Convolution Steps Explained

Convolution is a key operation in signal processing, often used to determine the output of a linear time-invariant (LTI) system given its input signal and impulse response. The process involves systematically combining two signals.

The correct sequence for performing continuous or discrete time convolution is outlined below:

1. Plot the signals (C): Visualize both signals, for example, $x(t)$ and $h(t)$ for continuous time or $x[n]$ and $h[n]$ for discrete time. This step aids in understanding the interaction between the signals.
2. Fold (time-reverse) one of the signal (A): Select one signal (let's say $h$) and reverse it in time to get $h(-t)$ or $h[-n]$.
3. Perform multiplication of the signal (B): Shift the time-reversed signal. For a shift $t$ or $n$, the expression becomes $h(t-\tau)$ or $h[n-k]$. Multiply the original signal $x(\tau)$ or $x[n-k]$ by the shifted, time-reversed signal $h(t-\tau)$ or $h[k]$ over the region where they overlap.
4. Perform addition of the magnitudes of the signal (D): Sum (for discrete signals) or integrate (for continuous signals) the product obtained in the previous step across all possible values of the shift variable ($\tau$ or $k$). This yields the final convolution output $y(t)$ or $y[n]$.