Function Generator Waveform Examples


The following table shows some examples for the Function Generator, the used equation and an image of the resulting waveforms.


Waveform General Equation Example
Unit Step If (x, XD, XMAX)
XD - Location of step in samples
XMAx - Duration of the waveform in samples

Example: if (x,8192,16384)
Unit Step
Time Reversed Step 1 - If (x, X0, XMAX)
X0 - Location of step in samples
XMAX - Duration of the waveform in samples

Example: 1-if (x,8192,16384)
Time Reversed Step
Unit Pulse If (x, XS , XE)
XS - Location of leading edge in samples
XE - Location of trailing edge in samples

Example: if (x,6192, 10192)
Unit Pulse
Rectangular Unit Pulse Train 0.5+0.5 *sign (sin (2*pi*x/XP))
XP - Period in samples

Example: 0.5+0.5*sign (sin (2*pi*x/1000))
Rectangular Unit Pulse Train
Bipolar Pulse Train rect (2*pi*x/XP , d)
XP - Period in samples
d - Duty cycle in percent (%)

Example: rect(2*pi*x/1000,50)
Bipolar Pulse Train
Ramp x*(DV/DX)
DV/DX - Slope of the ramp in volts/samples

Example: x*(1/16384)
Ramp
Delayed Ramp (x-XD)* (DV/DX)* if(x, XD, XMAX)
XD - Delay in samples
DV/DX - Slope of the ramp in volts/samples
XMAX - Duration of the waveform in samples

Example: (x-6192)*(1/16384)*if(x,6192,16384)
DelayedRamp
Truncated Ramp (Delayed) (x-XD)* (DV/DX)* if(x, XD, XE)
XD - Delay in samples
DV/DX - Slope of the ramp in volts/samples
XE - Location of trailing edge in samples

Example: (x-6000)*(1/4000)*if(x,6000,10000)
Truncated Ramp (Delayed)
Negative Ramp (Truncated) (x-XD)* (-1*DV/DX)* if(x, XD, XE)
XD - Delay in samples
DV/DX - Slope of the ramp in volts/samples
XE - Location of trailing edge in samples

Example: (x-6000)*(-1/4000)*if(x,6000,10000)
Negative Ramp (Truncated)
Periodic Triangle Wave Tri (x/ XP , d)
XP - Period in samples
d- Duty cycle in percent (%)

Example: tri(x/1000,95)
Periodic Triangle Wave
Sinewave sin(2*pi*x/XP)
XP - Period in samples

Example: sin(2*pi*x/1000)
Sinewave
Gated Sine sin(2*pi*x/ XP) * if(x, XS ,XE)
XP - Period in samples
XS - Location of leading edge in samples
XE - Location of trailing edge in samples

Example: sin(2*pi*x/1000)*if(x,6000,10000)
Gated Sine
Decaying Exponential e ^ (-1*(x/XT))
XT - Exponential time constant in samples

Example: e^(-1*(x/500))
Decaying Exponential
Delayed Decaying Exponential (e ^ (-1*(x- XD)/ XT))* if(x,XD ,XMAX)
XD - Delay in samples
XT - Exponential time constant in samples
XMAX - Duration of the waveform in samples

Example: (e^(-1*((x-6192)/500))) * if (x,6192,16834)
Delayed Decaying Exponential
Rising Exponential 1-(e^(-1*(x/XT)))
XT - Exponential time constant in samples

Example: 1-(e^(-1*((x)/500)))
Rising Exponential
Delayed Rising Exponential (1-(e^(-1*(x-XD /XT))))* if(x,XD ,XMAX)
XD - Delay in samples
XT - Exponential time constant in samples
XMAX - Duration of the waveform in samples

Example: 1-(e^(-1*((x-6192)/500)))) * if(x,6192,16384)
Delayed Rising Exponential
Exponential Pulse (1-(e^(-1*(x-XS /XT))))* if(x,XS ,XP) + (e ^ (-1*(x- XP)/ XT))* if(x,XP ,XMAX)
XT - Exponential time constant in samples
XMAX - Duration of the waveform in samples
XS - Location of start of rise in samples
XP - Location of peak in samples

Example: (1-(e^(-1*((x-6192)/500)))) * if(x,6192,8192) + (e^(-1*((x-8192)/500))* if(x,8192,16384))
Exponential Pulse
Exponentially Damped Sine (e ^ (-1*(x/XT))) * sin(2*pi*x/ XP)
XT - Exponential time constant in samples
XP - Period in samples

Example: e^(-1*(x/2500)) *sin(2*pi*x/500)
Exponentially Damped Sine
Gaussian Pulse e^((-1/2)*((x-XD)^2)/(XS^2))
XD - Delay (mean) in samples
XS - Pulse Width (sigma)

Example: e^((-1/2)*((x-8192)^2)/(1000^2))
Gaussian Pulse
Amplitude Modulation 0.5*sin(2*pi*x/XC)*(1+ KM *f(x))
XC - Carrier period in samples
KM - Modulation index 0 to 1
F(x) - modulation waveform

Example: 0.5*sin(2*pi*x/250)*(1+(0.75*cos(2*pi*x/5000)))
Amplitude Modulation
Sine Amplitude Sweep x*(DV/DX) * sin(2*pi*x/XC)
DV/DX - Slope of the ramp in volts/samples
XC - Carrier period in samples

Example: x*(1/16384)*sin(2*pi*x/250)
Sine Amplitude Sweep
Frequency Modulation Sin(2*pi*x/XC +(XM /XDev)*cos(2*pi*x/XM)
XC - Carrier period in samples
XM - Modulation Period in samples
XDev - Period deviation in samples

Example: sin(2*pi*x/250+(5000/500)*cos(2*pi*x/5000))
Frequency Modulation
Linear Frequency Sweep Sin(pi*(2*(x/XS)+(((1/XE)-(1/XS))/XMAX)*x^2))
XS - Start Period in samples
XE - End Period in samples
XMAX - Duration of the waveform in samples

Example: sin(pi*(2*(x/5000)+(((1/500)+ (-/5000))/16384)*x^2))
Linear Frequency Sweep
Logarithmic Frequency Sweep Sin*2*pi(XMAX /ln(XS /XE)/XS)*e^((ln(XS /XE)/XS)*x)-1)
XS - Start Period in samples
XE - End Period in samples
XMAX - Duration of the waveform in samples

Example: sin(2*pi*(16384/ln( 5000/500)/5000) * e^((ln(5000/500)/16384)*x)-1)
Logarithmic Frequency Sweep
Phase Modulation Sin((2*pi*(x/XC)+ K*Sin(2*pi*(x/XM)))
XC - Carrier period in samples
XM - Modulation Period in samples
K - Peak phase excursion in radians

Example: sin(2*pi*(x/500)+7* sin(2*pi*(x/5000)))
Phase Modulation
Lorentzian Pulse 1/(1+((x-XD)/(XW))^2)
XD - Time delay in samples
TW - Half width point of the pulse in samples

Example: 1/(1+((x-8192)/500)^2)
Lorentzian Pulse
Full Wave Rectified Sine Abs(Sin(2*pi*x/ XP))
XP - Sine wave period in samples

Example: Abs(Sin(2*pi*x/5000))
Full Wave Rectified Sine
Half Wave Rectified Sine 0.5*(sin(2*pi*x/XP)+Abs(Sin(2*pi*x/ XP)))
XP - Sine wave period in samples

Example: 0.5*(sin(2*pi*x/5000)+Abs(Sin(2*pi*x/5000)))
Half Wave Rectified Sine
Sinc sin((x-XD)/XP)/((x- XD)/ XP)
XD - Time delay in samples
XP - Sinc period in samples

Example: sin((x-8192)/500)/((x-8192)/500)
Sinc

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