You have just purchased a new automobile and made a loan for

You have just purchased a new automobile and made a loan for $16,000 at an interest rate of 6% per year. (What is the monthly rate?) You will be paying the loan off at $500 a month. Write the Z-transfer function for this and use partial fraction expansion to show the balance after 4 payments. Write a MATLAB program to compute the number of months needed to pay off the loan. Convert the months to years. Infinite Impulse Response (IIR) Filter Design Give the name of the three most commonly used techniques for designing IIR filters. (The Butterworth method is one of them.) Each of them gives an optimum design according to some criteria. State that criteria for each of them. The technique for designing a digital filter is to design an analog filter (in the s-domain) and then convert from the s domain to the z-domain to obtain a digital filter. Give the two techniques for converting from the s-domain to the z-domain.

Solution

2)

A) The three most common techniques used for designing IIR filters are

a) transformation of an analog prototype filter

b) optimization based approach allowing the approximation of an arbitrary frequency response.

c)using bi-linear transformation

B) The two techniques used in converting s domain to z domain are

a) Laplace transformation

b)z transformation