Linear Filters

Part 1: Discrete-Time Signals

Answer Question 1 here.

For Question 2, enter your function in place of ⬚⬚⬚ below.

\(\(Plot[⬚⬚⬚, \ {x, \ \(-5\) π, \ 5  π}, \ Frame -> True, \ 
        FrameLabel -> {"Time (seconds)", \ None}];\)\)

For Question 3, enter your formula for (Subscript[y, k]) in place of ⬚⬚⬚ below.

\(\(ListPlot[
        Table[{k/
              4, ⬚⬚⬚}, \ {k, \ \(-64\), \ 64}], \ PlotStyle -> PointSize[ .02], Frame -> True, \ 
        FrameLabel -> {"Time (seconds)", \ None}];\)\)

For Question 4, insert your plot here.

Use the following data to answer Question 5.

data = {{-5, 0.598472}, {-4, 0.909297}, {-3, 
          0.997495}, {-2, 0.841471}, {-1, 0.479426}, {0, 
          0. }, {1, -0.479426}, {2, -0.841471}, {3, -0.997495}, {4, -0.909297}, {5, -0.598472}}

Use the following data to answer Question 6.

data = {{-5, -2.59311}, {-4, -2.92405}, {-3, -0.566632}, 
{-2, 2.311745}, {-1, 3.06472}, {0, 
          1. }, {1, -1.98411}, {2, -3.14404}, {3, -1.41335}, {4, 
          1.61676}, {5, 3.16044}}

Answer Question 7 here.

Part 2: Difference Equations as Linear Filters

Use the following for Question 1.

Clear[k, y, z];
z[k_] := y[k + 4] - y[k + 2] + 2  y[k]
y[k_] := Sin[(π/2) k]

Answer Question 2 here.

For Question 3, enter your first formula for (Subscript[y, k]) in place of ⬚⬚⬚ below.

Clear[k, y, z];
y[k_] :=  ⬚⬚⬚
z[k]
Simplify[z[k]]

Now do the same steps for your second formula.

Part 3: Filtering Frequencies Out

Answer Question 1 here.  Set up and do any necessary calculations.

Enter your values for (Subscript[r, 1])and (Subscript[r, 2])below.

(Subscript[r, 1]) = ⬚
(Subscript[r, 2]) = ⬚

For Question 2, first use the following:

Clear[k, y, z];
z[k_] := y[k + 2] + y[k]
y[k_] := ((Subscript[r, 1])^k)
z[k]
Simplify[z[k]]

Now do the same steps for (Subscript[r, 2]).

Answer the rest of the Questions for this Part below.  Set up and do any necessary calculations.

Part 4: Passing Frequencies Through

Answer the Questions for this Part below.  Set up and do any necessary calculations.

Part 5: Summary

Answer the Questions for this Part below.