A signal is a function or a data set representing a physical quantity or variable. Usually, the signal encapsulates information about the behavior of a physical phenomenon, for example, electrical current flowing through a resistor, sonar sound waves propagating under water, or earthquakes. Mathematically, a signal is represented as a function of an independent variable t, typically representing time. Thus, a signal is denoted x(t).
Continuous-Time and Discrete-Time Signals
A signal x(t) is a continuous-time signal if t is a continuous variable. If t is a discrete variable, that is, x(t) is defined at discrete times, then x(t) is a discrete-time signal - often denoted as x(n), where n is an integer. A discrete-time signal x(n) may represent a phenomenon for which the independent variable is inherently discrete, such as the daily closing value of a stock price, or it may be obtained by sampling a continuous-time signal x(t) at t = nT, where T is the sampling period.
The following examples deal primarily with discrete-time signals. A few examples of frequently-encountered discrete time signals are given below.
The Unit Step Signal
1. Define the unit step function using the Heaviside Step function.
The Heaviside Step function states that f(0)=0.5
2. Define the range and plot the unit step function.
The Unit Impulse Signal
1. Define the unit impulse function.
2. Plot the unit impulse function.
3. Set a value of k to shift the impulse by k samples to the right.
Sinusoidal Signal
1. Set the frequency.
2. Define the sinusoidal function.
3. Plot the sinusoidal function.
Exponential Signal
1. Set the alpha factor.
2. Define the exponential function.
3. Plot the exponential function.
Exponentially Decaying Sinusoid
Plot the function resulting from the product of the sinusoidal function and the exponential function.
The result is an exponentially decaying sinusoid function.
Analog and Digital Signals
If a continuous-time signal x(t) can take on any value within a continuous time interval, then x(t) is called an analog signal. If a discrete-time signal x(n) can take on only a finite number of distinct values, then it is called a digital signal. To convert an analog signal into a digital signal, the analog signal needs to be sampled and quantized.
Real and Complex Signals
A signal x(t) is a real signal if its values are real numbers. Similarly, a signal x(t) is a complex signal if its values are complex numbers. Use functions phase and phasecor to manipulate complex signals.
Deterministic and Random Signals
Deterministic signals are those whose values are completely specified for any given time. Thus, a deterministic signal can be modeled by a known function of time x(t). Random signals, on the other hand, are those signals that can take random values at any given time. Random signals can only be characterized statistically. The noise-generator functions whiten, gaussn, and onefn are designed to produce pseudo-random signals characterized by user-defined statistical parameters.
