Signal Power Spectral Density via Intensity Modulation
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Solution Overview
Problem
Current techniques for characterizing power spectral density of signals, particularly those representing random processes, are limited by the Nyquist limit and detector frequency response, requiring a priori knowledge of the signal's functional form and struggling to capture frequencies above the Nyquist limit.
Innovation Solution
The method involves modulating a signal at a specific frequency to determine its power spectral density without prior knowledge of the signal's functional form, using intensity modulation and a class of impulse responses to convolve with the signal, allowing measurement beyond the Nyquist limit.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional sampling techniques are used to measure signal power spectral density, then measurements can be obtained within the Nyquist limit, but frequencies above the Nyquist limit cannot be captured
Solution Approach 1:
The patent applies parameter changes by modulating the signal at a known frequency to shift its spectral content. This frequency transformation allows the signal's power spectral density to be measured at frequencies above the Nyquist limit by mapping high-frequency components to lower, measurable frequencies through the modulation process.
Solution Approach 2:
The patent introduces a modulating signal as an intermediary to facilitate the measurement of high-frequency power spectral density. The modulator acts as a mediator that transfers information from the high-frequency signal to a lower frequency range where it can be accurately captured by the sampling system.
2Ease of manufacture
If a priori knowledge of the signal's functional form is required for PSD determination, then conventional analysis methods can be applied, but the method lacks versatility for unknown signals
Solution Approach 1:
The patent implements self-service by enabling the signal itself to reveal its power spectral density characteristics through modulation without requiring external knowledge of its functional form. The modulation process allows the signal to be analyzed in its native state, making the method automatically adaptable to any signal type regardless of whether its mathematical form is known.
3Loss of time
If high sampling rates are used to capture frequencies above the Nyquist limit, then time resolution improves, but the cost and complexity of the detection system increases
Solution Approach 1:
The patent employs periodic action through signal modulation at a known frequency to periodically shift the signal's spectral content. This periodic modulation allows the system to capture high-frequency information at lower sampling rates by exploiting the regular, predictable nature of the modulation to reconstruct the power spectral density without requiring ultra-high speed sampling hardware.
Data Source
AI summary
Methods, apparatus and systems for determining a power spectral density (PSD) of a signal, in which modulation of the signal is employed to facilitate determination of one or more PSD values over a wide range of frequencies. In some implementations, the signal may represent a wide-sense stationary random process. In one example, the signal is measured/sampled during a plurality of measurement windows, during which an intensity of the signal is modulated at one or more modulation frequencies. A variance of a set of quantities determined from the signal samples is calculated and used to determine respective values of the power spectral density (PSD) for the signal at the one or more modulation frequencies. The one or more modulation frequencies may be chosen in excess of the Nyquist frequency of the sampling process, such that the signal may be characterized for one or more frequencies above the Nyquist limit.