Fourier series of a 2step function?



Raymond E. Rogers wrote:
> Doug Stewart wrote:
> <clip>
>>
>>
>>
>> Fx =     0   -10<x<-5
>>           -5      -5<x<0
>>            5      0<x<5
>>            0      5<x<10
>>
>>
>>
>>                   |----------|
>>                   |          |
>>                   |          |
>> --------|          |          |----------
>>        |          |
>>        |----------|
>>
>> thanks in advance
>>
>> Doug
>>
> Okay, sorry if I was talking down.

No you wern't talking down. I just added some background so that we 
could get to the point faster :-)
> I never know.
> Somebody else mentioned doing the integrals in Maxima; one by one.  
> Good practice but not what you buy a CAS for.
> I looked at the Fourier package and have doubts.  It doesn't know 
> unit_step, signum(),del();although it is happy to return del() ).  
> demo(fourie)
> However it does know abs().  Although it does give a reasonable, if 
> superficial, answer to fourier(diff(abs(x)),x,1); it
> doesn't seem to evaluate fourier(diff(abs(x-1/5),x,1) appropriately.
> In all it seems to need serious repair; but I hope somebody corrects 
> me in this.
> It seems to fall back on integrate; but integrate doesn't seem to know 
> about del().  I think, I am not sure.
> There is also fourier_elim ; but I have no idea what it does.
> The Laplace xform  knows delta(x-a)  it doesn't seem to do 
> integrate(delta) which is what you need.
> Perhaps someone else can help.
> Sorry,
>
> RayR
>
>


My hand work is at
http://dougs.homeip.net/f2008/q10.pdf
http://dougs.homeip.net/f2008/q10g.pdf

Thanks for your effort. We will have to do these without Maxima.

Doug