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DynamicSystems

  

Chirp

  

generate a chirp waveform

 

Calling Sequence

Parameters

Options

Description

Examples

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

withDynamicSystems:

Chirp

&lcub;0t<0sin1&plus;ttotherwise

(1)

Chirpypk&comma;f0&comma;k&comma;t0&comma;y0

&lcub;y0t<t0y0&plus;ypksinf0&plus;kt0&plus;tt0&plus;totherwise

(2)

Chirphertz&equals;true

&lcub;0t<0sin2&pi;1&plus;ttotherwise

(3)

evalf&lsqb;2&rsqb;Chirpdiscrete&equals;true%T

0.0.910.280.540.910.990.920.520.250.89

(4)

plotChirp1&comma;0&comma;18&comma;0&comma;0&comma;hertz&equals;true&comma;t&equals;0..4

See Also

DynamicSystems

DynamicSystems[Ramp]

DynamicSystems[Sinc]

DynamicSystems[Sine]

DynamicSystems[Square]

DynamicSystems[Step]

DynamicSystems[Triangle]

 


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