Fourier Series / Fourier Transform Question

[SpeedBird]

Hello there,

Im sure someone on this forum must know how to go about this.
It is part of an exam question.

Firstly I must draw a sketch of this pulse:

v=0 when |t| > a
v=V0( 1 + t/a ) when -a < t <= 0
v=V0( 1 - t/a ) when 0 < t < a

v represents amplitude, V0 represents peak amplitude, t represents
time and 'a' is a constatnt.

i can draw the pulse ok, it is just a triangular pulse that goes from
0 at t = +a and -a to V0 when t = 0.

The bit I am unsure about is obtaining and sketching the frequency
spectrum of this pulse. Any ideas?

Thanks,

Nik

 

[Hurkyl]

Isn't there an ethics problem with getting assistance with an exam question?

 

[SpeedBird]

maybe if i was in the exam at the time.
it's a question from last years signal analysis exam.
thanks anyway!

 

[SpeedBird]

does anyone have any ideas?

 

[Hurkyl]

Well, have you computed the Fourier transform?

 

[SpeedBird]

i havnt computed the FT. the integration is huge and i get stuck pretty quickly. do you think getting the Freq spectrum could mean getting $$a_k$$ and $$b_k$$ coefficients for the Fourier series and plotting their magnitudes against $$k$$?

 

[Hurkyl]

I'm having difficulty seeing the trouble -- the integral should be something straight out of a calc II class, whether you use sines & cosines as your basis, or you use complex exponentials.