CT Fourier Transform Properties
* CT_Fourier_Int/Diff\; \; \; (1)\frac{dx(t)}{dt} \rightarrow j\omega \Chi (\omega)\; \; \; \; \; \; (2) \int_{-\infty}^{t}x(\tau)d\tau \rightarrow \frac{1}{j\omega}\Chi (\omega) + \pi \Chi (0) \delta (\omega)
* CT Time and Frequency Scaling : x(at) \leftarrow \rightarrow \frac{1}{|a|}X(\frac{j\omega }{a})\,
* CT Differentiation in Frequencyx(t)\rightarrow j\frac{d}{d\omega}X(j\omega)
* CT Convolution: F(x_1(t)*x_2(t)) = X_1(\omega)X_2(\omega) \!
* CT Frequency Shifting : F(e^{jw0t}x(t)) = X(j(w - w0)) \!
F(x(t)y(t))=\frac{1}{2\pi}X(j\omega)*Y(j\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(j\theta)Y(j(\omega-\theta))d\theta
* CT Time Reversal(-t) \leftarrow \rightarrow X(-j\omega )\,
* CT Multiplication Property Mimis VersionF(x_1(t)x_2(t)) = \frac {1} {2\pi} X_1(\omega)*X_2(\omega)
* CT Duality Property : F(x(t)) = X(w) = 2\pi x(-w) \!
F(x(t)) = X(w) = 2\pi x(-w) \!
* CT Conjugate Symmetry ==Conjugate Symmetry==
if
\ F(x(t)) = X(w)
then,
\ F(x(t)^*) = X^*(-w)
