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In this paper, digital speech is compressed using discrete Fourier transform, discrete cosine transform, and improved discrete cosine transform, and compressed sensing technology is proposed. Based on the compressed sensing technology, the frequency domain parameter compression algorithm and the speech coding and decoding algorithm are designed, and the interactive 3D virtual speech system design is completed through the pre-processing of the speech system, the extraction of speech features and the design of speech control commands. The virtual voice system designed in this paper is introduced in the teaching management mode of colleges and universities, and the main functions of the system include four major sections: notification management, online Q&A, virtual voice system interaction, and teaching resource management. The virtual voice system built using sensing technology is simulated and tested, and the practical application effect of the system is studied through empirical analysis. The experimental results show that the amplitude of the sound recorded by the compression sensor in the voice sensing experiment is more concentrated, the range is concentrated between [-0.025,0.025], and the detected voice is smaller and more effective than the amplitude recorded by the cell phone. Students were mainly satisfied and very satisfied with the four system functions designed in this paper, and in terms of the online Q&A function, only one student expressed great dissatisfaction and the total number of satisfied people was 119, and the students were highly satisfied with the teaching management of the system designed in this study.