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Formula:
The convolution of two functions or sequences, f and g, is a fundamental mathematical operation in many fields. It represents the amount of overlap between one function and a 'flipped' and 'shifted' version of the other.
Continuous Convolution: (f * g)(t) = ∫-∞∞ f(τ)g(t-τ) dτ
Discrete Convolution: (f * g)[n] = ∑m=-∞∞ f[m]g[n-m]
Where:
- f and g are the input functions or sequences.
- τ and m are integration/summation variables.
- t and n are the output variables.