动态测试信号处理中时-频域变换算法的讨论

Discussion on Time-Frequency Transformation of Measured Dynamic Signals

针对测试信号处理中时 -频变换运算时常见的几种错误 ,如对功率有限信号和能量有限信号套用同样的公式进行计算 ;直接将计算得到的离散谱线值连成连续曲线作为“连续频谱”的图形 ;频域图形的纵坐标表述常发生量纲上的错误等 ,本文通过典型的算例 ,分析了发生上述错误的原因 ,讨论了 FT,FS,DTFT和 DTFS的涵义以及频域表述的量纲 ,并强调指出 :DTFT所得到的频域图形原本就是连续频谱 ,在考虑时窗函数的影响后 ,在变换式中可以以任何非整数值运算 ,从而达到将频谱任意“细化”

The transformation between time and frequency domains is frequently operated in signal processing.But we may often find some mistakes in some engineering literatures,such as(1) indiscriminate use of the same algorithm for two different kinds of signal,i.e. for a power limited signal and for an energy limited signal;(2)direct connection of discrete data derived from FFT or DFT to form a continuous frequency spectrum;(3)mistake in the dimension of a continuous frequency spectrum density function.In the paper,starting from two typical examples,we will discuss how to use the algorithm correctly.The mathematical and physical meanings of FT,FS,DTFT,DTFS and their dimensions will be discussed in detail.Finally,it is emphasized that the curve derived from DTFT in the frequency domain is originally continuous,therefore in the DTFT operation,a fraction instead of an integer may be chosen for the number k to get ZOOM effect,provided the effect of the time window on the frequency resolution has been properly considered.