| Topic
| keywords
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| Course Overview
| Things we will talk about
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| Signals and Systems
| Analog and numeric signals, Communications point of view, Signal properties, classes and operations: Frequently used signals, Complex numbers and exponential; Linear and time invariant system, non-linear systems
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| Fourier series and signals space
| phasors, Fourier series, Parseval’s theorem, exponentials orthogonality, signal spaces, basis of representation, inner product, Schwartz inequality
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| Fourier transform and convolution
| Cross energy, Parseval's theorem, Fourier transform and its properties, Dirac impulse, Impulse response, Convolution, Filtering, Windowing
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| Sampling and digital signal processing
| Sampling, pulse train, aliasing, oversampling, decimation, interpolation, sample and hold, A/D and D/A conversion, uniform quantization, Discrete time Fourier transform, DFT, zeta transform, discrete and circular convolution, convolution via DFT, overlap and add
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| Signal Processing in Bioinformatics
| Spectral analysis of the genome, Filtering of the genome, Other representation spaces, Numerical representation of codons, Long range DNA correlation, Fourier Transforms of Protein Sequences, Fourier transform infrared spectroscopy (FTIR)
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| Filters
| Analog filters, polinomials, filter classes and design template, digital filters, Finite impulse response or FIR, First order infinite impulse response (IIR) filter, FIR synthesis starting from the continuous time description, Zeta transform and filtering, Synthesis of an IIR filter starting from an analog filter
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| Random signals and Wiener's theorem
| Stationary and ergodic processes, Correlation and covariance for signals, autocorrelation and intercorrelation, geometry and adaptation, power density spectrum, Wiener’s theorem, multidimensional Gaussian and process, Spectral estimation, spectral density at the output of a filter, statistical characteristics at the output of a filter, sum and product of random and deterministic signals
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| Information Theory and biochemical applicartions
| Information content of a discrete memoryless source, entropy, continuous sources, joint and conditional entropy, average mutual information, Discrete channel capacity, Distinguishing the type of biological signal, capacity, bottlenecks, measurements, bias, and allowable distortion
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| Intermediate tests
| 2022: 1st, 2nd, 3rd; 2023: 1st, 2nd
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