Combine a waveform from a set of sine waves which are linearly increasing in frequency

Hi,

I generate and plot multiple waveforms which have increasing frequency. I want to combine them at each time interval of t, but how? Please share if you know how...

for f = 1:1:200  % Upto 200 Hz
t=[0 : 0.01 : 1]  
y=sin (2 * pi .* f .* t);
hold on
plot (t,y)
end

thanks

Answer 1

[Star Strider]

Try this:

t = 0 : 0.01 : 1;
for f = 1:1:200  % Upto 200 Hz
    y(f,:) = sin (2 * pi .* f .* t);
end

plot (t,y)
hold on
plot(t, sum(y), ':r', 'LineWidth',2.5)
hold off

The sum is essentially zero for all columns.

[Star Strider]

Nathan Kennedy’s “Answer” moved here ...

Thats not quite exactly what I had in mind and I am confused with the plot output. Its a substantial amount of waveforms that cover the entire plot - even when I put this to 2 Hertz. I would have thought I would have only 2 waveforms when f is set to maximum of 2

f:1:1:2

What is that semi colon adding to the code

[Star Strider]

You wanted frequencies from 1:200 and your code produced them. I tweaked it to produce the result you wanted.

This will give you two waveforms at 1 Hz and 2 Hz, and the sum of them:

t = 0 : 0.01 : 1;
for f = 1:1:2  % Upto 200 Hz
    y(f,:) = sin (2 * pi .* f .* t);
end

plot (t,y)
hold on
plot(t, sum(y), ':r', 'LineWidth',2.5)
hold off

[Nathan Kennedy]

The attached image of the plot is what I am getting

[Star Strider]

That’s what I got as well, because that’s what you coded, and what you asked for in your original Question.

What do you want your code to produce?

[Nathan Kennedy]

Hi, I get that plot when the colon is used. My original code did not have all those waveforms if I reduced the frequencies. They seem to be there even when it's set to 2 Hz.

I want to plot multiple waveforms at different frequencies in time domain and also have one waveform that is the sum of each one at each time interval

[Star Strider]

My code does exactly that.

When I plot only 1 Hz and 2 Hz, I get the plot this code produces:

t = 0 : 0.01 : 1;
for f = 1 : 2  % Upto 2 Hz
    y(f,:) = sin (2 * pi .* f .* t);
end

plot (t,y)
hold on
plot(t, sum(y), ':r', 'LineWidth',2.5)
hold off

[Star Strider]

Nathan Kennedy’s “Answer” moved here ...

Yes I see. I needed to clear.

I'm trying to fft to Freq domain in the for loop and then plot that.

I've tried this but I'm way off

Fourier = fft(y(f,:))

Maybe it can't be done with this code?

[Nathan Kennedy]

The comment about fft is something I would like to add in

[Star Strider]

You will find this documentation for the fft (link) function helpful.

Example —

t = 0 : 0.01 : 1;
for f = 1 : 2  % Upto 2 Hz
    y(f,:) = sin (2 * pi .* f .* t);
end

figure(1)
plot(t,y)
hold on
plot(t, sum(y), ':r', 'LineWidth',2.5)
hold off

L = length(t);                                          % Signal Length
Ts = t(2) - t(1);                                       % Sampling Time Interval
Fs = 1/Ts;                                              % Sampling Frequency
Fn = Fs/2;                                              % Nyquist Frequency
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                     % Frequency Vector
Iv = 1:length(Fv);                                      % Index Vector
Fourier = fft(y, [], 2)/L;                              % Fourier Transform (Along Rows Of Matrix)

figure(2)
subplot(2,1,1)
plot(Fv, abs(Fourier(:,Iv))*2)
title('Amplitude')
grid
subplot(2,1,2)
plot(Fv, angle(Fourier(:,Iv)))
title('Phase')
xlabel('Frequency')
grid

The time-domain plots are in figure(1) and the frequency-domain plots are in figure(2).