Use the convolution property to Express the ztransform of yn

Use the convolution property to: Express the z-transform of y(n) = sigma^n_k = -infinity x(k) in terms of X(z). Determine the z-transform of x(n) = (n + 1) u(n). Use MATLAB to carry out the following multiplication of polynomials: x(x - 1.7)(x + 0.5)(x - 0.7)(x + 1.5) USING MATLAB CODE: The reciprocal Fibonacci psi is defined by the infinite sum: psi = sigma^infinity_n=1 1/F_n where F_n 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 element equal to 1, the F_n = F_n-1 + F_n-2. Write a MATLAB program in a script file that calculates psi for a given n. Execute the program for n = 10, 50, and 100.

Solution

2.73)

p1=[1 0];

p2=[1 -1.7];

p3=[1 0.5];

p4=[1 -0.7];

p5=[1 1.5];

p=conv(conv(p1,p2),conv(p3,p4));

matlab output:

p=1.0000 -0.4000 -2.8600 0.5800 0.8925 0