Sunday, September 23, 2018

filters - Separate Complicated Signal into Exponential Components


This morning, I asked a similar question about separating simple signals - with constant frequency - into exponential components. User @AndreasH suggested that a hilbert transform can do this as follows:


$$\cos(\omega_1 t) + j ~\textrm{Hilbert}[\cos(\omega_1 t)] = e^{j\omega_1 t}$$


This works great when $\omega_1$ is a real constant, and when time is linear. Is there a way to do it for a more complicated signal? For example,


$$x(t)=\cos(\omega_o t^2 ) $$


When I perform a hilbert transform on this one, I get something with a lot of error functions.



How can I get $y(t)=e^{j\omega_o t^2}$ from $x(t)$?




No comments:

Post a Comment

periodic trends - Comparing radii in lithium, beryllium, magnesium, aluminium and sodium ions

Apparently the of last four, $\ce{Mg^2+}$ is closest in radius to $\ce{Li+}$. Is this true, and if so, why would a whole larger shell ($\ce{...