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## Main Question or Discussion Point

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?