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Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

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Summary

This summary is machine-generated.

A novel phase spread frequency sampling method corrects beat frequency nonlinearity in measurement signals. This technique expands the measurement range and broadens the applicability of frequency sampling methods.

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Area of Science:

Signal Processing
Measurement Science

Background:

Nonlinearity in beat frequency signals limits measurement accuracy and range.
Existing frequency sampling methods have limitations in their applicability and measurement range.

Purpose of the Study:

To propose a phase spread frequency sampling method for correcting beat frequency nonlinearity.
To expand the applicability and measurement range of frequency sampling techniques.

Main Methods:

The proposed method involves expanding the phase of an auxiliary interference beat signal.
This expansion ensures compliance with the Nyquist sampling theorem.
Multiple phase expansions are utilized for flexible range extension.

Main Results:

Successfully corrected nonlinearity in the beat frequency of the measured signal.
Overcame the limitation of a restricted measurement range.
Expanded the conditions under which frequency sampling methods can be applied.

Conclusions:

The phase spread frequency sampling method effectively addresses beat frequency nonlinearity.
This approach offers a flexible and expanded measurement range for signal processing applications.