This paper proposes a new algorithm called the fast Projection algorithm, which reduces the computational complexity of the Projection algorithm from (p+1)L+O(p3) to 2L+20p (where L is the length of the estimation filter and p is the projection order.) This algorithm has properties that lie between those of NLMS and RLS, i.e. less computational complexity than RLS but much faster convergence than NLMS for input signals like speech. The reduction of computation consists of two parts. One concerns calculating the pre-filtering vector which originally took O(p3) operations. Our new algorithm computes the pre-filtering vector recursively with about 15p operations. The other reduction is accomplished by introducing an approximation vector of the estimation filter. Experimental results for speech input show that the convergence speed of the Projection algorithm approaches that of RLS as the projection order increases with only a slight extra calculation complexity beyond that of NLMS, which indicates the efficiency of the proposed fast Projection algorithm.

We investigated the dependence of the desired echo return loss on frequency for various hands-free telecommunication conditions by subjective assessment. The desired echo return loss as a function of frequency (DERLf) is an important factor in the design and performance evaluation of a subband echo canceller, and it is a measure of what is considered an acceptable echo caused by electrical loss in the transmission line. The DERLf during single-talk was obtained as attenuated band-limited echo levels that subjects did not find objectionable when listening to the near-end speech and its band-limited echo under various hands-free telecommunication conditions. When we investigated the DERLf during double-talk, subjects also heard the speech in the far-end room from a loudspeaker. The echo was limited to a 250-Hz bandwidth assuming the use of a subband echo canceller. The test results showed that: (1) when the transmission delay was short (30 ms), the echo component around 2 to 3 kHz was the most objectionable to listeners; (2) as the transmission delay rose to 300 ms, the echo component around 1 kHz became the most objectionable; (3) when the room reverberation time was relatively long (about 500 ms), the echo component around 1 kHz was the most objectionable, even if the transmission delay was short; and (4) the DERLf during double-talk was about 5 to 10 dB lower than that during single-talk. Use of these DERLf values will enable the design of more efficient subband echo cancellers.