digital signal processing problem

please i really need help in solving this problem:

A random process is defined by x(t) = A cos(2*pi*f0*t+Φ), 0≦t≧T, where A and f0 are constants and Φ is uniformly distributed random variable in the range -pi≦Φ≧pi . Generate samples (at the rate fs=80kHz ) over a time interval of length T. Choose the signal length T so that you get about 900 to 1000 samples of the simulated analog signal x(t).
i)Plot the time signal with the function plot so that the samples are connected. Make sure that you label the time axis of the simulated analog signal.
ii)Find the autocorrelation of the signal and plot it.
iii)Find the Fourier transform of the autocorrelation and plot it.

[Wayne King]

Hi Jamal, this is clearly a homework problem. What have you done to try and solve your homework problem?

Answer 1

[Jamal]

i don't have problem with matlab function that should be used to solve. my problem is to how to find T how can chose A & phi. i don't want whole solution i need only guide.

Answer 2

[Wayne King]

If your sampling frequency is 80 kHz, then to obtain 900 to 1000 samples, T must be between 0.0113-(1/80e3) and 0.0125-(1/80e3) seconds. If you have between 900 and 1000 samples, then that will take

 num_samples*dt

seconds, where num_samples is the number of samples and dt is the sampling interval.

You can use rand() to sample a phase angle from -pi to pi. For example, to get one such angle.

 phi = -pi+2*pi*rand(1);