# Definition:Convolution of Real Sequences

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*This page is about Convolution of Real Sequences. For other uses, see Convolution.*

### Definition 1

Let $\sequence f$ and $\sequence g$ be real sequences.

The **convolution** of $f$ and $g$ is defined as:

- $\ds \sequence {f_i} * \sequence {g_i} := \sum_{j \mathop = 0}^i f_j g_{i - j}$

### Definition 2

Let $f: \Z \to \R$ and $g: \Z \to \R$ be mappings from the integers to the real numbers.

The **convolution** of $f$ and $g$ is defined as:

- $\ds \map f i * \map g i := \sum_{j \mathop \in \Z} f_j g_{i - j}$

## Sources

- 1978: Ronald N. Bracewell:
*The Fourier Transform and its Applications*(2nd ed.) ... (previous) ... (next): Frontispiece - 1978: Ronald N. Bracewell:
*The Fourier Transform and its Applications*(2nd ed.) ... (previous) ... (next): Chapter $4$: Notation for some useful Functions: Summary of special symbols: Table $4.1$ Special symbols - 1978: Ronald N. Bracewell:
*The Fourier Transform and its Applications*(2nd ed.) ... (previous) ... (next): Inside Back Cover