光谱分析采样数据重建原始信号

Tracking the Process Reconstructing Original Signal with Sampled Data by Spectroscopy

用光谱分析方法分析信号的采样与恢复。用三个改进的升余弦脉冲构造对称的限带频谱F(ω),经理论推导获得时域信号f(t)。采用梳状函数δT(t)对f(t)采样,调节T值,获得Shannon采样。应用快速傅里叶变换,计算采样的频谱Fd(ω),比较计算频谱Fd(ω)与限带频谱F(ω)的差别,讨论由采样频谱Fd(ω)重建f(t)的方法。结果发现:计算频谱Fd(ω)与限带频谱F(ω)非常相似,由采样数据可以在时域直接重建原始信号,而由频谱数据经快速逆傅里叶变换,同样能准确重建原始信号。因此,信号存储,既可以存储其采样信号,也可以存储采样信号的数字频谱。

With spectroscopy, the principle and process of sampling and reconstructing a continuous-time signal are discussed. A symmetrical frequency-finite spectrum function F（ω） is constructed with three modified rise-cosine pulses. Its corresponding time-domain signal f（t） is worked out theoretically, f（t） is sampled with a comb function δr（t）. By modifying the value of T, Shannon sampling signal is obtained. With Fast Fourier Transform（FFT）, the frequency spectrum Fd （ω） of the sampling signal is figured out. The calculated Fd （ω） is compared with the constructed F（ω）. The processes to reconstruct f（t） with the sampling signal and its digital frequency spectrum Fd （ω） are discussed. As the result, there is little difference between the calculated Fd （ω） and the constructed F（ω）. The original signal can accurately be reconstructed with the sampling data in time domain, so can with the frequency spectrum Fd（ω） by FFT. As soon as signal storage is concerned, we can store the sampling data or its digital frequency spectrum.