LSPIV vs Fourier App

LSPIV (large-scale particle image velocimetry) is an image-based method for measuring velocity distribution on the water surface. Applications of LSPIV have been increasing for both field and laboratory experiments as unique and powerful tools for non-intrusive velocimetry using conventional imaging devices and specialized image processing software. This app utilizes a smartphone to implement LSPIV. By innovatively combining the sensors embedded in smartphones, the images captured with them can be intrinsically and instantly ortho-rectified without making recourse to GCPs. The app was developed under support by the River Fund in charge of the Foundation of River and Watershed Environment Management (FOREM), Japan; Grant-in-Aid for Young Scientists (B); and the Research Fund of Japan Institute of Country-ology and Engineering.

Fourier App is an interactive tool for visualizing and computing Fourier Series of piecewise functions. Define custom functions with multiple pieces and discontinuities, choose the time window, and instantly see the original signal x(t) alongside its series approximation s(t). Browse a built-in catalog with classic examples like sine, cosine, step function, rectangular, triangular, ramp, parabola, and more. View the frequency spectrum with an, bn, and cn coefficients, filter partial series terms, and explore how each harmonic contributes to the final waveform. Includes a theory section covering Fourier Series history, equations, and real-world applications such as audio streaming and noise cancellation.