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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.

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p...@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.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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Jerry Avins wrote:
> p...@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=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

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p...@yahoo.ca wrote:
> Jerry Avins wrote:
>> p...@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

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p...@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

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<p...@yahoo.ca> escribió en el mensaje 
news:1...@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). 



-- 
Posted via a free Usenet account from http://www.teranews.com

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