A working engineer's guide to the calculus that actually earns its keep: derivatives as sensitivity, gradients for optimization, the chain rule as backpropagation, and integrals as accumulation. Plus the curriculum you can safely forget.
Signal-Processing
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Calculus for the Person Who Forgot -
Computational Photography A modern phone camera captures one image to display and computes perhaps a dozen behind it, fusing them into a result no single exposure could deliver. We walk what the phone's pipeline actually does between shutter press and saved JPEG: multi-frame alignment, HDR fusion, night-mode stacking, semantic segmentation for portrait mode, and the honest line between optical capture and after-the-fact reconstruction.
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How GPS Computes Your Position GPS is one of the few consumer technologies that would fail within minutes if Einstein had been wrong. We walk the physics of fixing your position from four orbiting atomic clocks, why four and not three, the special- and general-relativistic corrections baked into every receiver, how the C/A code lets a phone hear a signal weaker than thermal noise, and why your first fix is slow and the next one is instant.
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How Noise-Cancelling Headphones Work Active noise cancellation is a real-time control loop fighting the wave equation. We walk through feedforward, feedback, and hybrid architectures, why ANC crushes low rumble but gives up on hiss, the latency budget that governs the whole design, and what transparency mode and adaptive ANC actually do to the signal.
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Wearable Sensor Accuracy: What Your Watch Can and Cannot Measure A measurement-engineer's reading of consumer wearables: which numbers on your watch are real signal, which are model-driven fiction, and how the underlying sensors (PPG, accelerometer, SpO2, ECG, skin temperature) actually behave under load, low perfusion, dark skin tones, and free-living conditions.
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The Fourier Transform, Finally Intuitive Any signal is a sum of sinusoids — that one sentence unlocks audio codecs, Wi-Fi, 5G, oscilloscopes, and JPEG. This post builds the Fourier transform from first principles, explains why the naive DFT is impractical and the FFT fixes it, covers windowing and spectral leakage, and shows the whole thing in working Python.