Subject: Speech Processing

Topic: Speech Analysis in Time Domain

Difficulty: High

(i) Median smoothing is used for removing noise present in the signals.

(ii) These filters basically remove noise by averaging the neighbourhood values of the signal.

(iii) Properties of running medians: Running medians of length L

a) ML ($\alpha$ x[n]) = $\alpha$ ML(x[n])

b) Medians are basically statistical operators that do not smear out discontinuities (jumps) in the signal if there are no discontinuities within half the length (L/2) of the sample.

c) $ ML (\alpha x_1[n]) + \beta x_2[n] \neq \alpha ML(x_1[n]) + \beta ML(x_2[n]) $

d) Sharp discontinuities in a signal are generally preserved by median smoother but they fail to smoothen the noise components.