Method to write a signal function f(t) ,if its graph is given

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Q. write function f(t) of  signal whose graph is given below ?

signal and system 1

 

Above given signal is represented in the form of  steps signal 

So we can write graph function as 

f(t) = (3-0) u(t-(-3)) + (-2-3)u(t-0) +(6-(-2))u(t-2) + (0-6)u(t-4)

f(t) = 3u(t-3) -5u(t) + 8u(t-2) -6u(t-4)

NOTE:  Amplitude of step at any time t= T will be 

              = value of amplitude of next step – value of amplitude of previous step 

             Amplitude at ( t=-3)  = (3)-(0)  =  3

             Amplitude at ( t=0)   =(-2)-(3)  = -5

              Amplitude at (t =2)  = (6)-(-2)  = 8

             Amplitude at( t=4)     = (0)- (6) =-6

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