Some broad topics of interest:
Some earlier topics (still of some interest)
Sampling Rate Conversion: (Interpolation/Decimation, Fractional Delay)
In general, communication systems operate at different bit-rates. The sampled input signal has to be converted from one rate to another one, if the initial sampling rate does not match the expected data rate of the communication system.
The task is: Changing the sampling rate by fractional rates, the classical interpolation/decimation problem but with non-integer rates.
The conversion can be achieved with exact accuracy theoreticaly. The problem is finding efficient techniques approximating the exact solution.
Efficient Structures for Resolution Increase in Fourier Domain:
DTFT takes discrete samples and produces a continuous spectrum representing the response of the system (whose impulse response is given sequence of samples) to a complex exponential. In DTFT the frequency of the complex exponential is a continuous variable in [0,2pi). DFT is the sampled version of the DTFT. That is, DFT output is simply the samples of the DTFT taken uniformly with the spacing 2pi/N in [0,2pi). At some applications, we may want to examine the spectrum in more detail. To do that, theclassical technique is taking more point DFTs, that is instead of N point DFT; we may take 10N point DFT and this results in a DFT output with 2pi/(10N) spacing, resulting in 10 fold increase in resolution. In some applications, we are only interested in a segment of spectrum say segment of interest is [pi/3, pi/2]. Application of 10N point DFT increases resolution in the whole range of [0,2pi). In this project, we want to study efficient methods resolution increase in a segment.
Keywords to search : Chirp Z-Transform, Zoom FFT, Non-Uniformly sampled DFT,
Fractional Fourier Transforms:
Fractional Fourier transform can be used as a tool for chirp tracking. Chirp tracking is known to be a difficult task due to its non-stationary nature. Fractional Fourier filterbanks can be used to follow time varying chirp signals.
Perspective mapping induce a chirp like on periodic signals. Estimation of perspective model.
Sampling theorems for fractional fourier transform. The analogs of Papoulis' Theorems.
Image Processing: (not of high interest any more)
Multiple Description Coding
Distributed Computing: (I keep my interest and enthusiasm but could not find any opportunity to develop a better understanding in these deeply rotted topics.)
Distributed Source Coding
Finite Difference Methods for Signal Processing Applications or vice versa (of some interest)