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DynamicSystems

 Square
 generate a periodic square waveform

 Calling Sequence Square( ) Square(yht, f, d, t0, y0, opts)

Parameters

 yht - (optional) algebraic; height of square wave; default is 1 f - (optional) algebraic; frequency of waveform; default is 1 d - (optional) algebraic; duty cycle from 0 to 1; default is 1/2 t0 - (optional) algebraic; delay to start of square wave; default is 0 y0 - (optional) algebraic; initial value; default is 0 opts - (optional) equation(s) of the form option = value; specify options for the Square 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 the value of sampletime in DynamicSystems[SystemOptions].

 • hertz = truefalse

Specifies that frequency is in hertz (cycles/second); otherwise frequency is in radians/second. The default is the value of hertz in DynamicSystems[SystemOptions].

Description

 • The Square command generates a periodic square waveform.
 • By default, Square returns an expression representing the waveform. If the option discrete is assigned true, Square returns a Vector of data points.
 • The optional parameter yht specifies the height of the signal. Its default value is one.
 • The optional parameter f specifies the frequency of the waveform. The default is one. The units of f are determined by the keyword parameter hertz.
 • The optional parameter d specifies the duty-cycle of the square wave. A numeric value must be between 0 and 1, inclusive.
 • The optional parameter t0 specifies the start time of the waveform. Its default value is zero.
 • The optional parameter y0 specifies the initial value. Its default value is zero.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{Square}\left(\right)$
 $\left\{\begin{array}{cc}{1}& {t}{-}{2}{}{\mathrm{\pi }}{}{\mathrm{trunc}}{}\left(\frac{{t}}{{2}{}{\mathrm{\pi }}}\right){<}{\mathrm{\pi }}\\ {0}& {\mathrm{otherwise}}\end{array}\right\$ (1)
 > $\mathrm{Square}\left(\mathrm{yht},f,d,\mathrm{t0},\mathrm{y0}\right)$
 $\left\{\begin{array}{cc}{\mathrm{y0}}& {t}{<}{\mathrm{t0}}\\ {\mathrm{y0}}{+}\left(\left\{\begin{array}{cc}{\mathrm{yht}}& {t}{-}{\mathrm{t0}}{-}\frac{{2}{}{\mathrm{\pi }}{}{\mathrm{trunc}}{}\left(\frac{\left({t}{-}{\mathrm{t0}}\right){}{f}}{{2}{}{\mathrm{\pi }}}\right)}{{f}}{<}\frac{{2}{}{d}{}{\mathrm{\pi }}}{{f}}\\ {0}& {\mathrm{otherwise}}\end{array}\right\\right)& {\mathrm{otherwise}}\end{array}\right\$ (2)
 > ${\mathrm{Square}\left(\mathrm{discrete}=\mathrm{true}\right)}^{\mathrm{%T}}$
 $\left[\begin{array}{cccccccccc}{1.}& {1.}& {1.}& {1.}& {0.}& {0.}& {0.}& {1.}& {1.}& {1.}\end{array}\right]$ (3)
 > $\mathrm{plot}\left(\mathrm{Square}\left(2,\frac{3}{4},\frac{1}{2},0\right),t=0..18\right)$ 