The measurement of power spectraR.B Blackman
The measurement of power spectra
from the point of view of communications engineering
by R.B Blackman · first published 1958
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…Mathematical Analysis and also his very careful treatment of the Fourier transform in his Real and Complex Analysis, also distributions in his Functional Analysis. Also read and used the Blackman and Tukey The Measurement of Power Spectra, wrote some corresponding software that pleased some people in the US Navy, etc. Then I took a course at the level of the second Rudin book, and in the class when the prof got to the Fourier transform…
on “New atomic clock loses only one second every 300B years” ↗…independently; and that was the research for my Ph.D. I continued that way in my career: E.g., in a software house working for the US DoD, I saw a problem in a specification, got Blackman and Tukey, 'The Measurement of Power Spectra', and read it carefully enough to see what was wrong with the specification and how to fix it. Right: without courses, lectures, problem sessions, .... As far as I can tell, nearly all the technical content…
on “Online Education's Dirty Secret - Awful Retention” ↗…tests to use. E.g., tests in regression can be F ratios and/or t-tests, and need to check some assumptions or at least robustness here. E.g., in power spectral estimation, see, Blackman and Tukey, 'The Measurement of Power Spectra', there is a severe trade off between resolution and stability, another case of a trade off between bias and variance. Tough to 'automate' that consideration. So, take a box of data. Divide it in half.…
on “Basics of Machine Learning” ↗…Olshen, Charles J.\ Stone, {\it Classification and Regression Trees,\/} ISBN 0-534-98054-6, Wadsworth \& Brooks/Cole, Pacific Grove, California, 1984.\ \ R.\ B.\ Blackman and J.\ W.\ Tukey, {\it The Measurement of Power Spectra:\ \ From the Point of View of Communications Engineering,\/} Dover, New York, 1959.\ \ William W.\ Cooley and Paul R.\ Lohnes, {\it Multivariate Data Analysis,\/} John Wiley and Sons, New York, 1971.\…
on “Acquisitions accelerate as tech giants seek to build AI smarts” ↗…stuff when working on US Navy sonar signal processing. Then at one point I moved on to power spectral analysis of wave forms, signals, sample paths of stochastic processes, as in Blackman and Tukey, The Measurement of Power Spectra: From the Point of View of Communications Engineering. Can get more on the relevant wave forms, signals, stochastic processes from Athanasuis Papoulis, Probability, Random Variables, and Stochastic…
on “Ask HN: What scientific phenomenon do you wish someone would explain better?” ↗…Navy wanted: (1) Start with recordings by US submarines of underwater sounds, and write software to estimate the power spectra using the FFT (Fast Fourier Transform) and the Blackman and Tukey, "The Measurement of Power Spectra". (2) Given ships at sea and a war, how long would the US submarines last? Start with some WWII analysis of search and encounters by Koopmans and do a Monte-Carlo Markov process, generate many independent…
on “What medieval people got right about learning (2019)” ↗…of ocean waves. Some of the input was actual ocean wave data. So, the goal was to generate simulated data with the same 'power spectrum' as observed. I got the famous book by Blackman and Tukey on measurement of power spectra and discovered that what the DoD lab wanted was poorly formulated; they were asking for too much 'resolution' from the data they had.. So, following the book, I wrote some software to illustrate what…
on “What It's Really Like To Pitch Lerer Ventures” ↗…student, I taught calculus successfully. As an MBA prof, I taught more in applied math successfully. In my career, I continued to learn on my own: E.g., for some weeks I carried Blackman and Tukey, The Measurement of Power Spectra to dinner at a seafood bar in Silver Spring, MD, and then one week, mostly on my own without my company knowing about it, wrote some corresponding software which was a big help in our company winning a…
on “Why do MOOCS have low completion rates?” ↗…measure theory approach is in Doob, Stochastic Processes, Loeve, Probability Theory, and several more texts by quite good authors. E.g., without measure theory, can just dive in via Blackman and Tukey, The Measurement of Power Spectra .... With all these sources, are able to get by without measure theory. Yes, without measure theory, at some places will have to not ask to understand too much and just skip over some details to get…
on “Foundations of probability theory” ↗…of books, university courses, and papers. E.g., at one time I needed to learn about estimating the power spectra of second order stationary stochastic processes. Sooo, I found Blackman and Tukey, The Measurement of Power Spectra, at dinners dug in, in a few days wrote some illustrative code, showed the code to our target customer, and, presto, bingo, won the competitive bid with "sole source". So, I know some statistics and…
on “Show HN: A job board for companies fighting ageism in tech” ↗…intricate structure on the tape. Then my code had to do various conversions and return easy to use data! It was a box of cards -- took a while. Later one week I raced through Blackman and Tukey, The Measurement of Power Spectra, got smart on power spectral estimation (mostly chi-squared statistics), typed PL/I code furiously, for about 1000 lines of code, and had the code generate white noise, pass it through a filter, record…
on “Say it's 1962, you're lucky enough to be a programmer working with an IBM 7090” ↗…the power spectrum of data collected at sea on ocean waves. Then for the simulation, generate sample paths of the stochastic process with that power spectrum. So, I dug into Blackman and Tukey, The Measurement of Power Spectra, saw the statistical basics, and quickly wrote some illustrative software that did the work. One of the lessons was, to get an accurate power spectrum takes, roughly, some number of cycles of data at…
on “How much math you need for programming (2014)” ↗…also in some competitive bidding on some software for that lab. I saw a problem with what the lab had requested and decided to spend the week on something risky: I got 'smart' on the statistics of the measurement of power spectra, wrote some illustrative software, and at the end of the week showed a guy from the Navy. The Navy was pleased, and our company got essentially 'sole source' and won the competitive bid. If my work…
on “How Solo Founders Beat The Odds and Get Into Top Accelerators” ↗