Digital Signal Processing
chantinh2004
Week3_assignment.docxAssignment 2: z-Transform
Note: You may use Matlab to solve the problems where necessary
All questions carry equal points
1. Find the z-transform and the ROC of the sequence x[n] = (0.5)n u[n].
2. Find the poles and zeros of the z-transform. Does this function correspond to a convergent sequence?
3. Determine the inverse z-transform corresponding to the function .
4. The impulse response of an LTI discrete-time system is given by h[n] = (0.2)n u[n]. If the input to this system is x[n] = (0.3)n u[n], calculate the output using z-transform method.
5. Consider the causal LTI discrete-time system described by y[n] = 3x[n] + 0.4y[n-1] + 0.05y[n-2]. Determine its transfer function.
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