- #1
maverick280857
- 1,789
- 4
Hi. I have a question regarding the continuous time Fourier Transform of an input signal:
[tex]x(t) \rightarrow X(j\omega)[/tex]
then
[tex]\int_{-\infty}^{t}x(\tau)d\tau \rightarrow \frac{X(j\omega)}{j\omega} + \pi X(0)\delta(\omega)[/tex]
but if I want to write it in terms of [itex]f = \frac{\omega}{2\pi}[/itex], should it be:
[tex]\int_{-\infty}^{t}x(\tau)d\tau \rightarrow \frac{X(j\omega)}{j\omega} + \frac{1}{2}X(0)\delta(f)[/tex]
How does the [itex]\pi[/itex] get replaced by [itex]\frac{1}{2}[/itex] here?
[tex]x(t) \rightarrow X(j\omega)[/tex]
then
[tex]\int_{-\infty}^{t}x(\tau)d\tau \rightarrow \frac{X(j\omega)}{j\omega} + \pi X(0)\delta(\omega)[/tex]
but if I want to write it in terms of [itex]f = \frac{\omega}{2\pi}[/itex], should it be:
[tex]\int_{-\infty}^{t}x(\tau)d\tau \rightarrow \frac{X(j\omega)}{j\omega} + \frac{1}{2}X(0)\delta(f)[/tex]
How does the [itex]\pi[/itex] get replaced by [itex]\frac{1}{2}[/itex] here?