<paulwvanc@yahoo.ca> escribi� en el mensaje
news:1165724267.257004.277870@79g2000cws.googlegroups.com...
> hi
>
> I'm a bit screwed up by the notation used in fourier transform, on
> convolution and product theorems. I'm drawing a blank with regard to
> what's the difference between:
> f1(t)*f2(t) <=> F1(w)F2(w) [convolution theorem]
> f1(t)f2(t) <=> F1(w)*F2(w) [product theorem]
> what's the difference between "f1(t)*f2(t)" and "f1(t)f2(t)"
> please give one example.
>
> Thanks.
The * stands for convolution, not multiplication (or product, so to speak).
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Reply by Rune Allnor●December 10, 20062006-12-10
paulwvanc@yahoo.ca skrev:
> hi
>
> I'm a bit screwed up by the notation used in fourier transform, on
> convolution and product theorems. I'm drawing a blank with regard to
> what's the difference between:
> f1(t)*f2(t) <=> F1(w)F2(w) [convolution theorem]
> f1(t)f2(t) <=> F1(w)*F2(w) [product theorem]
> what's the difference between "f1(t)*f2(t)" and "f1(t)f2(t)"
f(n)*g(n) represents convolution. You can also see this
as f(n)(*)g(n) if one wants to emphasize that '*' has nothing
to do with the ususal product.
> please give one example.
Assume the sequences
f(n) = ...,0,0,|1,2,3,2,1,0,0,...
g(n)= ...,0,0,|1,1,1,1,1,0,0,...
where the bar | indicates n = 0. Then
f(n)g(n) = ...,0,0,|1,2,3,2,1,0,0,...
f(n)(*)g(n) = ...,0,0,|1,3,6,8,9,8,6,3,1,0,0,...
Rune
Reply by Marc Brooker●December 10, 20062006-12-10
paulwvanc@yahoo.ca wrote:
> Jerry Avins wrote:
>> paulwvanc@yahoo.ca wrote:
>>> hi
>>>
>>> I'm a bit screwed up by the notation used in fourier transform, on
>>> convolution and product theorems. I'm drawing a blank with regard to
>>> what's the difference between:
>>> f1(t)*f2(t) <=> F1(w)F2(w) [convolution theorem]
>>> f1(t)f2(t) <=> F1(w)*F2(w) [product theorem]
>>> what's the difference between "f1(t)*f2(t)" and "f1(t)f2(t)"
>>> please give one example.
>> In that notation, "*" indicates convolution, not multiplication.
>
> "*" meaning "Convolution" in both theorem?
>
Yes, exactly that. You can state it as:
1) Convolution in the time domain is equivalent to multiplication in the
fourier domain.
2) Multiplication in the time domain is equivalent to convolution in the
fourier domain.
These statements change a little in discrete systems, but your use of t
suggests that you are concerned with the continuous case.
If you want to understand the difference between convolution and
multiplication, a text book with good diagrams is probably the best
place to look.
Cheers
Marc
Reply by ●December 10, 20062006-12-10
Jerry Avins wrote:
> paulwvanc@yahoo.ca wrote:
> > hi
> >
> > I'm a bit screwed up by the notation used in fourier transform, on
> > convolution and product theorems. I'm drawing a blank with regard to
> > what's the difference between:
> > f1(t)*f2(t) <=3D> F1(w)F2(w) [convolution theorem]
> > f1(t)f2(t) <=3D> F1(w)*F2(w) [product theorem]
> > what's the difference between "f1(t)*f2(t)" and "f1(t)f2(t)"
> > please give one example.
>
> In that notation, "*" indicates convolution, not multiplication.
"*" meaning "Convolution" in both theorem?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
> hi
>
> I'm a bit screwed up by the notation used in fourier transform, on
> convolution and product theorems. I'm drawing a blank with regard to
> what's the difference between:
> f1(t)*f2(t) <=> F1(w)F2(w) [convolution theorem]
> f1(t)f2(t) <=> F1(w)*F2(w) [product theorem]
> what's the difference between "f1(t)*f2(t)" and "f1(t)f2(t)"
> please give one example.
In that notation, "*" indicates convolution, not multiplication.
Jerry
--
Engineering is the art of making what you want from things you can get.
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Reply by ●December 10, 20062006-12-10
hi
I'm a bit screwed up by the notation used in fourier transform, on
convolution and product theorems. I'm drawing a blank with regard to
what's the difference between:
f1(t)*f2(t) <=> F1(w)F2(w) [convolution theorem]
f1(t)f2(t) <=> F1(w)*F2(w) [product theorem]
what's the difference between "f1(t)*f2(t)" and "f1(t)f2(t)"
please give one example.
Thanks.