Finding Systems
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]
Determine the difference equation representation for the following systems.
Specify the dCoeffs: d_0 \ldots d_j and the
cCoeffs: c_0 \ldots c_{k-1} for each of the
difference equations below.
For each question, enter a Python list containing the numbers representing the coefficients. If one set of coefficients is empty, enter the empty list, [].
- Let x[n] be an input sequence of digitized sound. We want to
output a sound sequence y[n] where every output sample is the average
of the previous two input samples, that is, n-1, n-2. Don't worry
about what happens on the first few samples.
Difference Equation:
dCoeffs (input):
cCoeffs (output):
- Assume that the input to a system is 0 for n < 0 and 1
for n \geq 0. The output is 0 for n < 0 and is equal to the sequence 10, 1, 1, 1, 1, . . . for n \geq 0.
Hint: the answer has no cCoeffs.Difference Equation:
dCoeffs (input):
cCoeffs (output):
- A Bank offers a 5% annual interest rate, the inputs are your deposits,
and the output is the balance in your account. Let x[n] represent the
amount of money you deposit in the bank during year n and y[n]
represent your balance in the bank at the end of year n. Assume that
deposits during year n are credited to the balance in year n
but earn no interest until year n + 1.
Difference Equation:
dCoeffs (input):
cCoeffs (output):
- Assume that you deposit $100 in the Bank in the year 2007 (n=0) and make no
further deposits. Solve your difference equation numerically to determine your
balance in the bank during years 0 through 25.What is your bank balance in the year 2011 (n=4)?
What is your bank balance in the year 2031 (n=24)?
