Definition:Rectangle Function
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Definition
The rectangle function is the real function $\Pi: \R \to \R$ defined as:
- $\forall x \in \R: \map \Pi x := \begin {cases} 1 : & \size x \le \dfrac 1 2 \\ 0 : & \size x > \dfrac 1 2 \end {cases}$
Graph of Rectangle Function
The graph of the rectangle function is illustrated below:
Also known as
The rectangle function is also known as the gate function, especially in the context of electronics.
The rectangle function of $x$ can be voiced rect $x$, and so written when the Greek alphabet is not conveniently to be used.
Sources
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (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