基于Matlab GUI的离散信号谐波分析

通过分析周期信号的傅里叶级数和傅里叶变换的关系，为谐波分析提供理论依据。由于存在频谱泄露和栅栏效应，使用快速傅里叶变换(FFT)进行谐波分析时计算精度不高。为此，本文提出采用频域采样点数等于离散信号长度的离散傅里叶变换(DFT)进行谐波分析，可以有效的减小频谱泄露和栅栏效应带来的影响。通过模拟分析，验证了相比于FFT算法，该算法具有较高的计算精度。最后，基于该算法，使用MATLAB GUI制作了一款具有界面友好且便于数据处理的谐波分析软件，其中包含误差计算模块。利用该软件对多个信号进行谐波分析并计算误差，结果表明，误差的均方差和标准差均较小，由此进一步证实该算法是有效的。

Harmonic analysis of discrete signals based on Matlab GUI

The relation between Fourier series and fourier transform of periodic signals are analyzed, and the theoretic basis is provided for harmonic analysis. Due to spectral leakage and barrier effect, the calculation accuracy of Fast Fourier Transform (FFT) in harmonic analysis is not high. Discreating Fourier Transform (DFT) with the point of frequency domain sampling are equal to the length of discrete signal for harmonic analysis is proposed, Which can effectively reduce the influence of spectral leakage and barrier effect. Through simulation and analysis, it is proved that the DFT algorithm has higher calculation accuracy than the FFT. Finally, based on this algorithm, a harmonic analysis software with friendly interface and easy data processing is made by using Matlab GUI. It comprises the error calculation module. The harmonic analysis and calculation errors of several signals are performed by using this software. The results show that the mean square error and standard deviation of the error are small, which further proves that the algorithm is effective.