Representations 1

The questions below are due on Monday February 18, 2019; 11:00:00 PM.

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Music for this Problem

Consider the system described by the following block diagram:

Part 1

Determine a difference equation that describes the same system as the block diagram above.

As in previous tutor problems, specify your answer as a list of dCoeffs and cCoeffs, where:

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]

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

Part 2

Calculate the first 6 samples of the unit sample response of the system, assuming the system starts at rest. Enter your answer as a Python list of 6 numbers [y[0], y[1], y[2], y[3], y[4], y[5]]

Part 3

Calculate the first 7 samples of the response of the system when the input signal is given as following, assuming the system starts at rest:

x[n] = \left\{ \begin{array}{lr} 0 & \text{if}~n = 0\\ 1 & \text{if}~n = 1\\ 0 & \text{if}~n = 2\\ 2 & \text{if}~n = 3\\ 0 & \text{if}~n \geq 4 \end{array} \right.

Enter your answer as a Python list of 7 numbers [y[0], y[1], y[2], y[3], y[4], y[5], y[6]]

Part 4

Assuming that x[n]=y[n]=0 for all n\lt 0, determine an input sequence [x[0], x[1], x[2], x[3], x[4]] such that

y[n] = \left\{ \begin{array}{lr} 0 & \text{if}~n = 0\\ 3 & \text{if}~n = 1\\ 0 & \text{if}~n = 2\\ -6 & \text{if}~n = 3\\ 24 & \text{if}~n = 4 \end{array} \right.

Enter your answer as a Python list of 5 numbers. Note that there may be multiple correct solutions; any such solution will be accepted.