13-09-2012, 01:32 PM
ECHO CANCELLATION USING ADAPTIVE FILTERING
[attachment=33699]
ABSTRACT
This report discusses the implementation of the least mean-square (LMS) algorithm on the Motorola 56K series digital signal processor in an echo cancellation system. This scheme identifies the frequency response of the echo system so that the adaptive filter generates an estimate of the echo and subtracts it from a distorted signal so that the original signal can be recovered. The LMS algorithm design is used extensively in communication networks to correct for the echoes created by line impedance mismatches and is useful to compensate for the imperfection in telephony networks. This paper shows how the LMS algorithm is useful to solve echo problems. This project is an attempt by two undergraduate seniors to acquire more knowledge in digital signal processing.
Introduction
A significant problem in communications is the generation of echoes. The echoes arise for a number of reasons, with the primary reason being an impedance mismatch. The impedance mismatch occurs when the two-wire network meets the four-wire network, this interface is known as the hybrid. This impedance mismatch causes some of the signal energy to be returned to the source as an echo [1]. This can be seen in Figure 1. (All figures/tables appear at the end of the report.)
The delays between primary and echo signals are directly related to the transmission distance. For example, if a signal was sent to a satellite that redirected the signal back to another location on earth, that signal would have a very large time delay compared to a signal sent to a local switching station and back. Short delays (less than 50 ms) will not affect the quality of the signal as much as longer delays. Delays of this length are not noticed by the receiver and therefore are not considered an annoyance. However, these echoes may have an effect on data being transmitted through transmission lines [3].
A sinusoid will be used as the input signal. The DSP board will create an echo of the sinusoid and add the echo to the original sinusoidal signal, thus creating a distorted version of the input signal. The DSP will then use LMS adaptive filtering to estimate the echo, and remove the echo from the distorted signal creating a reconstructed signal. The LMS algorithm seeks to minimize the excess mean-square error (MSE) between the echo signal and the estimated echo. The excess MSE refers to the LMS algorithm fluctuations about the adaptive filter coefficients after a large number of iterations [1].
Design Details
The input signal will be a sinusoidal at 2.0 kHz because telephone voice frequency spectrum exists from 0-4 kHz. The band limited frequency for telephone transmission is 4 kHz. Thus the Nyquist rate is set to eight thousand samples per second.
The echo filter uses the original signal to create the echo signal. The transfer function is chosen to be 0.5*z^-512. This signal will be delayed by 512 samples, which corresponds to sixty-four milliseconds delay at our sampling rate with an attenuated of fifty percent. This is a reasonable approximation for the system that creates the echo of the input signal. Human hearing has been tested to be intolerable to echo delays of more than 50 milliseconds [3].
The filter is chosen to be 20 taps. This number of taps was chosen for two reasons. It was small enough to limit processing time, however it was large enough to show good convergence in the MATLAB simulations. The adaptive filter taps at first are initialized to the null vector. Figure 3 shows the frequency response of the MATLAB simulation for the adaptive coefficients after several iterations with a value of 0.01. A learning curve is shown in Figure 4 with the MSE approaching –40 dB after approximately one hundred iterations. Figure 4 also shows the input signal added to the echo signal and plotted under it is the reconstructed signal. After approximately a hundred iterations, the original input signal is restored from the distorted signal. In Figure 5 the adaptive filter coefficients are shown after several iterations when the adaptive filter has fully been trained. The frequency plots in Figure 3 and adaptive filter coefficients in Figure 5 show similar shapes.
Conclusions
The LMS algorithm successful cancelled the echo and returned a reconstruction of the original signal. It identified the echo system’s transfer response within a small number of iterations. The LMS algorithm is a very powerful and simple tool for echo cancellation. The system worked in simulation and in real-time. Adjustments of the value were necessary due to the nonlinear effects that occurred in the experiment. The nonlinear quantization of the DSP most likely accounted for these effects. A method to expand the project would be to use an actual system with real echoes. A microphone and speaker with a box in between them could be used to create the echoes. Also, longer time delays could be used. Longer time delays would warrant more filter taps and faster DSPs since the number of calculations increases for the longer filter lengths.
[attachment=33699]
ABSTRACT
This report discusses the implementation of the least mean-square (LMS) algorithm on the Motorola 56K series digital signal processor in an echo cancellation system. This scheme identifies the frequency response of the echo system so that the adaptive filter generates an estimate of the echo and subtracts it from a distorted signal so that the original signal can be recovered. The LMS algorithm design is used extensively in communication networks to correct for the echoes created by line impedance mismatches and is useful to compensate for the imperfection in telephony networks. This paper shows how the LMS algorithm is useful to solve echo problems. This project is an attempt by two undergraduate seniors to acquire more knowledge in digital signal processing.
Introduction
A significant problem in communications is the generation of echoes. The echoes arise for a number of reasons, with the primary reason being an impedance mismatch. The impedance mismatch occurs when the two-wire network meets the four-wire network, this interface is known as the hybrid. This impedance mismatch causes some of the signal energy to be returned to the source as an echo [1]. This can be seen in Figure 1. (All figures/tables appear at the end of the report.)
The delays between primary and echo signals are directly related to the transmission distance. For example, if a signal was sent to a satellite that redirected the signal back to another location on earth, that signal would have a very large time delay compared to a signal sent to a local switching station and back. Short delays (less than 50 ms) will not affect the quality of the signal as much as longer delays. Delays of this length are not noticed by the receiver and therefore are not considered an annoyance. However, these echoes may have an effect on data being transmitted through transmission lines [3].
A sinusoid will be used as the input signal. The DSP board will create an echo of the sinusoid and add the echo to the original sinusoidal signal, thus creating a distorted version of the input signal. The DSP will then use LMS adaptive filtering to estimate the echo, and remove the echo from the distorted signal creating a reconstructed signal. The LMS algorithm seeks to minimize the excess mean-square error (MSE) between the echo signal and the estimated echo. The excess MSE refers to the LMS algorithm fluctuations about the adaptive filter coefficients after a large number of iterations [1].
Design Details
The input signal will be a sinusoidal at 2.0 kHz because telephone voice frequency spectrum exists from 0-4 kHz. The band limited frequency for telephone transmission is 4 kHz. Thus the Nyquist rate is set to eight thousand samples per second.
The echo filter uses the original signal to create the echo signal. The transfer function is chosen to be 0.5*z^-512. This signal will be delayed by 512 samples, which corresponds to sixty-four milliseconds delay at our sampling rate with an attenuated of fifty percent. This is a reasonable approximation for the system that creates the echo of the input signal. Human hearing has been tested to be intolerable to echo delays of more than 50 milliseconds [3].
The filter is chosen to be 20 taps. This number of taps was chosen for two reasons. It was small enough to limit processing time, however it was large enough to show good convergence in the MATLAB simulations. The adaptive filter taps at first are initialized to the null vector. Figure 3 shows the frequency response of the MATLAB simulation for the adaptive coefficients after several iterations with a value of 0.01. A learning curve is shown in Figure 4 with the MSE approaching –40 dB after approximately one hundred iterations. Figure 4 also shows the input signal added to the echo signal and plotted under it is the reconstructed signal. After approximately a hundred iterations, the original input signal is restored from the distorted signal. In Figure 5 the adaptive filter coefficients are shown after several iterations when the adaptive filter has fully been trained. The frequency plots in Figure 3 and adaptive filter coefficients in Figure 5 show similar shapes.
Conclusions
The LMS algorithm successful cancelled the echo and returned a reconstruction of the original signal. It identified the echo system’s transfer response within a small number of iterations. The LMS algorithm is a very powerful and simple tool for echo cancellation. The system worked in simulation and in real-time. Adjustments of the value were necessary due to the nonlinear effects that occurred in the experiment. The nonlinear quantization of the DSP most likely accounted for these effects. A method to expand the project would be to use an actual system with real echoes. A microphone and speaker with a box in between them could be used to create the echoes. Also, longer time delays could be used. Longer time delays would warrant more filter taps and faster DSPs since the number of calculations increases for the longer filter lengths.