Short time average over 0 rate

1. definition

In the case of discrete-time speech signals, if an adjacent sample has a different algebraic symbol, it is known to have occurred over 0. The number of times in a unit time is 0 and is called over 0. The short-term average over 0 rate is defined as

At the moment, I haven't figured out why the speech signal is truncated. Why should I convolution a window function, why not multiply it directly?

consider that the non-0 value range of w(n-m) is n-m≥ 0, which is m≤n, and n-m≤n -1, so m≥n-n+1, so the short-term average over 0 rate can be rewritten as:Here is the MATLAB program

Clear All[signal,fs,bit] = Wavread (' 1.wav '); subplot (3,1,1) plot (signal); title (' Voice signal waveform '); framelength = 150; Framenumber = fix (Length (signal)/framelength); For i = 1:framenumber;% frame processing    framesignal = Signal ((i-1) *framelength+ 1:i*framelength);% extract a frame signal    Z (i) = 0;    for j = 2:framelength-1;        Z (i) = Z (i) +abs (sign (framesignal (j))-sign (Framesignal (j-1)));% calculates the frame over 0 rate    Endendsubplot (3,1,2) plot (Z); Short time average over 0 ')

I recorded the sound myself. Below is the voice waveform, and over 0 rate picture

Short time average over 0 rate