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  3. 3 median filter the mean is a familiar statistic and...

Question: 3 median filter the mean is a familiar statistic and...

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3. Median filter: The mean is a familiar statistic, and is formed by taking the average of a list of data values. The median, in contrast, is computed by ordcring, i.c., sorting, a list of data. Spccifically, the median is the middle value in the sorted list. The median filter, a special case of an order statistic filter, is often used for the smoothing of signals corrupted by impulse noise, and preserves edges. It is implemented by sliding a window of odd length over the input sequence r[n one sample at a time. At the nth instant, the input samples in the window arc rank ordcred from the largest to the smallest in valucs, and the sample at the middle is the median value. (See faq page at course web site for links to applications). The output yn] of the median filter is then given by For example, with K 5, med 2, -3, 10, 5,-1) 2 (a) Is the system linear or non-lear? Justify your claim. (b) Is the system shift-invariant or shift-varying? Justify your claim (c) Is the system causal or non-causal? Justify your claim. (d) Is the system stable or non-stable? Justify your claim (e) What is the system impulse response?

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