- Thread starter
- Banned
- #1

- Thread starter Poirot
- Start date

- Thread starter
- Banned
- #1

- Jan 26, 2012

- 890

The particular form of the FT you are using is not that important, the basic idea is that:Let f(k) be the fourier transform of F(x). Prove that the fourier transorm of F(ax) is $\frac{1}{a}f(\frac{k}{a})$ where a>0 and the fourier transform is defined to have a factor of 1/2pi.

\[\mathfrak{F} \big[ F(ax) \big] (k) = \int_{-\infty}^{\infty} F(ax) e^{-kx{\rm{i}}}\; dx\]

Now make the change of variable \(x^{*}=ax\) and the result drops out.

CB

- Jan 26, 2012

- 890

There is confusion here about the thread title (Fourier series) and content (Fourier transform). I have answered for the FT, is that what you intended?Let f(k) be the fourier transform of F(x). Prove that the fourier transorm of F(ax) is $\frac{1}{a}f(\frac{k}{a})$ where a>0 and the fourier transform is defined to have a factor of 1/2pi.

CB