Trying to find the amplitude and phase spectrum of a sawtooth waveform

[[email protected]]

Hello everyone,

The given problem of mine is the eq'n x(t) = t/T, for 0<t<T, where T
is the fundamental period.

The time 0<t<T represents the first tooth in the periodic sawtooth
waveform.

I'm using the Fourier Series form:
X(t) = sum for n=-inf to +inf {Cn*e^j2*pi*n*f*t}, n=0, +\-1, +\-2, . .
..
Where,
Cn = 1/T*integral_over-T{x(t)*e^-j*2pi*n*f*t}

I come out with a 3 termed eq'n for Cn. One of the terms is
1/(2pi*n)^2. As the Fourier series is from n=-inf to +inf, the DC
component(when n=0), will make that term infinite.

Can anyone steer me in the right direction as to how I can find the
amplitude and phase spectrum of this problem? I know it's simple and
I apologize, but I've been at it for hours.

Thanking you in advance,

-Arthur

[Rune Allnor]

[email protected] skrev:
> Hello everyone,
>
> The given problem of mine is the eq'n x(t) = t/T, for 0<t<T, where T
> is the fundamental period.
>
> The time 0<t<T represents the first tooth in the periodic sawtooth
> waveform.
>
> I'm using the Fourier Series form:
> X(t) = sum for n=-inf to +inf {Cn*e^j2*pi*n*f*t}, n=0, +\-1, +\-2, . .
> .
> Where,
> Cn = 1/T*integral_over-T{x(t)*e^-j*2pi*n*f*t}
>
> I come out with a 3 termed eq'n for Cn. One of the terms is
> 1/(2pi*n)^2. As the Fourier series is from n=-inf to +inf, the DC
> component(when n=0), will make that term infinite.
>
> Can anyone steer me in the right direction as to how I can find the
> amplitude and phase spectrum of this problem? I know it's simple and
> I apologize, but I've been at it for hours.

Treat n==0 separately.

n == 0: C0 = integral t/T^2 dt = T^2 /2T^2 = 1/2

Then use what I am sure you already have done correctly
for the n=/= 0 situation.

Rune

[Major Misunderstanding]

"Rune Allnor" <[email protected]> wrote in message
news:[email protected] oups.com...
>
> [email protected] skrev:
> > Hello everyone,
> >
> > The given problem of mine is the eq'n x(t) = t/T, for 0<t<T, where T
> > is the fundamental period.
> >
> > The time 0<t<T represents the first tooth in the periodic sawtooth
> > waveform.
> >
> > I'm using the Fourier Series form:
> > X(t) = sum for n=-inf to +inf {Cn*e^j2*pi*n*f*t}, n=0, +\-1, +\-2, . .
> > .
> > Where,
> > Cn = 1/T*integral_over-T{x(t)*e^-j*2pi*n*f*t}
> >
> > I come out with a 3 termed eq'n for Cn. One of the terms is
> > 1/(2pi*n)^2. As the Fourier series is from n=-inf to +inf, the DC
> > component(when n=0), will make that term infinite.
> >
> > Can anyone steer me in the right direction as to how I can find the
> > amplitude and phase spectrum of this problem? I know it's simple and
> > I apologize, but I've been at it for hours.
>
> Treat n==0 separately.
>

Is there any reason why you use two equal signs == instead of one? Has C
language taken over maths?

M.



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