Subject: Speech Processing

Topic: Speech Analysis in Time Domain

Difficulty: Medium

(i) Linear smoother is used for removing noise present in the signal.

(ii) These filter basically remove noise by averaging the neighborhood values of the signal.

(iii) Linear smoother are not always useful, especially when the noise is present in extreme values.

(iv) Moreover linear smoother are not always useful for smoothing parameter estimates because they produce a lot of smearing and blurring discontinuities.

(v) Along with error being emphasized pitch period smoothing distorts the contour.

(vi) To overcome these problems, a non-linear smoother that consists of running medians can be combined with linear smoothing.

(vii) Linear smoothing performs the function of separating signals that have non-overlapping frequency content.

(viii) Non-linear smoothing does task of separating signals based on their characteristics.

Running medians of length L:

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

2) 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 samples.

3) $ ML(\alpha x_1[n] + \beta x_2[n]) \neq a \times ML(x_1[n]) + \beta ML(x_2[n]) $

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

(ix) Approximation signals S(x[n]). Performance of the system based on: y(n) = S(x[n]). The difference signal, Z[n] is formed as Z(n) = x(n) - y(n) = R(x[n]).

(x) The correction produced by the second pass of non-linear smoothing Z(n) is added to the y(n) to obtain W(n), which is a refined approximation to S(x[n]) and [w(n)] = S(x[n]) + S[R(x[n])].

(xi) If Z(n) and R(x(n)) are exactly equal i.e. an ideal non-linear smoother was used, then there is no necessity of including the correction term.