Representations 2

The questions below are due on Sunday February 24, 2019; 11:00:00 PM.

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Consider the system specified by the following block diagram:

Part 1

Write the difference equation for the block diagram, assuming that $K=12$.

A difference equation is in the form:

y[n] = c_0 y[n-1] + c_1 y[n-2] + \ldots + c_{k-1} y[n-k] + d_0 x[n] + d_1 x[n-1] + \ldots + d_j x[n-j]

Specify the dCoeffs: d_0 \ldots d_j and the cCoeffs: c_0 \ldots c_{k-1} for each of the difference equations below by entering a Python list of numbers in each box. If a set of coefficients is empty, enter an empty Python list.

Difference Equation:
dCoeffs (input):
cCoeffs (output):

Part 2

Write the System Functional for the block diagram, assuming that $K=8$.

The system functional is represented by the coefficients of the numerator and denominator polynomials. The coefficients of the polynomial are written with the zeroth order term first. Enter a Python list of numbers in each box. System functional:

System Functional:
Numerator coeffs (in {\cal R}):
Denominator coeffs (in {\cal R}):

Part 3

If you know that the poles are at $+0.5j$ and $-0.5j$, what is the value of $K$ (enter a floating point number)?

K =

Part 4

If you know that $K=14$ and the system is initially at rest, what is the response of the system to a unit sample? Enter a Python list below containing the first 8 samples of this system's unit sample response when $K=14$, starting with $n=0$.