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Practice Question on Causal LTI systems defined by a linear, constant coefficient difference equation
Consider the LTI system defined by the difference equation
$ y[n]-\frac{1}{2}y[n-1]=x[n]\ $
a) What is the frequency response of this system?
b) What is the unit impulse response of this system?
c) What is the system's response to the input $ x[n] = \left( \frac{1}{5}\right)^n u[n] \ $?
c) What is the system's response to the input $ x[n] =\cos \left(\frac{\pi}{2} n \right) \ $?
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Answer 1
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Answer 2
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Answer 3
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