Complete Communications Engineering

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:

Single line AEC architecture

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]

A typical normalized energy profile of a room impulse response is shown in Figure 2 showing that just about 50\% 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.

Sample room impulse response energy profile

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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