Scientific Computing · Cluster
Signal Processing
Transforms, filters, and sampling.
- 01 Sampling Rate, Aliasing, and the Folding of the Spectrum Why the Nyquist criterion constrains the signal rather than the converter, how aliasing folds frequencies arithmetically, and what reconstruction actually requires.
- 02 What the Discrete Fourier Transform Computes The DFT as a projection onto a fixed set of complex exponentials, why the transform matrix is orthogonal, and where the n log n cost of the fast algorithm comes from.
- 03 Quantization Step Size, the Six-Decibel Rule, and Dither Why each added bit buys roughly six decibels of signal-to-noise ratio, when the uniform-error model stops holding, and what dither trades away to fix it.
- 04 FIR Design by Windowing and the Gibbs Ripple Why truncating an ideal impulse response produces passband ripple, how window shape trades transition width against stopband rejection, and what the design formulas predict.
- 05 The Bilinear Transform and Frequency Warping How mapping the analog frequency axis onto the unit circle produces a stable digital filter, why the cutoff moves, and how prewarping compensates for it.
- 06 Zero-Phase Filtering by Forward-Backward Passes Running a filter twice in opposite directions cancels its phase at the cost of squaring its magnitude, and the initial-condition choice decides how much edge transient survives.
- 07 Spectral Leakage, Scalloping, and Segment Averaging Why a finite record smears tones across DFT bins, how scalloping loss depends on the window, and what averaging overlapping segments does to variance and bias.
- 08 Polyphase Decimation and the Cost of Changing Sample Rate Why a naive resampler computes samples it discards, how the polyphase decomposition removes that work, and what the filter length must satisfy before downsampling.
- 09 The Analytic Signal and Instantaneous Frequency How a Hilbert transform turns a real signal into a complex one with one-sided spectrum, why the derived phase derivative is not always a frequency, and where it fails.
- 10 Sparse Sampling and the Limits of Recovery Why a sub-Nyquist sample count can still determine a sparse signal, what the restricted isometry property guarantees, and where the guarantee stops being useful.