The spectrum of clipped noise

作者：John Hasbrouck Van Vleck, David Middleton · 发表于：Proceedings of the IEEE · 年份：1966 · DOI：10.1109/proc.1966.4567 · 被引用次数：529 · 研究领域：Power Line Communications and Noise、Semiconductor Quantum Structures and Devices、Electromagnetic Compatibility and Noise Suppression

The present report calculates in some detail the (intensity) spectrum to be expected for clipped (also called "limited") noise. Two cases are considered: (A), the clipping of an unmodulated noise band (DINA) [1] and (B) a carrier modulated by clipped noise. The computations are made for various shapes of noise bands before clipping, viz., 1) a uniform or rectangular structure, 2) a Gaussian distribution, 3) an "optical" (Lorentzian) shape factor of the type 1/[(v-v0)2+ δ2]. The simplest type of calculation to make is that for what we term "extreme clipping," wherein the limiting amplitude is very small compared to the rms amplitude before clipping. The mathematical theory for this is given in Section III, while Section IV develops the theory for clipping at an arbitrary level. The basic mathematical method, which is rather general and is useful, we believe, for a variety of noise problems, is presented in Section II and consists in utilizing a relation between the correlation function and the normal surface, along lines suggested by Rice [1]. The results of the calculation are discussed in Section I and are displayed in Figures 4-10 and Tables I and II. If the clipping is not down to more than the rms level before limiting (equivalent to clipping at about 1.4 times the rms level after clipping), there is practically no distortion of the spectrum. Even in the case of extreme clipping the wastage of power due to spoiling of the spectrum's uniformity is small, amounting to only ...