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Home / Week 2 Exercises / Different Summers

Different Summers

The questions below are due on Monday February 18, 2019; 11:00:00 PM.
 
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Determine a difference equation (with finitely many terms) for each of the systems below.

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.

Recall that we use x to represent the input to a system and y the output of the system.

For each question, enter a sequence of numbers representing the coefficients as a python list.

 

  1. The output at time n is the sum of its inputs up to and including time n.

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

 

  1. The output at time n is the sum of its inputs up to and including time n-1.

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

 

  1. The output at time n is the sum of the scaled inputs (each input scaled by 0.1) up to and including time n-1.

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