Thread Subject: symbolic integration of exp(-j*w*t) from 0 to infty

Dear all,

I have a problem with the symbolic integration of exp(-j*w*t) from 0 to
infty. On the matlab command prompt:

 > syms w t
 > f = exp(-j*w*t)
 > int(f,t,0,inf)

The output is NaN. I expect it to be 1/(jw). Have anyone encountered
similar problem?

> I have a problem with the symbolic integration of exp(-j*w*t) from 0 to
> infty. On the matlab command prompt:
>
> > syms w t
> > f = exp(-j*w*t)
> > int(f,t,0,inf)
>
> The output is NaN. I expect it to be 1/(jw). Have anyone encountered
> similar problem?
>
>

Hi,
if you expand exp(-j*w*t) in terms of sin() and cos() and then rewrite sin() and cos() in terms of an infinite sum of Bessel functions and Laguerre polynomials, you will immediately see, that the bessel functions grow faster as they approach infinity than the Laguerre polynomials can keep them bounded.
Thus it is quite obvious, that due to thus simple theoretical considerations, the integral must unbounded.

I further assumend, that the integral approaches infinity in a smooth way, thus it doesn't behave pathological close to infinity. But this assumption is still implied in the expansion in Bessel functions.

Hope that helps!

I think the problem is your lack of assumptions, and your lack of
declaring j as symbolic. The integral does not converge for negative or
some complex arguments.

The following works just fine:

syms j w t positive
f = exp(-j*w*t);
int(f,t,0,inf)

ans =

1/(j*w)

Alan Weiss
MATLAB mathematical toolbox documentation

funny.haha wrote:
> Dear all,
>
> I have a problem with the symbolic integration of exp(-j*w*t) from 0 to
> infty. On the matlab command prompt:
>
> > syms w t
> > f = exp(-j*w*t)
> > int(f,t,0,inf)
>
> The output is NaN. I expect it to be 1/(jw). Have anyone encountered
> similar problem?
>
>
>

On Jun 14, 11:30 pm, "funny.haha" <funny.h...@live.ca> wrote:
> Dear all,
>
> I have a problem with the symbolic integration of exp(-j*w*t) from 0 to
> infty. On the matlab command prompt:
>
>  > syms w t
>  > f = exp(-j*w*t)
>  > int(f,t,0,inf)
>
> The output is NaN. I expect it to be 1/(jw). Have anyone encountered
> similar problem?

No problem. If j is imaginary, NaN is correct. The integrals of cos
(w*t)
and sin(w*t) are not convergent. The areas under those curves is
undefined.

The integral will converge if real(j*w) > 0.

Hope this helps.

Greg