2. Median filter: Consider the discrete-time system given by
y[n] = median{x[n -2]; x[n - 1]; x[n]; x[n + 1]; x[n + 2]}
Recall that the median is the value in an ordered list of values above and below which there
is an equal number of values. The median filter is often employed when one wishes to remove
zero-mean additive noise while preserving sharp edges in the original signal.
a) Is the system linear? Shift-invariant?
b) Is the system causal?
c) What is the system's output for input x[n] =δ[n]


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