Concurrent Interests

My work involves the following. The details below give resources for each I have found useful.

Fourier Analysis

Why sinusoids for signal approximation when we come to signal processing? This question has trigerred me to know more on why? why? and why? of it. The answer is mathematical simplicity in modelling linear systems but this was not the motivation for J. Fourier. For him it turned out to be the solution to the heat transfer problem. Do mail if you have doubts or to share the insights.
  • Fourier Series, by Georgi P. Tolstov.
    A very insightful book written with elegant simplicity. Gives a thorough understanding of Fourier series.
  • Fourier Analysis, by T.W. Korner.
    Good for knowing some interesting physical and broad applications of Fourier analysis. Not for engineers.
  • Lecture Notes: Fourier Transform and Applications, EE 261 Stanford University, by Brad Osgood.
    One of the most informal academis book I have read. Along with being informal the concepts are present in a very intuitive (and also technical) way. I love to get hooked to it. Brad Osgood also has a video lecture series on the very same subject.
  • The Fourier Transform and Its Applications, by Ron Bracewell.
    Excellent treatment of the title of the book. A one and only one of its type for engineers.
  • The Fast Fourier Transform and Applications, by E.O. Brigham.
    To know what, why, how of DFT to FFT get hold of it. It tells all about DFT just in figures.
  • Who is Fourier? A Mathematical Adventure, by Translational College of LEX.
    A comic book to know Fourier analysis. Even a kid can understand from this. Great work by students.
I love to document the interesting concepts which confused me a lot. By writting them as I understand help me clarify my understanding and I know more of it. The following are some of the articles I have written by getting on the shoulders of great authors.

Time-Frequency Analysis

Change is an attribute which is associated with everything found in nature. All things change. Some change fast, some slow. Interestingly, many show a pattern in undergoing change. Everything is random till the hidden pattern is discovered. Earth moves around sun. Water cycles in between earth and its atmospheres. Ice age come and go. Heart beats periodically. Periodically. And what if the period keeps changing over time. Thus... we land in time-frequency analysis. Example when we sing the frequency keeps changing over time.
  • A Wavelet Tour of Signal Processing: The Sparse Way, by Stephane Mallat.
    A very smart book in terms of the way the author has written it and illustrates each therem and content.
  • Time Series Analysis, by Leon Cohen.
    I liked it for one read only.
  • Time Frequency Signal Analysis and Processing, by Boualem Boashash.
    Enlightening and easy in quick reading and getting an intuitive understanding.
An article by me:

Sampling

We are just an advanced breed of monkeys on a minor planet of a very average star. But we can understand the Universe. That makes us something very special. -Stephen Hawking. The nature floods us with data when we begin to study it. The data is continuous until we have not captured it. We have beautiful mathematical theories based on considering the data as continuous functions. Any processing we do has to be done in discrete form, we can only capture the data at discrete time instants, and with finite amplitude resolution or digitization. The reason for the former being the limitation in electronic devices and excess power limitation and the reason for the later being we have finite word length in our DSP devices and also associated with the redundancy of the signal being captured, if the signal has redundancy we need not have to store all of the values the signal takes. The former is carried out using sampling and the later using quantization. Both the operations are done in sequence by ADCs. To reduce the error because of capturing the data only at discrete instants (or sampling) it was thought that we should sample as closely as possible. It was Shannon-Whittaker theorem, in 1950s, which gave a breakthrough to sampling theory for discrete analysis of continuous functions. The theorem stated- any function from the vector space of band-limited functions needs to be sampled only at least at twice the maximum frequency content for perfect reconstruction of the original signal from these samples. The operation in a DSP chip to interface us with the real world data, at a very light level, can be described as: Low pass filtering the analog signal, sampling the signal based on Shannon-Whittaker theorem, quantization (a nonlinear function mapping), feed this to the DSP analysis and the analyzed output if to be sent back to the analog world (as in the case of music player) then reconstruct the signal using interpolation through a DAC.
  • Splines: A Perfect Fit for Signal and Image Processing by M. Unser
    (IEEE Signal Processing Magazine, vol. 16, no. 6, pp. 22-38, November 1999).
    A very smart book in terms of the way the author has written it and illustrates each therem and content.
  • Sampling, Wavelets, and , Tomography by Eds. J. Benedetto and A. I. Ahmed.
    Good.
  • Precise Undersampling Theorems by Donoho et. al
    (Proceedings IEEE, 2010)
    Enlightening and easy in quick reading and getting an intuitive understanding.
An article by me:

Sparse Reconstruction

Life only on earth is one instance of sparsity in solutions of the laws of universe.
While universe was being created. A complex system of equations had to be solved. The solution vector was to denote the number of heavenly bodies in which life will exist, subject to the constraints of the all the forces present in the universe. Interesting thing being that the solution vector turned out to be sparse, with only may be (few) bodies possible for supportng life forms, and one amongst it we call our Earth.
  • L1-L2 OPtimization in Signal and Image Processing by M. Zibulevsky /& M. Elad
    (IEEE Signal Processing Magazine, 2010).
    Enlightened.
  • Sparse and Redundant Representations by M. ELad
    Good.

Noise aid and Stochastic Resonance

Noise is abundant in processing we do. And we always filter it out. Can we deal it by using it to aid the signal of interest?
  • Stochastic resonance, by L. Gammaitoni, P. Hanggi, Peter Jung, and Fabio Marchesoni
    (Rev. Mod. Phys., vol. 70, pp. 223–287 Jan 1998).
    Thorough introduction from physics point of view.

Noise Aided Processing

  • Some ahaa! quotes I came across,
    • Math isn’t the hard part of math, motivation is.
    • A recurring theme in calculus: Big things are made from little things. And sometimes the little things are easier to work with.
    • sine is for a circle what line is for a rectangle.
  • 23/10/11: I set this webpage after some decoding of coding in html and css.

On Ear: An Engineer's Bibliography

  • [09/06/2012] An interesting video on insight on the ear: http://www.youtube.com/watch?v=lD1A3iEmZqA

Auditory Signal Processing

  • Some ahaa! quotes I came across,
    • Math isn’t the hard part of math, motivation is.
    • A recurring theme in calculus: Big things are made from little things. And sometimes the little things are easier to work with.
    • sine is for a circle what line is for a rectangle.
  • 23/10/11: I set this webpage after some decoding of coding in html and css.

Internship links

Below are some links I think may be of use to undergrad and grad studenst in assimilating some information on internships in India. The links may go old. So you may need to refresh the links by googling similar titles.

  • http://mhrd.gov.in/National_Scholarships
  • http://www.serc.iisc.ernet.in/sip/
  • http://www.ias.ac.in/index.html
  • http://www.jncasr.ac.in/main_page.php/Undergraduate-Prefinal/61/1/33/
  • http://iisc.wordpress.com/tag/iisc-internship/
  • http://students.iitm.ac.in/thefifthestate/2011/07/internship-stories-midhun-iisc/
  • http://letmeknow.in/
  • http://iisc.ernet.in/