Search⌘ K
AI Features

Convolution of Complex Signals

Explore the convolution process for complex digital signals by breaking down inphase and quadrature components. Understand how four real convolutions combine to form complex convolution, highlighting practical aspects of implementation in digital systems.

We'll cover the following...

The convolution output y[n]y[n] between two signals x[n]x[n] and h[n]h[n] is expressed as:

y[n]=mx[m]h[nm]y[n]=\sum _m x[m]h[n-m]

Real and imaginary parts

When the two signals are complex, we can write

x[n]=xI[n]+jxQ[n]h[n]=hI[n]+jhQ[n]\begin{align*} x[n] &= x_I[n]+jx_Q[n]\\ h[n] &= h_I[n]+jh_Q[n] \end{align*} ...