# February 2011 Archives

## Proteus (2005)

I composed this electroacoustic composition in 2005 to accompany a video by a friend. I generated most of the sound material by altering the scanning frequency of sample wavetables using the energies of simulated systems of particles in harmonic potentials. (I describe the genesis of this approach here.) I think this approach to synthesis works well for generating dynamic spatialized sound textures, but I definitely need to remaster this track at some point. I remember a lot of composition was necessary to shape the material just how I liked it after I generated the sounds. Also, I added the reverse piano notes because my teacher Curtis Roads once told me that he thought such sounds were remarkably beautiful.

## More thoughts on OMP performance limits from SIC

I am not too satisfied with my interpretation yesterday of Jin and Rao's condition (JRC). When I look at it again and refer to their text, i.e., $$\frac{\log N}{M} \le 0.5 \log \left [1 + \frac{s_i^2}{\sigma_n^2 + \sum_{j=i+1}^K s_j^2} \right ] \; \forall i \in \{1, 2, \ldots, K\}$$ this is a condition for asymptotic success (as the number of measurements $$M$$ goes to infinity) and not failure. Other aspects of the sparse signals can influence the recovery performance, such as which elements of the measurement matrix are active, and how much they are active in relation to each other.

## Successive Interference Cancellation

I am meeting this Thursday with a professor more specialized than I in digital communications, which will catalyze my understanding of the application and limits of successive interference cancellation (SIC) to picking the bits off a received signal ripe with messages for other receivers. To prepare for this meeting, I am reviewing over the next few days SIC in D. Tse and P. Viswanath, "Fundamentals of Wireless Communication," Cambridge University Press, 2005 -- which I see will require some skimming of several of the other chapters to get a feel for what is going on. I am most interested in learning more about the theoretical underpinnings used by Jin and Rao in analyzing the performance limits of OMP.

## There Will Be Blood

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Did you enjoy There Will Be Blood? Well, now you can experience the full drama of being an oilman on the brink of insanity on your own desktop computer! See if you, Daniel Plainview, can make the most money before you either die or become insane. (I created this program to teach finite state machines in my artificial intelligence class.)

Play There Will Be Blood!

How much money can you make?

## A few graphs before I leave

Coming up next week: my seven consecutive lectures and workshops in artificial intelligence programming! In the meantime, I leave you with the following. Both of the graphs below represent recovery results of sparse signals from compressive measurements. The first uses sparse signals from the constant-amplitude random signs ensemble; the second uses sparse signals with non-zero elements distribute Normal. We see quite a difference between the two cases, as several of my previous experiments have shown, as well as the work by many others. However, I do not feel confident claiming that COLS (cyclic OLS) performs the best of those algorithms tested because once we no longer have perfect recovery, "best" becomes "least worst". Still, when I look at the mean $$\ell_2$$ and $$\ell_\infty$$ norms of the latter simulations, COLS has the smallest values of all.

I was hoping to write up some of these results to submit to EUSIPCO 2011, but before I do I want to at least do a proper analysis of these cyclic algorithms, and involve some theoretical work in successive interference cancellation. Perhaps SPARS 2011...

## Symbolic Logic by Lewis Carroll

I have just finished reading Lewis Carroll's "Symbolic Logic" on my new iPhone during the dark morning commutes to university, and just love one of his final example problems:

What is the inescapable logical complete conclusion given the following premises?
1. All the policemen on this beat eat dinner with our cook;
2. No man with long hair can fail to be a poet;
3. Amos Judd has never been in prison;
4. Our cook's 'cousins' all love cold mutton;
5. None but policemen on this beat are poets;
6. None but her 'cousins' ever eat dinner with our cook;
7. Men with short hair have all been in prison.

## First day of courses!

23rd grade. Dozens of dollars. Grants on the ground. All so true!

Happy first day of the new semester!

Bob L. Sturm, Associate Professor
Audio Analysis Lab
Aalborg University Copenhagen
A.C. Meyers Vænge 15
DK-2450 Copenahgen SV, Denmark
Email: bst_at_create.aau.dk