# Question: A certain LTI system has an input output relationship given

A certain LTI system has an input/ output relationship given by

(a) Find the output autocorrelation, RYY (τ), in terms of the input autocorrelation, RXX (τ).

(b) Find the output PSD, SYY (τ), in terms of the input PSD, SXX (τ).

(c) Does your answer to part (b) make sense in the limit as to → 0?

(a) Find the output autocorrelation, RYY (τ), in terms of the input autocorrelation, RXX (τ).

(b) Find the output PSD, SYY (τ), in terms of the input PSD, SXX (τ).

(c) Does your answer to part (b) make sense in the limit as to → 0?

## Answer to relevant Questions

The input to a filter is a discrete- time, zero- mean, random process whose autocorrelation function is RXX [n] = | a | n, for some constant a such that |a| A filter has a transfer function given by (a) Is this filter, lowpass, highpass, or bandpass? (b) Find the noise equivalent bandwidth of this filter. A square pulse of width to = 1µs plus zero- mean white Gaussian noise is input to a filter with impulse response, h (t) = exp (–t / t1) u (t). (a) Find the value of the constant such t1 that the SNR at the output of the ...Suppose we are allowed to observe a random process Z (t) at two points in time, to and t1. Based on those observations we would like to estimate Z (t) at time t= t2 where t0 < t1 < t2. We can view this as a prediction ...If the input to a linear filter is a random telegraph process with c zero- crossings per second and amplitude A, determine the output PSD. The filter impulse response is h (t) = bexp(– at) u ( t).Post your question