Median filter: The median value of a series of length n is the value at position n/2 for even values of n, (n+1)/2 for odd values of n.
Since position n/2 is not given in the sequence and its value has to be interpolated, while (n+1)/2 is given in the sequence, odd sequence lengths are preferred.
The function of the median filter is to reject `obvious' discrepancies, such as some types of noise, in the signal.
Median filters are a variety of low pass filter, and have frequently been used to `smooth' 
curves after extraction, in order to reduce octave errors.
In this application, the median filter is a moving window covering an odd number of samples and with a length between 40 msec and 80 msec; for any given window position, the median of the values at the current window position is selected.
A practical implementation procedure is to sort the values numerically and take the value at position (n+1)/2:
where w is the length of the window.
Mean filter (integration, low pass filter): The mean filter or averaging filter is a simple low-pass filter or smoothing filter; its main function is to smooth sampling jitter in time functions, often in visual displays. For general filtering, however, more complex filter types are used. The mean filter, like the median filter, is represented by a moving window of length n, and the mean of the values at all positions in the window is selected:
where w is the length of the window.
Differentiation (high pass): The difference between neighbouring signal values is a means of emphasising high frequency components; for discrete signals the operation is known as differencing rather than differentiation. Differencing is a common operation in the extraction of acoustic features from the speech signal, and is a first step in time-domain segmentation procedures: steeper slopes are mapped on to higher peaks, which are taken as hypotheses about the boundaries.