generate and plot a sampled sine wave with fs8khz

Question

Generate and plot a sampled sine wave with f_s=8kHz, of 4 seconds duration, with frequency ω₀ = Π/10 and amplitude A = 1.2. The waveform equation is

x(n)   =  A sin nω                                                      

Explain the role of each of the variables in this equation.  What is the true (Hertz) fre- quency generated in this case?

Generate a Gaussian random signal vector, v(n), of the same length. Then generate a noisy signal of the form

y(n)   =  x(n) + αv(n)                                                     

(2) Listen to the resulting signal y(n) for various values of α.  You will have to choose the value of α experimentally - try both small and large, and investigate the differences. Plot one of the waveforms, and comment briefly on your results.