应用FFT计算△Σ调制器信噪比的分析

Analysis on Computing SNR of △Σ Modulators Using FFT

针对许多设计者存在错误使用快速傅里叶变换计算△Σ调制器输出信号信噪比的问题,在分析△Σ调制器工作原理和推导计算△Σ调制器信噪比理论模型的基础之上,详细地阐述了使用快速傅里叶变换计算△Σ调制器信噪比和绘制其功率谱密度的过程。以二阶△Σ调制器为例,在MATLAB和Simulink环境中完成了信噪比的计算和功率谱密度的绘制,实验结果证明了所述方法的正确性,对正确设计△Σ调制器具有重要的实际应用价值。

The Fast Fourier Transform （FFT） is widely used to estimate the power spectral density （PSD） and of signal- to- noise ratio （SNR） of delta- sigma （△Σ） data, but is sometimes abused by many △Σ designers. The operation principle of △Σ modulator is analyzed and the theoretical model of SNR of △Σ modulator is derived in this paper. And then, the process of computing SNR and drawing the PSD using the FFr are described in detail. The SNR and PSD of a 2nd order △Σ modulator are computed and drawn respectively in the MATLAB and Simulink environment. The results indicate that the method described is valid and has the practical value for the design of △Σ modulator.