In signals and system, we need to use some standard or elementary signals. In this section, we will show some important standard signal graphically and express them mathematically.
Some of the standard continuous and discrete time signals are :
A DC signal is shown in the figure. As seen from the figure or waveform the amplitude A of a direct current signal remains constant independent of time.
Sinusoidal signal :
The sinusoidal signal includes sine and cosine signals.
Mathematically the can be represented as follows :
A sine signal x(t) = A sin ωt = A sin (2∏ft )
Same way in a cosine signal x(t) = A cos ωt = A sin (2∏ft )
Here = A = Amplitude
ω = Angular frequency = 2∏f
Signum function :
The signum function is as shown in figure. It is represented mathematically as follows :
sgn(t) = 1 for t > 0
= - 1 for t < 0
Delta or unit impulse function :
The delta function is an extremely function used for the analysis of the communication system. The impulse response of a system is its response to a delta function applied at the input signal.
Delat function : = 0 for t ≠ 0
Unit ramp function :
A continuous time unit ramp signal is denoted by ramp called r (t). Mathematically it is expressed as,
r (t) = t for t >= 0
= 0 for t< 0
Some of the standard continuous and discrete time signals are :
- A DC signal
- Unit step signal
- Delta or unit impulse function
- Sinusoidal signal
- Exponential function
- Signum function
- Sinc function
A DC signal is shown in the figure. As seen from the figure or waveform the amplitude A of a direct current signal remains constant independent of time.
A DC signal is x (t) = A - ∞ < t < ∞
The sinusoidal signal includes sine and cosine signals.
Mathematically the can be represented as follows :
A sine signal x(t) = A sin ωt = A sin (2∏ft )
Same way in a cosine signal x(t) = A cos ωt = A sin (2∏ft )
Here = A = Amplitude
ω = Angular frequency = 2∏f
Unit step signal :
The unit step signal is as shown in the figure. It has a constant amplitude of unity(1) for the zero of the positive value of time "t" . Whereas it has zero value for a negative value of t.
The unit step signal is mathematically represented as,
Unit step signal called as u (t) = 1 for t > 0
= 0 for t < 0
The signum function is as shown in figure. It is represented mathematically as follows :
sgn(t) = 1 for t > 0
= - 1 for t < 0
Delta or unit impulse function :
The delta function is an extremely function used for the analysis of the communication system. The impulse response of a system is its response to a delta function applied at the input signal.
Delat function : = 0 for t ≠ 0
A continuous time unit ramp signal is denoted by ramp called r (t). Mathematically it is expressed as,
r (t) = t for t >= 0
= 0 for t< 0
