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About Those Gaussian Envelopes (2014)

peter_d_sherman 2y ago
Perplexity.ai: Me: "Explain 'Gaussian Envelope'" Perplexity: "A Gaussian envelope is a mathematical function used to modulate another function, often a wave or signal, by applying a Gaussian-shaped curve. This modulation results in a smooth, bell-shaped curve that outlines the extremes of the modulated signal... [...] Application: In signal processing, a Gaussian envelope is often used to shape or control the amplitude of oscillating signals or wave packets... [...] Wave Packets: In physics, particularly in quantum mechanics and optics, Gaussian envelopes are used to form wave packets. A wave packet can be described as a plane wave modulated by a Gaussian envelope, which helps localize the wave in space and time... [...] Signal Processing: Gaussian envelopes are used in generating pulses with specific characteristics... [...] For instance, a sinusoidal pulse can be modulated with a Gaussian envelope to control its amplitude over time. Fourier Transform: The Fourier transform of a Gaussian function is also a Gaussian, which makes it particularly useful in frequency domain analysis. This property allows for efficient analysis and manipulation of signals with Gaussian envelopes. Related: https://en.wikipedia.org/wiki/Envelope_(waves) https://en.wikipedia.org/wiki/Envelope_(waves) https://en.wikipedia.org/wiki/Gaussian_function https://en.wikipedia.org/wiki/Gaussian_function https://en.wikipedia.org/wiki/Fourier_transform https://en.wikipedia.org/wiki/Fourier_transform Paper: "A Fourier Approach to Mixture Learning" (It has Gaussian stuff, it has Fourier stuff, what's not to love? :-) <g>): https://openreview.net/pdf?id=thirVlDJ2IL https://openreview.net/pdf?id=thirVlDJ2IL Star Trek IV: (Computer to Mr. Spock): "Adjust the sine wave of this magnetic envelope so that anti-neutrons can pass through it, but anti-gravitons can not..." https://www.youtube.com/watch?v=u2ooUXjNPS8&t=51s https://www.youtube.com/watch?v=u2ooUXjNPS8&t=51s :-)

Perplexity.ai: Me: "Explain 'Gaussian Envelope'" Perplexity: "A Gaussian envelope is a mathematical function used to modulate another function, often a wave or signal, by applying a Gaussian-shaped curve. This modulation results in a smooth, bell-shaped curve that outlines the extremes of the modulated signal... [...] Application: In signal processing, a Gaussian envelope is often used to shape or control the amplitude of oscillating signals or wave packets... [...] Wave Packets: In physics, particularly in quantum mechanics and optics, Gaussian envelopes are used to form wave packets. A wave packet can be described as a plane wave modulated by a Gaussian envelope, which helps localize the wave in space and time... [...] Signal Processing: Gaussian envelopes are used in generating pulses with specific characteristics... [...] For instance, a sinusoidal pulse can be modulated with a Gaussian envelope to control its amplitude over time. Fourier Transform: The Fourier transform of a Gaussian function is also a Gaussian, which makes it particularly useful in frequency domain analysis. This property allows for efficient analysis and manipulation of signals with Gaussian envelopes. Related: https://en.wikipedia.org/wiki/Envelope_(waves) https://en.wikipedia.org/wiki/Envelope_(waves) https://en.wikipedia.org/wiki/Gaussian_function https://en.wikipedia.org/wiki/Gaussian_function https://en.wikipedia.org/wiki/Fourier_transform https://en.wikipedia.org/wiki/Fourier_transform Paper: "A Fourier Approach to Mixture Learning" (It has Gaussian stuff, it has Fourier stuff, what's not to love? :-) <g>): https://openreview.net/pdf?id=thirVlDJ2IL https://openreview.net/pdf?id=thirVlDJ2IL Star Trek IV: (Computer to Mr. Spock): "Adjust the sine wave of this magnetic envelope so that anti-neutrons can pass through it, but anti-gravitons can not..." https://www.youtube.com/watch?v=u2ooUXjNPS8&t=51s https://www.youtube.com/watch?v=u2ooUXjNPS8&t=51s :-)