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Convolution Operation

The fundamental operation behind filtering

Input Signal x[n]

Impulse Response h[n]

Output y[n] = x * h

Convolution Animation - Flip, Shift, Multiply, Sum

y[n] = Σ x[k] · h[n - k] = x[n] * h[n]

Understanding Convolution

Convolution combines two signals to produce a third. In signal processing, it applies a filter (impulse response) to an input signal.

The Steps:

1. Flip the kernel (impulse response) horizontally

2. Shift it across the input signal

3. Multiply overlapping samples point-by-point

4. Sum the products to get one output sample

Applications: Smoothing, sharpening, edge detection, reverb, echo, blur effects