; num_w = 10; [w0,n] = ndgrid(linspace(0,4*pi/45,num_w), 0:max_dft_number-1); 

max_dft_number determines how many dft numbers want compute. in case, 256. can vary according how many dft numbers want. num_w gives how many w0 points want between 0 4*pi/45, linspace gives set of linearly spaced points 0 4*pi/45 have num_w of these points. set 10 here give illustration.

once have this, use x , y , substitute code above. don't define w1 , w2, i'll assume it's constant:

w1 = 0.1; w2 = 0.2; x1 = exp(n.*(w1*1j)); %// change - vectorized x2 = 0.8.*exp(n.*((w2-w0)).*1j); %// change - vectorized z = bsxfun(@times,hamming(max_dft_number).', x1+x2); %// change - make sure hamming window applies on each row y = abs(fft(z, [], 2)); %// change - fft first, magnitude after.  apply each row 

i had use bsxfun apply hamming window on each row of x1 + x2. remember, each row dft result particular w0 parameter. had transpose hamming(256) default output column. bsxfun in case use of @times duplicate hamming window coefficients every row gets multiplied same window. if provide matrix fft, default applies fft on each column of matrix. don't want that, , want apply every row, , need fft(z,[],2); that.

now, achieve desired plot, have use waterfall function, takes in set 2d grid coordinates , corresponding output in z direction. assumes each row individual trace of 3d function.... wanted.

so:

waterfall(n, w0, y); xlabel('dft number'); ylabel('w0'); zlabel('magnitude'); colormap([0 0 0]); %// make plot black view(-12,64); %// adjust view better 

we get: