Simple Algorithm for Fitting a Gaussian Function

A Simple Algorithm for Fitting a Gaussian Function
Hongwei Guo
IEEE Signal Processing Magazine
Volume 28, September 2011, page 134

This short article was a nice quick read which taught me a few new things and reminded me of several key points. 1) To curve fit data to a Gaussian function it is helpful if you first take the natural log of the data, then fit a quadratic to it. 2) The logarithm naturally weights the small values of noise much more than you want, so this approach has several drawbacks. What the authors did which was cools was instead of fitting to ln(data) then fitted to data*ln(data) which helped aliveiate the weighting issues. This also had some drawbacks so they introduced an interative process which was not dependent on the initial guess to quite persuasively fit the data well. It was a nice reminder of how to do least squares linear algebra with a Newton-Raphson iterative algorithm.

Low-Pass Filtering of Irregularly Sampled Signals

Low-Pass Filtering of Irregularly Sampled Signals Using a Set Theoretic Framework [Lecture Notes], Signal Processing Magazine, IEEE, Issue Date: July 2011, Volume: 28 Issue:4

This was an interesting article which introduced me to a class of processing called Papoulis-Gerchberg signal interpolation. This processing is essentially an iterative one which successively applies constraints in the time and then frequency domain. The end result is one which is the intersection of time-frequency constraints.

I would like to know if I could use such an approach to perform the inverse Fourier transform to logarithmically spaced frequency samples of an interconnect. If such a transform is possible then much of the causality headaches I have with s-parameter data could be reduced. I could then ask my EM simulators to provide me log spaced samples up to what every frequency I need (500 GHz for 1 ps time sample).

Fanless Spinning Heat Sink

Just saw this cool paper about a fanless spinning heat sink. It says that the fundamental reason behind poor heat sink performance is the molecular layer of stale air which insulates the surface to be cooled. So this guy has his heat sink spin to resolve this problem! This also reduces the fouling of the surface from dust and other things as well.

Even for a guy who doesn't know much about thermal stuff like myself the paper is very approachable and interesting.

http://prod.sandia.gov/techlib/access-control.cgi/2010/100258.pdf

http://www.extremetech.com/extreme/89710-the-fanless-spinning-heatsink-the-heatsink-is-the-fan

Optical Receiver Sensitivity

Accurately Estimating Optical Receiver Sensitivity
http://pdfserv.maxim-ic.com/en/an/AN607.pdf

Converting Between RMS and Peak-to-Peak Jitter at a Specified BER
http://pdfserv.maxim-ic.com/arpdf/AppNotes/3hfan402.pdf

100G Ethernet

The last six months I have had a crash course with the IEEE 802.3ba standard (100G Ethernet). It is a alphabet soup! I went to an ethernet summit last month and some of the talks were incomprehensible because of all the acronyms which themselves are often acronyms of acronyms. I have been working on reading the actual spec but recently found a great white paper which I would call 100G Ethernet for dummies. It describes the intent, architecture and IEEE process which is very enlightening.

Opto-Electronic Circuit Simulation

Gunupudi, P., Smy, T., Klein, J., Jakubczyk, Z.J., "Self-Consistent Simulation of Opto-Electronic Circuits Using a Modified Nodal Analysis Formulation," Advanced Packaging, IEEE Transactions, Volume: 33 Issue:4, On page(s): 979 - 993

This was my first introduction to optical circuit simulation and the issues involved. It deals with how to properly model optical interference, chirps, dispersion, scattering and thermal dependence of the device. They do this by defining an optical node which is a physical snap shot of a particular place in the system. An optical node is characterized by the mode (which is basically determined by the geometry of the waveguide), direction, polarization, carrier frequency and magnitude/phase of the complex envelope. They had a good discussion on why they chose the magnitude/phase representation rather than real/imaginary which is harder to model in some situations.

Here are some good quotes from the paper:

Electrical and magnetic fields in optical devices are nonconservative unlike their electrical counterparts. As such these fields cannot be represented by variables such as voltages and currents.

These state variables can be used to calculate the total electric field at an optical node at any time-point of interest if so desired. In order to calculate the electric field, the complex envelopes represented by magnitude and phase, for each mode in every channel, are modulated at the carrier frequency and multiplied with their corresponding mode-shapes. These waveforms are summed to obtain the total electric field present at the optical node.

Optical mode overlap integrals are used to determine the coefficients of optical reflection and transmission matrices for these interfaces.