The block diagram shown below implements a discrete time system with input on the left and output on the right. The variables , , , , , , and , are scalar constants and the blocks labeled are unit delay elements. a) Without assigning numerical values to any of the constants, determine the difference equation that relates the input to the output as a function of the scalar constants. b) Use the result of part a) to obtain as a function of the scalar constants. From this point forward, it will be assumed that . This simplifies the system and makes the math a little easier. With the bottom delay element has no role to play so it can be eliminated. For convenience define the parameter to take on the value .
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First case: set , , , , . Plot the magnitude of as a function of . Plot the phase of as a function of . What type of filter does this system implement?
Second case: repeat the first case except that now . How is this system different than the system of the first case?
Third case: using the value for given in the first case, set , , , , . Plot the magnitude of as a function of . Plot the phase of as a function of . What type of filter does this system implement?
Fourth case: repeat the third case except that now . How is this system different than the system of the third case?
For the cases below, two new parameters will be defined, and . Numerical values will be provided for these two parameters below.
Fifth Case: set , , , , . Plot the magnitude of as a function of . Plot the phase of as a function of . In this case use and . What type of filter does this system implement?
Sixth case: repeat the fifth case except that now and . How is this system different than the system of the fifth case?
Seventh Case: set , , , , . Plot the magnitude of as a function of . Plot the phase of as a function of . In this case use and . What type of filter does this system implement?
Eighth case: repeat the seventh case except that now and . How is this system different than the system of the seventh case?
The experiment will consist of using MATLAB to evaluate the output that is produced when various sinusoidal signals are applied to the various systems. Depending on the system and the frequencies of the sinusoids, different outputs will be observed. The goal is to be able to observe the effect that the system has on the input signal.
When a specific input is given, the output will be computed using recursive methods. A recursion written in MATLAB will have to be created in order to determine as a function of . This will be plotted and comparisons will be made between the input and the output in order to be able to determine the effect that the system has on the input signal.
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ECE124ExperimentDW.docx
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