where w[n] is zero-mean white noise random process with variance ow?. a) Find the power spectrum of y[n], algebraic ex

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Where W N Is Zero Mean White Noise Random Process With Variance Ow A Find The Power Spectrum Of Y N Algebraic Ex 1 (15.16 KiB) Viewed 114 times

It is second order random process whşch is generated
by the difference equation
y[n] = -2 y[n-1] - y[n-2] + w[n] - w[n-2]

Where W N Is Zero Mean White Noise Random Process With Variance Ow A Find The Power Spectrum Of Y N Algebraic Ex 2 (114.04 KiB) Viewed 114 times

where w[n] is zero-mean white noise random process with variance ow?.

a) Find the power spectrum of y[n], algebraic expression in terms of “ow?, cos(w)” only ? Py (ej") = ? N.B. Algebraic means that “square-root”, “square”, “log”, “exp” (like) (of) functions of w are prohibited. b) Find the extremum points (if any) of the power spectrum ( max Py (ejw) and min Py (ejw) for real w) c) Prove that the power spectrum (Py (ew) ) have singular points at which the spectrum goes to infinity. Py (@jw) = ( eiw Pw (@jw) |H(@JW)p2 = ? where H(@jw) = Y(@jw) / W(@jw) and DTFT{ y[n-k] } = e. jwk YeJW)