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.
help with convolution and product theorem
Started by ●December 10, 2006
Reply by ●December 10, 20062006-12-10
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. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
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==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
Reply by ●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
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 ●December 11, 20062006-12-11
<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). -- Posted via a free Usenet account from http://www.teranews.com
