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About The Fourier Transform: From Sine Waves to MRI

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Master the mathematics and practice of frequency-domain analysis: build up from Fourier series to the continuous and discrete transforms, understand why the FFT made spectral analysis cheap, and learn the sampling, aliasing, leakage, and windowing pitfalls that corrupt real measurements. Finish by seeing the same machinery at work in audio equalization, JPEG compression, MRI image reconstruction, and infrared spectroscopy.

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What You'll Learn

Concepts:
Aliasing Nyquist–Shannon Sampling Theorem Frequency-Domain Filtering Audio Equalization Fourier Series Spectrogram Fourier Transform Infrared Spectroscopy Convolution Theorem Short-Time Fourier Transform Fast Fourier Transform JPEG Compression MRI k-Space Discrete Fourier Transform Window Functions Spectral Leakage Continuous Fourier Transform

What you will learn

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