Sinc - Maple Help

DynamicSystems

 Sinc
 generate a sinc pulse

 Calling Sequence Sinc( ) Sinc(yht, Tw, t0, y0, opts)

Parameters

 yht - (optional) algebraic; height of main pulse above baseline; default is 1 Tw - (optional) algebraic; half-width of main pulse; default is 1 t0 - (optional) algebraic; delay to main pulse; default is 0 y0 - (optional) algebraic; baseline; default is 0 opts - (optional) equation(s) of the form option = value; specify options for the Sinc command

Options

 • discrete = truefalse

Specifies that the output is a Vector containing samples of the waveform. Elements of the Vector are samples of the waveform. The number of elements in the Vector is given by samplecount. The i-th element corresponds to a sample at time t=(i-1)*sampletime. The default is the value of discrete in DynamicSystems[SystemOptions].

 • samplecount = posint

Specifies the number of samples in the output Vector. It is used with the discrete option. The default is the value of samplecount in DynamicSystems[SystemOptions].

 • sampletime = positive

Specifies the time between samples in the output Vector. It is used with the discrete option. The default is half the value of sampletime in DynamicSystems[SystemOptions].

Description

 • The Sinc command generates a sinc pulse.
 • By default, Sinc returns an expression representing the waveform. If the option discrete is assigned true, Sinc returns a Vector of data points.
 • The optional parameter yht specifies the height of the main pulse above the baseline. Its default value is one.
 • The optional parameter Tw specifies the half-width of the base of the main pulse; this is the duration from t=t0 to the first crossing of y=y0.
 • The optional parameter t0 specifies the temporal location of the center of the main pulse. Its default value is zero.
 • The optional parameter y0 specifies the baseline. Its default value is zero.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{Sinc}\left(\right)$
 $\frac{{\mathrm{sin}}{}\left({\mathrm{\pi }}{}{t}\right)}{{\mathrm{\pi }}{}{t}}$ (1)
 > $\mathrm{Sinc}\left(\mathrm{yht},\mathrm{Tw},\mathrm{t0},\mathrm{y0}\right)$
 ${\mathrm{y0}}{+}\frac{{\mathrm{yht}}{}{\mathrm{sin}}{}\left(\frac{{\mathrm{\pi }}{}\left({t}{-}{\mathrm{t0}}\right)}{{\mathrm{Tw}}}\right){}{\mathrm{Tw}}}{{\mathrm{\pi }}{}\left({t}{-}{\mathrm{t0}}\right)}$ (2)
 > ${\mathrm{Sinc}\left(\mathrm{discrete}=\mathrm{true}\right)}^{\mathrm{%T}}$
 $\left[\begin{array}{cccccccccc}{1.}& {0.6366197722}& {-1.305728676}{×}{{10}}^{{-10}}& {-0.2122065907}& {1.305728676}{×}{{10}}^{{-10}}& {0.1273239544}& {-1.305728676}{×}{{10}}^{{-10}}& {-0.09094568174}& {4.488827538}{×}{{10}}^{{-10}}& {0.07073553024}\end{array}\right]$ (3)
 > $\mathrm{plot}\left(\mathrm{Sinc}\left(2,2,0,0\right),t=-10..10\right)$