Real time implementations utilize finite impulse responses (FIR) to cancel out far end echo signals. Though adequate in most cases, there is always a non-zero residual echo, which may be substantial in certain applications. Consider the systems depicted in Figure 1 below:
Figure 1: Single line AEC architecture
The received signals are of the form:
![y[n] = s[n] + \underbrace{\sum\limits_{i=0}^{L-1} h[n]x[n-i]}_{x_{aec}[n]} + \underbrace{\sum\limits_{i=L}^{\infty} h[n]x[n-i]}_{x_{res}[n]} +\nu[n]](https://s0.wp.com/latex.php?latex=y%5Bn%5D+%3D+s%5Bn%5D+%2B+%5Cunderbrace%7B%5Csum%5Climits_%7Bi%3D0%7D%5E%7BL-1%7D+h%5Bn%5Dx%5Bn-i%5D%7D_%7Bx_%7Baec%7D%5Bn%5D%7D+%2B+%5Cunderbrace%7B%5Csum%5Climits_%7Bi%3DL%7D%5E%7B%5Cinfty%7D+h%5Bn%5Dx%5Bn-i%5D%7D_%7Bx_%7Bres%7D%5Bn%5D%7D+%2B%5Cnu%5Bn%5D&bg=ffffff&fg=000000&s=0 "y[n] = s[n] + \underbrace{\sum\limits_{i=0}^{L-1} h[n]x[n-i]}_{x_{aec}[n]} + \underbrace{\sum\limits_{i=L}^{\infty} h[n]x[n-i]}_{x_{res}[n]} +\nu[n]")
A typical normalized energy profile of a room impulse response is shown in Figure 2 showing that just about 
of the energy is contained in the first 20 milliseconds (~256 samples) . Thus, using an echo tail of 20m milliseconds will leave some substantial residual echo.
Figure 2: Sample room impulse response energy profile
The residual echo can be considered as a stationary interference with spectral domain cancellations being employed to reduce it.
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