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This paper addresses the design, development, evaluation, and implementation of efficient low bit rate speech coding algorithms based on the sinusoidal model. A series of algorithms have been developed for pitch frequency determination and voicing detection, simultaneous modeling of the sinusoidal amplitudes and phases, and mid-frame interpolation. An improved sinusoidal phase matching algorithm is presented, where short-time sinusoidal phases are approximated using an elaborate combination of linear prediction, spectral sampling, delay compensation, and phase correction techniques. A voicing-dependent perceptual split vector quantization scheme is used to encode the sinusoidal amplitudes. The perceptual properties of the human auditory system are effectively exploited in the developed algorithms. The algorithms have been successfully integrated into a 2.4 kbps sinusoidal coder. The performance of the 2.4 kbps coder has been evaluated in terms of subjective tests such as the mean opinion score and the diagnostic rhyme test, as well as some perceptually-motivated objective distortion measures. Performance analysis on a large speech database indicates that the use of the proposed algorithms resulted in considerable improvement in temporal and spectral signal matching, as well as improved subjective quality of the reproduced speech.