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Convolution of Complex Signals

Convolution of Complex Signals

Explore why convolution between two complex signals is more computationally expensive compared to real signals.

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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*} ...