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Signal Processing
@DSP_fact
Digital signal processing, acoustics, Fourier analysis, etc.
JohnDCook.com/DSPJoined April 2013
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The Hilbert transform commutes with differentiation, i.e. H(u'(t)) = (H(u))'(t).
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Relationship between Fourier transform F and Hilbert transform H: F(H(u))(w) = (-i sgn(w))F(u)(w).
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Unfortunately, there are three common definitions of the Fourier transform
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DSP software from Rice University dsp.rice.edu/software
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The Scientist and Engineer's Guide to Digital Signal Processing dspguide.com
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Why a leaf blower has a definite pitch
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Sampling a signal is equivalent to periodizing its Fourier transform. For non-smooth signals (with non-compact Fourier transform), it creates aliazing. en.wikipedia.org/wiki/Nyquist%E
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DSP software that comes with Mathematica: reference.wolfram.com/language/guide
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Rice wavelet toolbox ece.rice.edu/dsp/software/r
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New blog post: Decoding Lunar Flashlight. I look at a 3 minute recording of the X-band telemetry beacon done by the day after launch. The modulation is 48 kbaud PCM/PM/bi-phase-L, and coding is r=1/6 Turbo with 8920 bit frames. (1/4)
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An interactive guide to the Fourier transform betterexplained.com/articles/an-in
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If the Fourier transform of f(x) is F(t), the transform of f(x/m) is m F(mt).
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The Butterworth filter is designed to have as flat a frequency response as possible in the passband.
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The Fourier Transform, explained in one sentence
blog.revolutionanalytics.com/2014/01/the-fo
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Uncertainty principle and spectrogram with pylab glowingpython.blogspot.com/2011/09/uncert
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Signal Identification Wiki
sigidwiki.com/wiki/Signal_Id
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The mother wavelet for Ricker wavelets, also known as 'Mexican hat wavelets,' is proportional to 2nd derivative of a Gaussian density.
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A 'mother wavelet' is a function used to create a family of wavelets by shifting and scaling.
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The word 'wavelet' was coined in the early 1980's.
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The correlation of f(t) and g(t) is the convolution of f(t) and g(-t).
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Compressed sensing also makes, and effectively exploits, an assumption that classical signal processing does not: sparsity.
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Compressed sensing accomplishes things that seem to violate the Nyquist sampling theorem.
But compressed sensing is playing by different rules.
It samples randomly, not linearly, and gives good results with high probability, not with certainty.
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Oldies but goldies: C. Shannon, 1949, Communication in the presence of noise.
States the Nyquist–Shannon sampling theorem. Explains the aliasing of signals. en.wikipedia.org/wiki/Nyquist%E
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The more concentrated a signal is in time, the more spread out it is in frequency.
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A linear chirp is a signal whose instantaneous frequency increases linearly with time.
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New blog post: Decoding ArgoMoon. Another post in the Artemis I series. Here I decode the X-band signal of 's ArgoMoon cubesat using some Allen Telescope Array IQ recordings done on the day of the launch. (1/3)
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Critical sampling of a sine wave is two sample points per cycle.
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