ASN4 - Fourier Transform property: Parseval's Theorem: Difference between revisions

Revision as of 02:02, 30 November 2009

$\int _{-\infty }^{\infty }(|s(t)|)^{2}dt$ in time transforms to $\int _{-\infty }^{\infty }(|S(f)|)^{2}df$ in frequency

The magnitude of $s(t)$ is also the Inverse Fourier Transform of $S(f)$ .

$|s(t)|=F^{-1}[S(f)]=|\int _{-\infty }^{\infty }S(f)e^{j2\pi ft}df|$

Note that $|e^{j2\pi ft}|={\sqrt {cos^{2}(2\pi ft)+sin^{2}(2\pi ft)}}=1$

So then $|s(t)|=\int _{-\infty }^{\infty }S(f)df$

$Insertformulahere$

@@ Line 4: / Line 4: @@
 <math>\int_{- \infty}^{\infty} (|s(t)|)^2 dt</math> in time transforms to <math>\int_{- \infty}^{\infty} (|S(f)|)^2 df</math> in frequency
-First find the magnitude of <math>s(t)</math> which is also the Inverse Fourier Transform of <math>S(f)</math>.
+The magnitude of <math>s(t)</math> is also the Inverse Fourier Transform of <math>S(f)</math>.
 <math> |s(t)|= F ^{-1}[S(f)]=|\int_{- \infty}^{\infty}S(f)e^{j 2 \pi f t} df | </math>
@@ Line 11: / Line 11: @@
 So then <math>|s(t)|= \int_{- \infty}^{\infty}S(f) df</math>
+<math>Insert formula here</math>