Fourier TransformsDate: 10/19/2001 at 12:24:28 From: Stuart Park Subject: Fourier Transforms I can't get my head around the sinc function. I know what the sinc function is, but I can't convert my expression (in terms of sin) to an expression (in terms of sinc). i.e. sinc(x) = sin ((pi*X)/(pi*X)) What should I do to the right-hand term to get it into the form on the left? Do I divide by through by pi? Thank you for taking the time to read my question. Date: 10/19/2001 at 12:52:50 From: Doctor Douglas Subject: Re: Fourier Transforms Hi Stuart, and thanks for writing. I'm not exactly sure what you mean by "get it into the form on the left." I'll make a guess, though, and if it doesn't answer your question, please feel free to write back: sinc(x) = sin(pi*x)/(pi*x) Notice that your parentheses above yield a right-hand side of sin(1), sin(pi*x) which is surely not what you meant. = ----------- pi * x This formula gives us sinc(x) in terms of x. If we know what x is, we simply plug it in here. Now let's solve for sin(x) here. But to avoid confusion, let's say y = pi*x, so x = y/pi, and rewrite the above as sinc(y/pi) = sin(y) / y Looks much easier now, doesn't it? So we now can solve for sin(y) as sin(y) = y * sinc(y/pi). Of course, we can substitute any variable we like now for y. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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