Generate periodic signals (square waves and triangular waves), exponential signals, sinusoidal signals, exponentially damped signals with MATLAB. To visualize the discrete time signal use stem command.

Periodic signal:

A periodic signal x (t) is a function of time that satisfies the condition –

                         x (t) =x (t + T) .............(1)    for all  t,

                                             Where T is a constant. Clearly, if this condition is satisfied for T = T₀ ,say, then it is also satisfied for T = 2T₀, 3T₀, 4T₀,...... The smallest value of T that satisfies the eq-1 is called the fundamental period of x (t). Accordingly, the fundamental period T defines the duration of one complete cycle of x (t). The reciprocal of the fundamental period T is called the fundamental frequency of  the periodic  signal x (t); it describe  how  frequently the periodic signal x (t) repeats itsself. we thus formally write-

                   f = 1/T

The frequency f is measured in hertz or cycle per second. The angular frequency, measured in radians per second, is defined by-       

                        

                ω = 2πf = 2π/T 

Example of periodic signal:

                                           

                                   Continuous time Square wave

                                                                     

MAT LA Bcommand:

                                  >>A=2;

                                       >>w = 10*pi;

                                       >>rho = 0.5;

                                       >>t = 0: .001: 1;

                                       >>sq=A*square (w * t , rho );

                                       >>plot (t , sq )

 Description:

                        Here

 A= Amplitude of the signal 

w = Fundamental frequency (measured in radians/second)

                                    rho = Duty cycle

                                    t = 0 : .001 : 1

                                   Time interval = 0 to 1 second

                                  Sampling interval = .001 second

                           plot (t , sq ) is for to plot a continuous time signal

Discrete time square wave

 MAT LAB command:

                                     

  >>A =1;

                                       >>0mega = pi/4;

                                       >> n= -10:10;

                                       >> x = A* square (omega * n);

                                        >> stem (n , x )       

Triangular wave

MAT LA Bcommand:

                                      >>A = 1;

                                                >>w₀ =10*pi;

                                                >>w =0.5;

                                                >>t =0 : .001 : 1;

                                                >>tri =A*sawtooth (w₀*t ,w);

                                                >>plot (t ,tri )

Discrete time triangular wave

MAT LA Bcommand:

                                     >>A =1;

                                            >>0mega = pi/18;

                                            >> n= -20:20;

                                            >> x = A* sawtooth (omega * n);

                                            >> stem (n , x )   

Exponential signal:

MAT LAB commands for decay exponential signal( x(t) = 5 e^-at ):

                                           >>B = 5;

                                           >>a = 6; 

                                           >>t = 0 : .001 : 1;

                                           >>x = B*exp (-a*t );

                                           >>plot (t ,x )

MAT LA Bcommand  for discrete time decay exponential signal:

                                     

>>B = 1;

                                                >>r = 0.85;

                                                >>n = -10 :10;

                                                >>x = B*r. ^ n;

                                                >>stem (n , x )

                         

 Note that , in this example , the base  r is a scalar but the exponent is a vector. Hence the use of the symbol  .^  to denote element by element power. 

MAT LABcommand for growing exponential signal (x(t) = 5e^at):

                                     

>>B = 1;

                                                >>a = 5;

                                                >>t =0 : .001 : 1;

                                                >>x = B*exp( a*t );

                                                >>plot( t ,x )

Here B and a are real parameters. The parameter B is the amplitude of the exponential signal measured at the time t = 0.

MAT LABcommand for discrete time growing exponential signal:

                                     

>>B = 1;

                                                >>r = 0.85;

                                                >>n = -10 :10;

                                                >>x = B*r. ^ -n;

                                                >>stem (n , x )