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In this paper, a new technique for the estimation of the formant frequency of noise-corrupted speech signals is presented. A ramp-cepstrum model for a one-sided autocorrelation function of the voiced speech is proposed considering the vocal-tract system as an autoregressive model with a periodic impulse-train excitation. A residue-based least- squares optimization algorithm is introduced to estimate the ramp-cepstrum model parameters which are then used to compute the formant frequencies. Synthetic and natural vowels as well as some naturally spoken sentences in noisy environments are tested. The experimental results demonstrate the efficacy of the proposed method at low levels of signal-to- noise ratio (SNR).