The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized...

diffraction from rectangular vs. circular apertures, which can be visualized in terms of the product of two sinc functions vs. an Airy function, respectively...

probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such...

system. The rectangular function, the normalized boxcar function, is used to model a unit pulse. The integer part function is not a step function according...

wave or pulse train or rectangular wave is a non-sinusoidal waveform that is the periodic version of the rectangular function. It is held high a percent...

everywhere and hence an entire function. The π-normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used...

brackets Negative number Rectangular function Sign function Sine integral Step response Weisstein, Eric W. "Heaviside Step Function". MathWorld. Bracewell...

response is a sinc function and whose frequency response is rectangular, or to a sinc-in-frequency filter whose impulse response is rectangular and whose frequency...

Equivalently, it may be defined as the convolution of two identical unit rectangular functions: tri ⁡ ( x ) = rect ⁡ ( x ) ∗ rect ⁡ ( x ) = ∫ − ∞ ∞ rect ⁡ ( x...

The Huber loss is the convolution of the absolute value function with the rectangular function, scaled and translated. Thus it "smoothens out" the former's...

\left[-{\frac {1}{2}},{\frac {1}{2}}\right]} , also known as the rectangular function, then: η ε ( x ) = 1 ε rect ⁡ ( x ε ) = { 1 ε , − ε 2 < x < ε 2 ...

domain by a rectangular function causes ripples in the frequency domain for the same reason as a brick-wall low pass filter (rectangular function in the frequency...

low-pass filter. Boxcar averager Rectangular function Step function Top-hat filter Weisstein, Eric W. "Boxcar Function". MathWorld. Retrieved 13 September...

For example, the Fourier transform of the rectangular function, which is integrable, is the sinc function, which is not Lebesgue integrable, because...

can also be defined with respect to the Heaviside step function u(t) or the rectangular function Π(t): x ( t ) = 2 [ ∑ n = − ∞ ∞ Π ( 2 ( t − n T ) T −...

a signal by the rectangular function in the frequency domain or, equivalently, convolution with its impulse response, a sinc function, in the time domain...

Heaviside step function Negative number Rectangular function Sigmoid function (Hard sigmoid) Step function (Piecewise constant function) Three-way comparison...

The integral of the Dirac delta function. Sawtooth wave Square wave Triangle wave Rectangular function Floor function: Largest integer less than or equal...

{\displaystyle \Pi (x)\,\!} (Pi function) – the gamma function when offset to coincide with the factorial Rectangular function π ( n ) {\displaystyle \pi (n)\...

rect ⁡ ( ⋅ ) {\displaystyle \operatorname {rect} (\cdot )} is the rectangular function, so the impulse response approaches h ( t ) = 1 T sinc ⁡ ( t T )...

properties of the sinc function, as the Fourier pair relationship between the rect (the rectangular function) and sinc functions was well known by that...

In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common...

c t ( ⋅ ) {\displaystyle \mathrm {rect} (\cdot )} is the rectangular function. The function r e c t ( t − T / 2 T ) {\displaystyle \mathrm {rect} \left({\frac...

Anti-aliasing filter, Spatial anti-aliasing Rectangular function Sampling (signal processing) Signal (electronics) Sinc function, Sinc filter Lanczos resampling...

These can be found in pulse waves, square waves, boxcar functions, and rectangular functions. In digital signals the up and down transitions between high...

functions into a sum of sine waves representing the odd component of the function plus cosine waves representing the even component of the function....

{\displaystyle \ast } [basis] × {\displaystyle \times } rectangular function, where the rectangular function has a value 1 inside the crystal and 0 outside it...

x(t)={\begin{cases}1&|t|<1/2\\0&{\text{otherwise}}\end{cases}}\qquad } , the rectangular function ⇒ W x ( t , f ) = { 1 π f sin ⁡ ( 2 π f { 1 − 2 | t | } ) | t | <...

introducing a shift in the output function. Boxcar averager Rectangular function Step function Boxcar function Broughton, S. A.; Bryan, K. (2008). Discrete Fourier...

be the rectangular function; then α ≡ sinc ∈ PW {\displaystyle \alpha \equiv \operatorname {sinc} \in \operatorname {PW} } is the sinc function and both...