Related Experiment Video
Updated: Jun 23, 2026

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
Published on: December 1, 2023
Genuine cross-spectral densities and pseudo-modal expansions
R Martínez-Herrero1, P M Mejías, F Gori
1Departamento de Optica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040-Madrid, Spain.
Abstract:
A necessary and sufficient non-negative definiteness condition for the cross-spectral density (CSD) is provided. It is also shown that any genuine CSD can be expanded in terms of the so-called pseudo-modes of the source, understood as coherent contributions, not orthogonal to one another, that, superposed in an uncorrelated way, give rise to the CSD. Their evaluation is analyzed by means of an illustrative example.
Related Concept Videos
Graphical and Analytic Representation of Sinusoids
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
Trigonometric Fourier series
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
Exponential Fourier series
Euler's identity...
Inverse z-Transform by Partial Fraction Expansion
To begin the process, the poles of the function are identified and the function is...
Cross Product
The magnitude of the cross product is obtained by multiplying the magnitude of both the vectors and the sine of the angle between them. This means that a larger angle between the vectors will lead to a greater magnitude of the cross product.
Properties of Fourier series II
A function f(t) is...

