# Fourier series help

Hey, I am trying to solve this question:

obtain a fourier series for a saw-tooth wave, a periodic signal, with period T, defined such that

x(t)=At -T/2<= t >= T/2

where A has a value of 1 at the maximum value of x(t)

i) obtain the fourier series for this periodic signal in form

x(t)= $$\frac{A0}{2}$$+$$\sum$$[An*cos(2*pi*j*n*f0*t) + Bn*sin(2*pi*j*n*f0*t)]

where the limits of the $$\sum$$ are infinity and n=1

then,

ii) obtain the series in the form

x(t)= $$\sum$$Cn* exp(2*pi*j*n*f0*t)

where the limits of the $$\sum$$ are infinity to n=- infinity

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mheslep
Gold Member
Hey, I am trying to solve this question:

obtain a fourier series for a saw-tooth wave, a periodic signal, with period T, defined such that

x(t)=At -T/2<= t >= T/2

where A has a value of 1 at the maximum value of x(t)

i) obtain the fourier series for this periodic signal in form

x(t)= $$\frac{A0}{2}$$+$$\sum$$[An*cos(2*pi*j*n*f0*t) + Bn*sin(2*pi*j*n*f0*t)]

where the limits of the $$\sum$$ are infinity and n=1

then,

ii) obtain the series in the form

x(t)= $$\sum$$Cn* exp(2*pi*j*n*f0*t)

where the limits of the $$\sum$$ are infinity to n=- infinity

A0=0 from inspection the average of the ramp signal is zero.
An=0 since the signal is odd, no cosine terms allowed.
Bn left as an exercise to the reader Hey, I dont really understand. Firsty, what is A ? And could explain into detail the way you found Ao and An, thanks a lot !

Redbelly98
Staff Emeritus