The spectrum/auto-correlation of a process is independent of its distribution, and vice versa.
Thus, it should be possible to generate a signal where one specifies both its auto-correlation and its distribution. Write a Matlab program that can generate a signal with a uniform [-1 1] PDF, and an auto-correlation given by, R_xx (τ)=σ_x^2 e^((-|τ|)/10) where is the time between samples (i.e. if you generate a signal x = rand(N,1), will range from 0 to N - 1. Generate a signal with N = 1000 points, and compare its PDF (estimated via an appropriately histogram) with a uniform distribution. Also compare its autocorrelation (estimated using a suitable time average) with Rxx( ) given above. Include a copy of your program with the solution.
Hint Hunter, I.W. and Kearney, R.E., Generation of random sequences with jointly specified probability density and autocorrelation functions, Biological Cybernetics, (47):141-146, 1983.