To design a low-cost non-contact respiratory monitoring system based on the magnetic eddy current sensing principle, a fast digital lock-in algorithm combining undersampling and oversampling is proposed in this paper. This algorithm enables direct digital sampling and fast demodulation of high-frequency respiratory modulated signals, decreasing the performance requirements of the analog-to-digital converter (ADC) and the microcontroller (MCU). In addition, a current source combined with the load characteristic is designed to reduce the cost of waveform generation. The experimental results show that the low-cost amplitude modulation (AM) system constructed based on the above studies can detect respiratory signals in different states with the signal-to-noise ratio (SNR) higher than 92 dB. Compared with the results of the medical monitor, the relative error range of the respiratory rate (RR) measured by the AM system is 1.15%–3.12%, and the measurement accuracy is higher than 98.9%.