To test the recording for nonlinear distortions you can use a test signal, consisting of two sinusoidal signals (for example, tones of 300 and 1800 Hz could be used). The recording must also contain these two frequencies but there will always be other frequencies in the spectrum of the recorded signal because of the tones undergoing nonlinear distortions in the aforementioned hardware. If you run this recording through spectrum analyzing software you will see all of these frequencies. Obviously, due to the distortions, there will be harmonics of each tone, e.g. 2*300=600 Hz and 2*1800=3600 Hz, and there will also be combinations of the two frequencies, e.g. sum and difference: 300+1800=2100 Hz and 1800-300=1500 Hz. We just showed nonlinearity, which of the second-order. If the nonlinearity is of a higher order, which is always the case in reality, then there will be many more frequencies in the recording. The main thing here is that the amplitudes of the original frequencies (e.g. 300 Hz and 1800 Hz) must exceed the amplitudes of all other frequencies by at least 16 dB (or equivalently, the absolute ratio of the amplitudes must be greater than 1016/20 = 6.31). Presented is a very simple test and while it can reveal certain nonlinearities, a more thorough method should be used to measure the nonlinear distortions, please see the ITU-T recommendation O.42 for more information on this.
You should perform such or similar test to make sure your hardware is OK in terms of nonlinear distortions. If the testing shows that this is not the case, you must find and fix the problem before thinking of any AEC integration. To find whether or not the problem is in the ADC/DAC, use its analog loop-back mode when doing this test. Beware, the problem may have to do with incorrect ADC/DAC programming!
Also, the nonlinear distortions can be a result of limiting (clipping) the signal in either ADC/DAC or elsewhere, for example, in the amplifiers. If by expecting the waveform, which you recorded from ADC, you see that many of the samples values reach their minimum and maximum values, then you must attenuate the signal somewhere so the clipping doesn't occur.
Note that there can be interference between the digital and analog parts in the device. The interference may be in form of additive noise superimposed on the Vcc if the power supply is overloaded or there is no good power supply decoupling. The decoupling capacitors must be placed as close to the power supply pins of the chips as possible.
As it has already been mentioned, the acoustic echo exists between the loudspeaker and the microphone in hands-free phones inside their cases. The echo can be transmitted by both the air inside the case and by the case itself in a form of mechanical waves (vibrations) in the case parts. To reduce this form of the echo, there should be a good acoustic decoupling between the loudspeaker and the microphone. The microphone should be acoustically and mechanically insulated by a soft material, absorbing the case vibrations and sound coming out of the speaker. The microphone should not be directed to the speaker. It can be useful to have a directional microphone, so it can be directed away from the speaker.
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