Manuals/calci/SINC

SINC(X)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} is any real number.

Description

• This function shows the value of the cardinal sin function.
• In $SINC(X)$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} is any real number.
• The full name of the function is sine cardinal,but it is commonly referred to by its abbreviation, Sinc.
• The unnormalized SINC function is defined by

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SINC(X) = \begin{cases} 1 & \mbox{for }n\mbox{ x=0} \\ \frac{Sin x}{x}, & \\mbox{otherwise} \end{cases}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SINC(X)=\begin{cases} 1 & for & x=0 \\ \frac{Sin x}{x} & Otherwise\\ \end{cases}}

• The normalized SINC function is defined by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SINC(X)= \frac{SIN(pi())x}{pi()x}} .
• The value at x = 0 is defined to be the limiting value Sinc(0) = 1.
• The only difference between the two definitions is in the scaling of the independent variable (the x-axis) by a factor of π.