Signal Processing for Computer Scientists

"Learn your signal processing on the street" "A two-month long review article"

Summer 2015, Tuesdays, 12:00-1:30, AMP Lab, 465H

Signal processing was the original "big data" -- your cell phone processes nearly 2TB of RF data daily. All the high-throughput communications technologies we take for granted -- WiFi, gigabit ethernet, 4G cellular, USB 3, home broadband, GPS -- are made possible by advanced signal processing algorithms. Machine learning technologies like deep learning have fundamental signal processing operations (such as convolution) at their core. Yet most computer scientists have at best a superficial understanding of these technologies, the underlying mathematics, and how they can contribute.

The goal of this class is to develop an intuition for the basic language of signal processing, to highlight some of the recent cool advances, and to show how the emergence of programmable hardware (such as software-defined radios) enable software engineers to do “signal processing without the soldering”

Topics:

• Complex and periodic signals. "What is phase?" Why do we always use complex signals? Analytic representations of real-valued data, the complex plane, the unit circle, a little bit of complex analysis
• Sampling theory -- discrete mathematics for signal processing. "Doing things on computers”, and the associated caveats. Sampling theory, resampling
• Spectral analysis. What is the relationship between the Fourier Transform, the Discrete-Time Fourier Transform, and the FFT? "Why does matlab’s FFT() always give me complex outputs?" forward, inverse transforms.
• Linear time-invariant systems -- filtering, spectral analysis, signal processing
• Nonlinearity -- modulation, communication, spread-spectrum technology, etc.
• Adaptive filtering, control, and learning from data
• image processing -- deconvolution, inpainting, deblurring, computational optics
• Time-space representations - STFT, wavelets, the Wigner transform

Protocols and technologies

• Amplitude Modulation, Frequency Modulation, single-sideband, etc.
• More modern modulation schemes like QAM for DTV
• wired protocols and encodings : LVDS signalling, 8b/10B for gigabit ethernet, PCI express, and the like
• The classic phone system, modems, modern protocols like GSM
• WiFi
• GPS

Background:

I'm going to assume you've taken calculus and linear algebra and at one point in your life have run matlab's fft and ifft. Examples will all be in python and placed on github.

Software Defined Radio

Software defined radio gives you a UDP interface to the entire radio spectrum. The Ettus Research N210 Software Defined Radio has a bandwidth of DC-6GHz and can sample at 50 MSPS, broadcasting the data over gigabit ethernet. That’s right, you open a UDP socket and you’re measuring the electromagnetic spectrum! I’ll be using this hardware to capture sections of the RF Spectrum for analysis and demonstrations.

Schedule

• June 9: Overview, analytic functions, continuous-time and discrete-time signals, linear time-invariant systems, convolution
• June 16: The Fourier transform, the discrete-time Fourier transform, the discrete Fourier transform, and the fast Fourier transform.
• June 23: [No class, Eric traveling]
• June 30: The basics of sampling theory, modulation, AM and FM. Introduction to SDR.
• July 7: Time-space representations -- Uncertainty relations, the short-time fourier transform, wavelets, the wigner distribution
• July 14: Applications: spread-spectrum technology, WiFi, GPS
• July 21: Applications: Adaptive filtering, internet broadband, a little control theory
• July 28: Applications: Deconvolution, image processing, sparse methods