communication systems lab 1

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  Lab 1 By: Amjad Iqbal  Lab 01-Study of Signal Characteristics using  MATLAB ã   Basic Signal Generation in MATLAB: Unit Step Function: The Heaviside step function, or the unit step function, usually denoted by u , is a discontinuous function whose value is zero for negative argument and one for positive argument The function is used in the mathematics of control theory and signal processing to represent   a signal that switches on at a specified time and stays switched on indefinitely. Mathematically, a continuous time unit step function is written as In discrete form, a unit step function can be mathematically written as As explained in the previous lab, generation of continuous time signals is an artificial concept in MATLAB, so we would be dealing with discrete time unit step sequence. Graphically, unit step sequence is shown in figure 1.1. Figure 1.1: Unit Step Sequence  Lab 1 By: Amjad Iqbal Unit Impulse Sequence: Unit Impulse sequence is very important to characterize the impulse response of the system. Mathematically an impulse sequence is represented as: Graphically an impulse sequence is shown in figure 1.2 Figure 1.2: Impulse Sequence  Ramp Sequence: Mathematically a ramp sequence is defined as: Graphically a ramp sequence is shown in figure 1.3  Lab 1 By: Amjad Iqbal Figure 1.3: Ramp Sequence Signum Sequence: Signum sequence can be mathematically written as: Graphically, signum sequence is shown in figure 1.4 Figure 3.4: Signum Sequence  Lab 1 By: Amjad Iqbal Square Wave: Square wave is very important in communications related aspect. For example all the line coding techniques like RZ, NRZ etc consists of square waves. For wireline communications the line coded bits are communicated and for wireless communications the bits are first coded and then modulated. 5Hz square wave is shown in shown in figure 1.5. Figure 1.5: Square Wave ã    Periodic Sequences in MATLAB: A discrete-time signal is said to be periodic if there exist a positive constant N (the period) for which, for all. We can easily generate periodic signal in MATLAB. For example, consider we have a vector, and we want to periodically repeat the given vector four times, following is the MATLAB code to do this x=[1 1 0 0 -1 -1];   n=1:length(x);   subplot(2,1,1)   stem(n,x,'fill', 'Linewidth',2),grid on   y=repmat(x,1,4);  
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