基于傅里叶变换的非正弦时域正交调制系统实现方法

A Novel Method for Realization of Non-Sinusoidal Orthogonal Modulation System in Time Domain Based on Fourier Transform

针对基于椭圆球面波函数(PSWF)的非正弦时域正交调制系统在硬件实现时遇到的PSWF实时产生困难、系统实现复杂度高等问题,从PSWF的傅里叶级数展开形式出发,分析研究了其正余弦展开形式及展开项系数与脉冲信号能量和脉冲间正交性的关系.在此基础上,理论推导了基于离散傅里叶逆变换(IDFT)的非正弦时域正交调制方法和基于离散傅里叶变换(DFT)的解调方法,并给出了基于快速傅里叶(逆)变换(FFT&IFFT)的调制和解调方法.该方法将成熟的傅里叶变换技术运用到非正弦系统的实现上,建立了非正弦系统实现与离散傅里叶(逆)变换之间的联系,为非正弦系统的研究提供了一种新思路.

In the application of the non-sinusoidal orthogonal modulation system based on PSWF （prolate spheroidal wave function） in time domain it is difficult to generate PSWF in real-time and complex to realize the non-sinusoidal orthogonal modulation system. Therefore, starting from the Fourier series expan- sion of PSWF, the relationships between the expansion coefficients and the energy and orthogonality of PSWFs were analyzed. Then, a modulation method based on the inverse discrete Fourier transform （IDFT） and a demodulation method based on the discrete Fourier transform （I）FT） were deduced. After that, structures of the modulator and demodulator based on the （inverse） fast Fourier transform （FFT ＆ IFFT） were given. As the idea of Fourier transform was introduced to the realization of non-sinusoidal communication system the connection between non-sinusoidal communication system and （inverse） dis-crete Fourier transform was established. This method may provide reference for the study of non-sinusoidal technology.