project1 - ECEN 314 Project # 1 Georghiades Echo...

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ECEN 314 Project # 1 Georghiades Echo Cancelation Fall 2009 Given: November 10, 2009 Due: November 19, 2009. The impulse response h ( t ) of a room that models the effects of echo on audio signals in the room at a specific location is approximated by: h ( t ) = δ ( t ) + αδ ( t - T ) , where the delayed term corresponds to a single dominant echo component which is attenuated by an amount α < 1 and delayed by T seconds compared to the direct path term. 1. Derive an expression for the transfer function of the channel. 2. Derive an expression for the transfer function of a linear equalizer (echo canceler) which removes the echo from the signal. Expand the resulting transfer function into an infinite series. 3. Compute the impulse response of the echo canceler using the infinite series expression for it. Clearly, in a practical implementation, one must truncate the impulse response of the echo canceler to a finite (and preferably small) number of terms. The more terms one retains, the better the performance, but
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project1 - ECEN 314 Project # 1 Georghiades Echo...

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