The unit impulse and step functions in Discrete-time

1.The Discrete-time Unit Impulse 

The the unit impulse is defined as  eq. 1 and it is shown in fig. 1 with the duration from -10 to 10 ;

                                     Equation 1                                                        Figure 1  Discrete-time unit impulse 

To create a figure like fig.1 in MATLAB ，you may need the code  as below 

>> n = -10:10; delta = [(n==0)];>> stem(n,delta,'r','filled');>> xlabel('n'); ylabel('delta(n)');>> title('Discrete-time Unit Impulse');

2.The Discrete-time Unit step 

The discrete-time unit step is denoted by u[n] , where 'u' is probably the abbreviation of 'unit'.  u[n] is defined by the equation 2 and the unit sequence is shown in figure 2 .

                                Equation 2                                                                Figure 2 : Discrete-time unit step sequence 

Again, we can use MATLAB to create the unit step sequence and plot it by the following lines of codes .

>> n = -10:10; unitstep = [(n>=0)];>> stem(n,unitstep,'r','filled');>> xlabel('n');ylabel('u[n]');>> title('Discrete-time Unit Step Sequence');