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This paper describes objective quality measures to evaluate speech quality for various kinds of voiceband CODECs in common. The voiceband CODECs studied were PCM, ADM, ADPCM, ATC (Adaptive Transform Coding) and APC-AB (Adaptive Predictive Coding with Adaptive Bit Allocation). First, several objective quality measures in time and frequency domain were defined. They were SNR, Segmental SNR, Spectral Distortion, LPC Cepstrum Distance, COSH, Likelihood Ratio and Weighted Likelihood Ratio. Second, speech quality for voiceband CODECs were evaluated by subjective and objective quality measures. The subjective measures used were based on opinion test and articulation test. Finally, the relationship between objective measures and subjectively evaluated values was studied. It was concluded that the LPC Cepstrum Distance measure had best correspondence to Mean Opinion Score, among the objective measures studied. It was also concluded that the Wighted Likelihood Ratio measure had best correspondence to Articulation Score.