Standard Test Signals

Standard Test Signals

The standard test signals are:-

• Impulse Signal
• Step Signal
• Ramp Signal
• Parabolic Signal

These signals are used to know the performance of the systems with time.

Unit Impulse Signal [ δ(t) ]
A unit impulse signal, δ(t) is defined as

[tex]\delta (t)=0[/tex] for [tex]t\neq 0[/tex]

and [tex]\int_{0^-}^{0^+} \delta (t)dt=1[/tex]

So, the unit impulse signal exists only at ‘t’ is equal to zero. The area of this signal under small interval of time around ‘t’ is equal to zero is one. The value of unit impulse signal is zero for all other values of ‘t’.

Unit Step Signal [ u(t) ]
A unit step signal, u(t) is defined as

[tex]u(t)=1;t\geq 0[/tex]

[tex]=0; t<0[/tex]

So, the unit step signal exists for all positive values of ‘t’ including zero. And its value is one during this interval. The value of the unit step signal is zero for all negative values of ‘t’.

Unit Ramp Signal [ r(t) ]
A unit ramp signal, r(t) is defined as

[tex]r(t)=t; t\geq 0[/tex]

[tex]=0; t<0[/tex]

We can write unit ramp signal, [tex]r(t)[/tex] in terms of unit step signal, [tex]u(t)[/tex] as

[tex]r(t)=tu(t)[/tex]

So, the unit ramp signal exists for all positive values of ‘t’ including zero. And its value increases linearly with respect to ‘t’ during this interval. The value of unit ramp signal is zero for all negative values of ‘t’.

Unit Parabolic Signal [ p(t) ]
A unit parabolic signal, [tex]p(t)[/tex] is defined as,

[tex]p(t)=\frac{t^2}{2}; t\geq 0[/tex]

[tex]=0; t<0[/tex]

We can write unit parabolic signal, [tex]p(t)[/tex] in terms of the unit step signal, [tex]u(t)[/tex] as,

[tex]p(t)=\frac{t^2}{2}u(t)[/tex]

So, the unit parabolic signal exists for all the positive values of ‘t’ including zero. And its value increases non-linearly with respect to ‘t’ during this interval. The value of the unit parabolic signal is zero for all the negative values of ‘t’.