Question

Do the z transform of the following

x(n)=(0.8)nu(n−2). Verify the z-transform expression using MATLAB.
x(n)=[(0.5)n+(−0.8)n]u(n). Verify the z-transform expression using MATLAB.
x(n)=2ncos(0.4πn)u(−n). x(n)=(n+1)(3)nu(n). Verify the z-transform expression using MATLAB.

Answer 1

To verify the Z-transform expression using MATLAB, use the 'ztrans' function. Here's how you can do it for each given expression.

Step-by-step explanation:

The Z-transform can be used to analyze discrete-time signals. To verify the Z-transform expression using MATLAB, you can use the 'ztrans' function. Here is how you can do it for each given expression:

1. x(n) = (0.8)^{n}u(n-2)
   syms z;
   X1_z = ztrans((0.8)^n*u(n-2), n, z)
2. x(n) = [(0.5)^n + (-0.8)^n]u(n)
   syms z;
   X2_z = ztrans([(0.5)^n + (-0.8)^n]*u(n), n, z)
3. x(n) = 2n*cos(0.4*pi*n)*u(-n)
   syms z;
   X3_z = ztrans(2*n*cos(0.4*pi*n)*u(-n), n, z)
4. x(n) = (n+1)*(3)^n*u(n)
   syms z;
   X4_z = ztrans((n+1)*(3)^n*u(n), n, z)