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Fourier Uncertainty Principle Fourier Transform 2D Gaussian Visualization python
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1. Fourier transform of a Gaussian is a Gaussian (with different variance) • 2. Visualizing Fourier Uncertainty Principle (which states that a function and its Fourier transform cannot both be localized) through Fourier Transform of a 2D Gaussian function (which is another Gaussian but with different variance) • Demonstration with python (here uncertainty is measured with variance, observe that spatial domain variance increases only to decrease frequency domain variance, so that we have var(G).var(H) ≥ 1/4π^2) • #python #imageprocessing #imageprocessingpython #fourier #fouriertransform #fft #uncertaintyprinciple
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