Given the system/filter $H(\omega)=\frac{1}{5-j\omega}$, find $h(t)$, it's magnitude response and phase and identify what type of filter it is.
Now clearly given it's form, $h(t)=e^{5t}u(-t)$, but I'm confused on finding it's magnitude and phase as every example uses the form $\frac{1}{a+j\omega}$.
Another confusing function in regards to its magnitude, phase and type is $H(\omega)=\pi\delta(\omega)+\frac{1}{j\omega}$, again this is simply $h(t)=u(t)$ but has infinite magnitude at $\omega=0$ with $\omega$ approaching positive and negative infinity the manitude approaches 0 while it's phase is $\frac{\pi}{2}$, correct? Would this be a high-pass filter?