purnapragna
Advanced Member level 4
fourier transform of u(t)
Hey,
I wish to find the Fourier transform of the signal \[u(t)\] which is unit step using the property of differentiation. i.e.,
\[\frac{d}{dt}u(t)=\delta(t)\]. Thus applying the differentiation property we get
\[j\omega F\left[u(t)\right]=1\] and thus,
\[F\left[u(t)\right]=\frac{1}{j\omega}\] which is obviously wrong!!!
But we already know that
\[F\left[u(t)\right]=\frac{1}{j\omega}+\pi \delta(\omega)\]
So what is the wrong with the property?? is that we should not use it as we wish???
help me out in this!!!
Hey,
I wish to find the Fourier transform of the signal \[u(t)\] which is unit step using the property of differentiation. i.e.,
\[\frac{d}{dt}u(t)=\delta(t)\]. Thus applying the differentiation property we get
\[j\omega F\left[u(t)\right]=1\] and thus,
\[F\left[u(t)\right]=\frac{1}{j\omega}\] which is obviously wrong!!!
But we already know that
\[F\left[u(t)\right]=\frac{1}{j\omega}+\pi \delta(\omega)\]
So what is the wrong with the property?? is that we should not use it as we wish???
help me out in this!!!