Chirp - Maple Help

DynamicSystems

 Chirp
 generate a chirp waveform

 Calling Sequence Chirp( ) Chirp(yht, f0, k) Chirp(yht, f0, k, t0, y0, opts)

Parameters

 yht - (optional) algebraic; height of chirp; default is 1 f0 - (optional) algebraic; initial frequency of waveform; default is 1 k - (optional) algebraic; linear coefficient of frequency versus time; default is 1 t0 - (optional) algebraic; delay to start of chirp; default is 0 y0 - (optional) algebraic; initial value; default is 0 opts - (optional) equation(s) of the form option = value; specify options for the Chirp 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 Chirp command generates a linear chirp waveform, that is, a sinusoidal waveform whose frequency varies linearly with time.
 • By default, Chirp returns an expression representing the waveform. If the option discrete is assigned true, Chirp returns a Vector of data points.
 • The optional parameter yht specifies the height of the signal. Its default value is one.
 • The optional parameter f0 specifies the initial frequency of the waveform. Its default value is one. The units of f are radians/second unless the option parameter hertz is assigned true, in which case the units are hertz.
 • The optional parameter k specifies the rate of frequency increase with time. Its default value is one. The instantaneous frequency is f0 + k*(t-t0).
 • The optional parameter t0 specifies the start time of the waveform. Its default value is zero.
 • The optional parameter y0 specifies the vertical offset. Its default value is zero.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{Chirp}\left(\right)$
 $\left\{\begin{array}{cc}{0}& {t}{<}{0}\\ {\mathrm{sin}}{}\left(\left({1}{+}{t}\right){}{t}\right)& {\mathrm{otherwise}}\end{array}\right\$ (1)
 > $\mathrm{Chirp}\left(\mathrm{ypk},\mathrm{f0},k,\mathrm{t0},\mathrm{y0}\right)$
 $\left\{\begin{array}{cc}{\mathrm{y0}}& {t}{<}{\mathrm{t0}}\\ {\mathrm{y0}}{+}{\mathrm{ypk}}{}{\mathrm{sin}}{}\left(\left({\mathrm{f0}}{+}{k}{}\left({-}{\mathrm{t0}}{+}{t}\right)\right){}\left({-}{\mathrm{t0}}{+}{t}\right)\right)& {\mathrm{otherwise}}\end{array}\right\$ (2)
 > $\mathrm{Chirp}\left(\mathrm{hertz}=\mathrm{true}\right)$
 $\left\{\begin{array}{cc}{0}& {t}{<}{0}\\ {\mathrm{sin}}{}\left({2}{}{\mathrm{\pi }}{}\left({1}{+}{t}\right){}{t}\right)& {\mathrm{otherwise}}\end{array}\right\$ (3)
 > ${\mathrm{evalf}}_{2}\left({\mathrm{Chirp}\left(\mathrm{discrete}=\mathrm{true}\right)}^{\mathrm{%T}}\right)$
 $\left[\begin{array}{cccccccccc}{0.}& {0.91}& {-0.28}& {-0.54}& {0.91}& {-0.99}& {-0.92}& {-0.52}& {0.25}& {0.89}\end{array}\right]$ (4)
 > $\mathrm{plot}\left(\mathrm{Chirp}\left(1,0,\frac{1}{8},0,0,\mathrm{hertz}=\mathrm{true}\right),t=0..4\right)$