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This paper proposes improvements to the electrolarynx device, which allows a patient to speak after the larynx is removed. Speech through existing electrolarynx devices is corrupted by high levels of noise and sounds unnatural. The proposed algorithm is based upon spectral subtraction techniques and modifies the magnitude of the speech signal in the frequency domain. Here, with the introduction of Discrete Cosine Transform (DCT) domain analysis using minimum statistics, the proposed algorithm effectively reduces high levels of noise generated by the electrolarynx. Unlike existing methods, the proposed algorithm does not require the use of a voice activity detector and the Discrete Cosine Transform domain is more proficient at isolating speech signal energy. The new algorithm presented in this paper is readily adaptable to hardware implementation and has the potential to be included in a handheld electrolarynx device in the future.