Convolution and the Fourier Transform: Math! (in pictures!!)
summary
Airborne ice-penetrating radar on a DC-3 transmits 6,000 pulses per second and images kilometers of ice (records past ~48 km). Replacing a square pulse with a chirp pulse narrows the correlation peak and improves vertical resolution from tens of meters to about 3 meters. Electronic hums are identified in frequency space and subtracted, yielding roughly 10 dB deeper signal visibility. The convolution theorem plus the 1965 FFT makes convolutions feasible in n log n time.
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chapters (11)
- 0:00Convolution and the Fourier Transform: Math! (in pictures!!)
- 1:07Detour: Ice-Penetrating Radar
- 3:22Cross-Correlation vs. Convolution
- 3:42Pulse Compression
- 5:29Image Processing
- 5:43Gaussian Blur
- 6:00Edge Detection
- 6:20What's a Fourier Transform?
- 7:24Frequency Spectrum
- 8:14Noise Characterization
- 10:39Convolution Theorem
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