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Hilbert transform and its geometrical meaning

In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function of a real variable and produces another function of a real variable. The Hilbert transform has a particularly simple representation in the frequency domain: It imparts a phase shift of 90 degrees to every frequency component of a function, the sign of the shift depending on the sign of the frequency. The Hilbert transform is important in signal processing, where it is a component of the analytic representation of a real-valued signal (for instance, this can be used to find the envelope of a signal). This is an excerpt of a course called "Mathematical Theory of Complex Calculus". If interested, you can find the course here: https://www.udemy.com/course/mathemat... #complexanalysis #complexcalculus #mathematics #mathematician #lovemath #mathlover #calculus #integrals #contourintegration #physicslover #physicist #mathteacher #physicsteacher #mathchallenge #physicschallenge