Procedure of the following three simulation experiment

 

 

     Exp-2(a) Linearity and Non linearity property

 

     Exp-2(b) Time variant and Time invariant property

 

     Exp-2(c) Causality and Non causality property

 

 

   -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ -- ♦ --

   

 

    Exp-2(a) Procedure for Linearity and Non-linearity property:

 

• The block diagram of this experimental setup to verify the linearity/non-linearity of the system is shown on a separate tab.
  

 

• The experimental setup has two input signals [ f(t) and g(t) ] which are applied separately to the system under test. The responses of the system [ x(t) and y(t) ] to each of the inputs are shown in corresponding scopes of different colors. The linear combination of these input signals [ A f(t) + B g(t) ] is also applied separately to the system and its response is shown in a separate colored scope. The linear combination of the individual response signals [ C x(t) + D y(t) ] is also shown in the same scope.

 

• The two inputs to be applied can be chosen from the selection menu By default, the input signal f(t) is Sine and  g(t) is also Sine. Similarly system under test can also be selected from a menu and by default "system 1" is selected. By default the weights (A,B,C,D) of the input and output linear combiners are all set to zeros and they can be changed separately with help of the appropriate knobs. 

 

• Run the experiment by pressing""button.
  

 

• The two scopes on the right hand side of the page will show the responses of the system to the corresponding inputs. The middle scope shows the zero signals. This is the degenerate case. Change the gains of the combiners to verify the intended property of the system under test.

 

• As soon as any inference about the intended property of the system is made an appropriate message about the system property is displayed in the "Message Board" shown at the top of the middle scope.

 

• Once the property of a chosen system is verified, you may select the different kind of signals provided for either of the  inputs and note that the inference about the system remains the same. But when same kind of signals are chosen as inputs, we can verify only the homogenity property of the system and make an appropriate inference which would be displayed in the "Message Board".

 

• Press the""button to stop the experiment.
  

                                                                                                                                                                                          Top

 

    Exp-2(b) Procedure for Time variance and Time invariance property: 

 

• The block diagram of the experimental setup to verify the time variance and time invariance property of the system is shown on the experiment page.

 

• The top and bottom scopes on the left hand side of the page show the input signal and its shifted version respectively. The top and the bottom scopes on the right hand side of the page show the responses of the system to the chosen input and its shifted version respectively. The middle scope shows the shifted version of the output waveform. 

 

• By default the input applied to the system is truncated sine signal and time shifts of the input and output signal time shifters are set to zero.

 

• Run the experiment by pressing""button.
  

 

• Modify the input and output shifter to get a match between the shifted value of the output and response to shifted input.
  

 

• As soon as the match occurs the inference about the intended property of the system displayed in the "Message Board" shown at the top of "Output Time Shifter" knob.

 

• Once the intended property is verified for a chosen system you may select other inputs and see that it holds for any other input.

 

• Stop the experiment by pressing ""button.
                                                                                                                                                                  

                                                                                                                                          Top

 

    Exp-2(c) Procedure for Causality and Non causality property:

 

• Run the experiment by pressing"" button.

 

• By default system 1 is selected and the input signal is a unit impulse.

 

• The response of the system is shown on the right hand side. As the input is an unit impulse so the response of the system is an impulse response.
  

 

• The "Message Board" shows the characterization of causality property of the chosen system.
  

 

• Select different input systems from the selection menu and note their causality property.

 

• In case of noncausal / anticausal systems, introduce the delay in the system so as to make them causal.
  

 

 

  Warning: As the systems given are discrete-time, do not type the time delay values directly in window showing  the modified value. Instead use the up/down buttons only for modifying the values.

                                                                                                                                                          

                                                                                                                                    Top