How to plot this sawtooth wave and its fourier approximation

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.

Answer 1

[Utkarsh Belwal]

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

Answer 2

[Aasha]

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How to plot this sawtooth wave and its fourier approximation

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Tawhid Khan on 9 Jun 2019

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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.

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Answers (1)

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

Answer 3

[Aasha]

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

Answer 4

[Aasha]

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