How to plot this sawtooth wave and its fourier approximation

109 views (last 30 days)
Tawhid Khan on 9 Jun 2019
Answered: Aasha on 10 Sep 2022
I am trying to plot this wave and its fourier approximation for first 5 harmonics. This is what I want the final result to be like (note the wave approximated in the picture is a square wave)
This is the wave I want to approximate:
I know how to plot a sawtooth wave using the sawtooth funciton I was confused by the delay between the sawtooths in the picture. I tried using a piecewise function repeated 3 times to generate the wave.
f = @(x)[.5*x.*(0<=x & x<=2) + 0.*(2<=x & x<=3) + ((.5*x)-1.5).*(3<=x & x<=5)];
x = linspace(0,3);
intvl = [-6 6];
pfx = repmat(f(x+1),1,diff(intvl)/3);
px = linspace(intvl(1),intvl(2),length(pfx));
figure(1)
plot(px, pfx)
grid
This code can generate the sawtooth wave with some problems as shown here:
Now my question is how to properly plot the function in the original question then plot a fourier transform for it. The fourier transform for this normal sawtooth below is given where L is half the length of the sawtooth.

Utkarsh Belwal on 11 Jun 2019
Edited: Utkarsh Belwal on 11 Jun 2019
freq = 1 ; % Sawtooth frequency 1Hz
T = 4 * freq ;
fs = 1000; % Sampling Rate
t = 0:1/fs:T-1/fs;
x = sawtooth(2*pi*freq*t);
plot(t,x)
acc = 0 ;
n = 3 ; % Number of harmonics.
for i = 1 : n
acc = acc + (1 / i) * sin((i * pi * t) / 0.5) ;
end
acc = 0.5 - (1 / pi)*(acc) ;
hold on
plot(t , acc)
hold off
grid on

Aasha on 10 Sep 2022
Close Mobile Search
How to plot this sawtooth wave and its fourier approximation
Follow
79 views (last 30 days)
Tawhid Khan on 9 Jun 2019
Edited: Utkarsh Belwal on 11 Jun 2019
I am trying to plot this wave and its fourier approximation for first 5 harmonics. This is what I want the final result to be like (note the wave approximated in the picture is a square wave)
This is the wave I want to approximate:
I know how to plot a sawtooth wave using the sawtooth funciton I was confused by the delay between the sawtooths in the picture. I tried using a piecewise function repeated 3 times to generate the wave.
Theme
f = @(x)[.5*x.*(0<=x & x<=2) + 0.*(2<=x & x<=3) + ((.5*x)-1.5).*(3<=x & x<=5)];
x = linspace(0,3);
intvl = [-6 6];
pfx = repmat(f(x+1),1,diff(intvl)/3);
px = linspace(intvl(1),intvl(2),length(pfx));
figure(1)
plot(px, pfx)
grid
This code can generate the sawtooth wave with some problems as shown here:
Now my question is how to properly plot the function in the original question then plot a fourier transform for it. The fourier transform for this normal sawtooth below is given where L is half the length of the sawtooth.
Utkarsh Belwal on 11 Jun 2019
Edited: Utkarsh Belwal on 11 Jun 2019
Theme
freq = 1 ; % Sawtooth frequency 1Hz
T = 4 * freq ;
fs = 1000; % Sampling Rate
t = 0:1/fs:T-1/fs;
x = sawtooth(2*pi*freq*t);
plot(t,x)
acc = 0 ;
n = 3 ; % Number of harmonics.
for i = 1 : n
acc = acc + (1 / i) * sin((i * pi * t) / 0.5) ;
end
acc = 0.5 - (1 / pi)*(acc) ;
hold on
plot(t , acc)
hold off
grid on

Aasha on 10 Sep 2022
freq = 1 ; % Sawtooth frequency 1Hz T = 4 * freq ;
fs = 1000; % Sampling Rate t = 0:1/fs:T-1/fs;
x = sawtooth(2*pi*freq*t);
plot(t,x)
acc = 0 ; n = 3 ; % Number of harmonics.
for i = 1 : n acc = acc + (1 / i) * sin((i * pi * t) / 0.5) ; end
acc = 0.5 - (1 / pi)*(acc) ;
hold on plot(t , acc) hold off grid on

Aasha on 10 Sep 2022
freq = 1 ; % Sawtooth frequency 1Hz T = 4 * freq ;
fs = 1000; % Sampling Rate t = 0:1/fs:T-1/fs;
x = sawtooth(2*pi*freq*t);
plot(t,x)
acc = 0 ; n = 3 ; % Number of harmonics.
for i = 1 : n acc = acc + (1 / i) * sin((i * pi * t) / 0.5) ; end
acc = 0.5 - (1 / pi)*(acc) ;
hold on plot(t , acc) hold off grid on

Categories

Find more on Matched Filter and Ambiguity Function in Help Center and File Exchange

R2018a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!