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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.

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

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Updated: Jul 7, 2026

Interictal High Frequency Oscillations Detected with Simultaneous Magnetoencephalography and Electroencephalography as Biomarker of Pediatric Epilepsy

Interictal High Frequency Oscillations Detected with Simultaneous Magnetoencephalography and Electroencephalography as Biomarker of Pediatric Epilepsy

Published on: December 6, 2016

Point-source localization in blurred images by a frequency-domain eigenvector-based method.

M Gunsay¹, B D Jeffs

¹Dept. of Electr. and Comput. Eng., Brigham Young Univ., Provo, UT.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 1, 1995

Summary

This summary is machine-generated.

This study introduces a novel image restoration method for resolving blurred point sources, like stars. The technique adapts direction of arrival estimation algorithms for enhanced image deblurring and super-resolution.

Related Experiment Videos

Last Updated: Jul 7, 2026

Interictal High Frequency Oscillations Detected with Simultaneous Magnetoencephalography and Electroencephalography as Biomarker of Pediatric Epilepsy

Interictal High Frequency Oscillations Detected with Simultaneous Magnetoencephalography and Electroencephalography as Biomarker of Pediatric Epilepsy

Published on: December 6, 2016

Area of Science:

Astronomy and Astrophysics
Signal Processing
Image Restoration

Background:

Telescopic images often suffer from blurring due to atmospheric turbulence and optical aberrations.
Resolving and localizing blurred point sources is crucial for astronomical observations and other imaging applications.

Purpose of the Study:

To develop a new image restoration technique for accurately resolving and localizing blurred point sources.
To adapt direction of arrival (DOA) estimation methods for image deblurring.

Main Methods:

Modeled blurred point source images in the frequency domain analogous to linear sensor array responses.
Adapted eigenvector-based subspace decomposition algorithms (e.g., MUSIC) for DOA estimation.
Introduced a generalized array smoothing method for rank enhancement in the presence of blur.

Main Results:

Achieved inter-pixel super-resolution in deblurred images.
Demonstrated computational efficiency of the new algorithm.
Successfully applied the method to deblur star images.

Conclusions:

The proposed method offers an effective approach to image restoration for blurred point sources.
The generalization of DOA techniques provides a powerful tool for image deblurring and super-resolution.