Steve Smith (@SteveSmith)

Steve Smith specializes in developing novel imaging systems for medical, security, and industrial applications. His interests include: digital signal processing, analog electronics, x-ray physics and sensory systems. Dr. Smith is the author of "The Scientist and Engineer's Guide to Digital Signal Processing," freely distributed over the internet in electronic form. For the last ten years he has been the president and technical director of Spectrum San Diego, Inc., a research and development group specializing in imaging and instrumentation systems.

Benford's law solved with DSP

Steve Smith ● February 22, 2008●7 comments

Steve Smith shows that standard DSP tools give a clean, intuitive explanation of Benford's law by treating leading-digit counts as signals on the number line and using convolution and Fourier analysis. He publishes the full derivation as an online chapter after traditional journals showed little interest. The result highlights how time- and spatial-domain DSP techniques can be applied to numeric distributions.

Waveforms that are their own Fourier Transform

Steve Smith ● January 16, 2008●12 comments

Steve Smith admits a long-standing mistake and overturns the claim that only Gaussians are their own Fourier transform. He gives trivial and nontrivial examples, explains why infinitely many such waveforms exist, and shows a quick discrete construction using the DFT with a 1/sqrt(N) normalization. Engineers get an intuitive 30-second argument plus a practical recipe to build self-Fourier signals.

An Interesting Fourier Transform - 1/f Noise

Steve Smith ● November 23, 2007●25 comments

Power-law signals have a neat Fourier trick: their transforms are power laws too, but with important caveats. Steve Smith walks through the t^α ↔ ω^{-(α+1)} relation, shows how the unit step, the Gamma scaling and a nontrivial phase change the picture, and highlights the special α = -0.5 case that links to 1/f noise. The post frames why phase and physical interpretation keep 1/f noise mysterious.