Reference no: EM131219843
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Problem 1: Topics: Pole-Zero Plot, Stability, Causality, FIR vs. IIR
Given the Pole-Zero plot of a LTI discrete time filter:
a) Is this filter FIR or IIR?
b) Is this filter stable BIBO?
c) Is this filter Causal or Anticausal?
Problem 2: Topics: Stability, FIR vs. IIR, Difference Equation
Given the unit sample response of a LTI discrete time filter:
h[n] = (1/3)δ[n]+(1/3)δ[n-1]+(1/3)δ[n-2]
a) Is this a FIR or IIR filter?
b) Stable BIBO?
c) Write the filter difference equation.
Problem 3: Topics: Inverse Z transform
Given the Z transform of a signal X(z)= z-7/(1+0.9z-1) with R.O.C |z|< 0.9
a) Find x[n]=Z-1{X(z)}
Problem 4: Topics: Fourier Series Coefficients
Given the following periodic signal: x(t)
a) Give an expression for the signal in the interval 0 <= t < 10
b) Find the Trigonometric Fourier Series coefficient an using the appropriate formula.
c) Find the Trigonometric Fourier Series coefficient an using any method.
d) Find the average power in x(t).
e) Write the integral expression that leads to the calculation of the Exponential Fourier Series coefficient cn. Include the actual values for the period To and ωo (Do not perform the actual calculation).
Problem 5: Topics: Linear Convolution
Assume first entry in all depicted sequences correspond to discrete time zero: n=0. Given the discrete time linear time (shift) invariant system with input x[n] = [9 4 10 -1 6 -2]
a) Using any method find the filter output y[n].
Problem 6: Topics: Discrete Time Systems
Now consider a causal filter with difference equation y[n] = x[n] + 0.8 y[n-1]
a) Is this filter IIR or FIR?
b) Find the System Function H(z) including R.O.C.
c) Find the system unit sample response (impulse response) h[n] =
d) Sketch the Pole_Zero plot including R.O.C.
e) Find the filter unit-step response (output y[n] when the input is a unit-step function u[n]).
f) Direct Form 1 Block Diagram realization of the filer.
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