QUESTION 172 Use the convolution property to a Express the t

QUESTION: 1.72 Use the convolution property to: (a) Express the transform of x (k) y(n) in terms of X(z). that x(n) (b) Determine the z-transform of x (n) In 1)u (n) [Hint: Show first u(n) u(n) [10 points] QUESTION 2.73 Use MATLAB to carry out the following multiplication of polynomials x(x- 1.7) (x 0.5)(x-0.7)(x 1.5) QUESTION 2.74 USING MAT LAB CODE The reciprocal Fibonacci constant y is defined by the infinite sum: where F are the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13,... Each element in this sequence of numbers is the sum of the previous two. Start by setting the first two elements equal to 1, then F FN-it F Write a MATLAB pro- gram in a script file that calculates y for a given n. Execute the program for 10, 50, and 100

Solution

2.74:

n=10,50 and 100

n=input(,enter the value of n \ \');

y(1)=1;y(2)=1

s=0

for i=3:n

y(i)=y(i-2)+y(i-1)

end

for i=1:n

s=s+1/y(i);

end

fprintf(\'the fibonacci constant for n=%i is %i \ \',n,s)

The MATLAB output is,

Enter the value of n 10

The Fibonacci cnstant for n=10 is 3.3305

Enter the value of n 50

The Fibonacci constant for n = 50 is 3.3598

Enter the value of n 100

The Fibonacci constant for n=100 is 3.3598

Thus, the Fibonacci constant is calculated using MATLAB program