Abstract: An acoustical audible alarm is generally requested in the medical electronics devices to posit where an alarm happen. At present, the medical audio alarm signals are mainly generated by voice recording or pulse-based signals. With those methods, many shrill voices and sharp noises are easily produced to affect the quality of an alarm. Therefore, aim at a qualified medical audible alarm, the traditional Goertzel algorithm was simplified into the real number field from the complex number field. Based on this simplified Goertzel algorithm, a recursive algorithm was proposed to generate a serial of sinusoidal fundamental and its harmonic signals. The algorithm was programmed and tested with an audio processing circuit. The audio circuit was designed based on microcomputer LM3S9B92. According to the tested signal waveforms and the frequency spectrum, a group of low-noise and multi-overtone audible alarm signals were produced.