Notes

microphones과 loudspeakers 사이의 acoutic coupling에 의해서 발생되는 Acoustic echo는 음성 통신의 품질을 굉장히 좋지 않게 만든다. 이러한 acoustic echo 문제를 해결하기 위한 분야가 Acoustic echo cancellation (AEC), acoustic echo suppression (AEC) 인데, 일반적으로 Time/Frequency 도메인에서 linear adaptive filter (NLMS, and etc) 사용하고, 다른 여러 방법이 존재한다.

하지만 far-end power amplifier/far-end loudspeakers/non-linear echo path(transfer function)/ imperfect AEC 등에 의해 nonlinearity 가 반영되기 때문에, 단순한 linear filtering 접근 방법으로는 acoustic echo를 완전히 제거할 수 없다는 한계가 존재한다. 이러한 nonlinear echo 성분들을 제거하기 위해서 residual echo suppression (RES) 모듈을 이용해서 잔여 echo를 추가로 제거한다. 

일반적인 에코제거 관련 문제를 좀 더 정확하게 이해하기 위해 그림, 수식을 첨부한다.

Acoustic echo, caused by the acoustic coupling between microphones and loudspeakers, significantly degrades the quality of voice communication. The fields of Acoustic Echo Cancellation (AEC) and Acoustic Echo Suppression (AES) address this problem, typically employing linear adaptive filters (like NLMS) in the Time/Frequency domain, among other methods.

However, there are limitations due to nonlinearity introduced by factors such as far-end power amplifiers, far-end loudspeakers, nonlinear echo paths (transfer functions), and imperfect AEC, which means simple linear filtering approaches can't completely eliminate acoustic echo. To mitigate these nonlinear echo components, a Residual Echo Suppression (RES) module is used to further reduce the remaining echo.

For a more precise understanding of the issues related to echo removal, diagrams and equations are often included.

y(t) = s(n) + d(n) + v(n)

d^(n) = h^(n) * x(n)

s_AEC(n) = y(n) - d^(n)

s_AEC(n) = e(n) = y(n) - d^(n) =  [ d(n) + s(n) + v(n) ] - d^(n)

y(n) : microphone signal

d(n) : echo signal

s(n) : near-end speech

v(n) : background noise

e(n) : AEC output signal

d^(n) : linear echo estimate produced by an AEC filter

x(n) : Far-end signal

h^(n) : adaptive filter

* : convolution operation