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May 2, 2016
Dear friends,

A lot has happened in the past two weeks of the UCLA SETI course.  We obtained excellent data with the Green Bank Telescope (GBT) on April 15.  Students are now in the thick of writing computer algorithms to analyze the data.  In the past four lectures, we proceeded methodically with (1) theory and calculation of Fourier transforms, (2) creation of two-dimensional plots for time-frequency analysis, (3) theory and calculation of Doppler shift, and (4) algorithms to search for and detect the Voyager 1 signal in a large data set.  I devote a paragraph to each lecture below.

The Fourier transform, named in honor of Joseph Fourier (1768 – 1830), allows the calculation of a spectrum, i.e., the decomposition of a function of time into its constituent frequencies.  It is an extraordinarily powerful mathematical tool that is used in almost all branches of science and engineering.  The analytical expression requires an integral, which is why calculus is one of the prerequisites for the UCLA SETI course.  In practice, we often sample a function at discrete times, like we did with the GBT, and compute a discrete Fourier transform with efficient algorithms.  In the first hour of the lecture, students learned about properties and theorems related to the Fourier transform.  In the second hour, they wrote computer programs to calculate the Fourier transform of our GBT test tone data.  You may recall that we had recorded 30 seconds of data with a signal of known frequency injected near the telescope receiver.  Because this signal includes a single frequency, its spectrum is unmistakable: a sharp spike appears in the frequency domain.  By the end of the lecture, about half of the class had succeeded in detecting the test tone signal and confirming the expected frequency of 1 MHz (1 million cycles per second).  The verification of the test tone data is quite significant: it means that both the hardware and the software behaved as expected during our observations.  It also meant smiles and twinkles in the eyes of all the students who computed their first Fourier transform.  Instructor delight was off the charts.
The GBT test tone data is detected at a frequency of 1 MHz in this spectrum.
The next lecture introduced the student to two-dimensional plots that are quite powerful in analyzing the time-frequency content of signals.  Let's say you compute the Fourier transform of the first second (0 <= t < 1 s) of a data stream and store the associated signal power as the first line of a two-dimensional array.  Then you compute the Fourier transform of the next second (1 <= t < 2 s) of data and store the result as the second line of the two-dimensional array.  And so on.  At the end of the procedure, your array contains one spectrum per line, with frequencies increasing from left to right, and consecutive lines representing time, increasing from top to bottom.  Students learned to compute and display these plots.  Can you picture how the test tone data would look on one of these plots?  It shows up as a bright vertical line.

The Doppler shift is a well-known physical effect that you have certainly experienced.  It affects the frequency of a signal when there is motion between a source and an observer.  The pitch of the sound made by an approaching car, for example, is higher than that made by a receding car.  The Doppler shift is a central concept in SETI because it allows us to discriminate between terrestrial sources (most of which are fixed or moving slowly with respect to the telescope) and extraterrestrial sources (most of which have a considerable velocity with respect to the telescope).  During the third lecture, I asked the students to compute the Doppler shift affecting the signal emitted by Voyager 1.  This venerable spacecraft was launched in 1977 and provided the first detailed reconnaissance of the Jupiter and Saturn systems.  It is currently our most remote ambassador at a distance of 135 astronomical units from the Sun.  Students used the web interface to the NASA JPL Horizons system, written by my colleague and friend Jon Giorgini, to compute Voyager 1's velocity and associated Doppler shift.  Then they started creating time-frequency diagrams of Breakthrough Listen data that contain the Voyager 1 signal.

The fourth lecture started with the description of a friendly competition and prize.  The first student who found the Voyager 1 signal would get rewarded with a scale model of the spacecraft (assembly not included).  This is not a simple task.  The data are divided in 64 channels of about 3 MHz each.  At a frequency resolution of about 1 Hz, which is what the students worked with, there are over 200 million channels to examine.  If you could examine one channel per second on average, it would take over 6 years to complete the task.  This realization was a turning point for several students.  The course is squarely in the realm of "big data" where computers and efficient search algorithms are absolutely essential.  Students adopted multiple strategies.  Generally, they relied on calculating time-frequency diagrams of the signal power, summing the signal power over the entire observation interval, sorting the result in order of decreasing power, and displaying subsets of the data around frequencies where the peaks in power are observed.  By the end of the lecture, almost all students had found the faint but distinctive Voyager 1 signal, and one student walked away with a scale model of Voyager 1.  Discovering the signal among millions of channels brought much satisfaction to the students and their instructor.
A UCLA student's detection of the faint signal from Voyager 1 in a time-frequency analysis plot.  The detected frequency and the slight change in frequency over the roughly 4-minute period both match expectations.
An unassembled scale model of Voyager 1.
Students now have a set of tools that they will continue to refine and build on to analyze additional data, including our GBT observations of 14 exoplanets, most of which are potentially habitable.  I am very excited about our progress so far.  Recently, I learned that I will have the opportunity to describe our results at a SETI session during the International Astrononautical Congress in September.  I very much look forward to presenting the educational and research impact of the UCLA SETI initiative.

Warm regards,

Jean-Luc Margot
Copyright © 2016 UCLA SETI Group. All rights reserved.

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