Spectral Density Analysis: Frequency Domain Specification and Measurement of Signal Stability

Stability in the frequency domain is commonly specified in terms of spectral densities. The spectral density concept is simple, elegant, and very useful, but care must be exercised in its use. There are several different but closely related spectral densities, which are relevant to the specification and measurement of stability of the frequency, phase, period, amplitude, and power of signals. Concise, tutorial descriptions of useful spectral densities are given in this survey. These include the spectral densities of fluctuations of (a) phase, (b) frequency, (c) fractional frequency, (d) amplitude, (e) time interval, (f) angular frequency, and (g) voltage. Also included are the spectral densities of radio frequency power and its two normalized components, Script X(f) and Script %(f), the phase modulation and amplitude modulation portions, respectively. Some of the simple, often-needed relationships among these various spectral densities are given. The use of one-sided spectral densities is recommended. The relationship to two-sided spectral densities is explained. The concepts of cross-spectral densities. spectral densities of time-dependent spectral densities, and smoothed spectral densities are discussed.