by perceptually optimizing the decoded (synthesis) signal in a closed loop. In theory, the best CELP stream would be produced by trying all possible bit combinations and selecting the one that produces the best-sounding decoded signal. This is obviously not possible in practice for two reasons: the required complexity is beyond any currently available hardware and the “best sounding” selection criterion implies a human listener. In order to achieve real-time encoding using limited computing resources, the CELP search is broken down into smaller, more manageable, sequential searches using a simple perceptual weighting function. Typically, the encoding is performed in the following order: Linear prediction coefficients (LPC) are computed and quantized, usually as line spectral pairs (LSPs). The adaptive (pitch) codebook is searched and its contribution removed. The fixed (innovation) codebook is searched. Noise weighting Most (if not all) modern audio codecs attempt to shape the coding noise so that it appears mostly in the frequency regions where the ear cannot detect it. For example, the ear is more tolerant to noise in parts of the spectrum that are louder and vice versa. That's why instead of minimizing the simple quadratic error, CELP minimizes the error for the perceptually weighted domain. The weighting filter W(z) is typically derived from the LPC filter by the use of bandwidth expansion: where . See also MPEG-4 Part 3 (CELP as an MPEG-4 Audio Object Type) G.728 – Coding of speech at 16 kbit/s using low-delay code excited linear prediction G.718 – uses CELP for the lower two layers for the band (50–6400 Hz) in a two-stage coding structure G.729.1 – uses CELP coding for the lower band (50–4000 Hz) in a three-stage coding structure Comparison of audio coding formats CELT is a related audio codec that borrows some ideas from CELP. References B.S. Atal, "The History of Linear Prediction," IEEE Signal Processing Magazine, vol. 23, no. 2, March 2006, pp. 154–161. M. R. Schroeder and B. S. Atal, "Code-excited linear prediction (CELP): high-quality speech at very low bit rates," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), vol. 10, pp. 937–940, 1985. External links This article is based on a paper presented at Linux.Conf.Au Some parts based on the Speex codec manual reference implementations of CELP 1016A (CELP 3.2a) and LPC 10e. Linear Predictive Coding (LPC) Selected readings Introduction to CELP Coding Speech Processing: Theory of LPC Analysis