Thanks for the help, Dyad!
\int_{-\infty}^{\infty}-j Sgn(f)e^{j2\pi ft}e^{-b|f|}df = \\
\int_{-\infty}^{0}je^{j2\pi ft}e^{bf}df - \int_{0}^{\infty}je^{j2\pi ft}e^{bf}df
The e^{-b|f|} added convergence.
I ended up with
j[\frac{1}{j2\pi t+b}+\frac{1}{j2\pi t-b}]
But as b...
Hi Dyad,
Thanks for your response. Could you please give me more details? Even Mathematica hates the integral.
By the way, I am only confident that the first part is correct.
h(t) = \int_{-\infty}^{0} je^{j2\pi f t}df + \int_{0}^{\infty} -je^{j2\pi ft}df
=...
Hello,
I am working through Signals and Systems Demystified, but I am at an impasse.
I would like to take the inverse Fourier transform of
H(f)=\begin{cases}
-j&\text{if } f > 0\\
j&\text{if } f<0\end{cases}
So
h(t) = \int_{-\infty}^{0} je^{j2\pi f t}df +...
I am working through Signals and Systems Demystified on my own. I need to integrate:
\int_{-\infty}^{\infty}{sin(2t)e^{-|t|}e^{-j2\pi ft}} dt
I first went about dealing with the absolute value sign by using the following
\int_{-\infty}^{\infty} e^{-|t|} dt = \int_{-\infty}^{0}...