Sumários SIGARRA

Foi feita a comunicação de que o início efetivo de aulas seria na semana seguinte por causa de se assegurar funcionamento simultâneo com a UC homóloga do MAP-tele: ATSP.

A review of the Z-Transform, the Discrete Fourier Transform (DFT), and the Fast Fourier Transform (FFT). The use of the DFT/FFT in fast linear convolution and correlation studies in the frequency domain. Interpretation of the DFT as a filter bank: general formulation and analytical characterization of the impulse response of the different filters.

Interpretation of the DFT as a bank of parallel filters whose frequency responses are frequency-shifted versions of the frequency response of the analysis window. Illustrative examples using different windows.
Review of random signals and processes: basic concepts (ensemble averages, jointly distributed random variables, moments and joint moments, independent, uncorrelated and orthogonal random variables, Gaussian random variables). Stationary processes: strict sense and wide sense stationarity.

Autocorrelation and autocovariance matrices and their properties. Eigenvalues and eigenvectors. Linear transformation of random vectors.
Innovations representations of random vectors (eigenanalysis and the Karhunen-Loève transform). Ergodicity, white noise, and the power spectrum.
The PDF of the sum of independent random vectors. Illustrative examples.

Ten-minutes quiz on random processes.
Spectrum estimation using periodogram-based methods and their variations. Importance of the analysis window regarding spectral resolution and leakage. Periodogram-based accurate frequency estimation of sinusoidal components.

Frequency estimation using eigendecomposition of the autocorrelation matrix, the orthogonality between noise subspace and signal subspace, and the pseudo-spectrum. Classic particular cases: the Pisarenko Harmonic Decomposition and the MUSIC algorithm. Principal components spectrum estimation.
Presentation of the home assignment.

Adaptive filtering from a practical perspective: concept and examples. Wiener's optimal filtering. Gradient-based algorithms in adaptive filtering: the gradient descent method, the LMS and NLMS algorithms. Connection with the area of Machine Learning.

The matched filter: theory and applications. Application to the estimation of the impulse response of LTI systems. Orthogonality of multiple signals for efficient separation. The Fourier series as a special case of orthogonal signals. Introduction to OFDM modulation. Description of the assignment concerning OFDM signal decoding.

Ranging from wave propagation and scattering. Usage of complex signals and matched filter. Relationship between resolution and bandwidth. Derivation and properties of the LFM (chirp) signal. Autocorrelation properties and windowing. Design of a Sonar experiment using audio waves.

Combination of multiple echoes to implement a synthetic aperture. Azimuth compression equations. Two of the algorithms to implement azimuth compression: back projection and range-doppler. Relationship between range, aperture length and resolution. Testing using a synthetic aperture sonar signal.

Sampling requirements in synthetic aperture systems to avoid aliasing in the azimuth direction. The range-doppler algorithm and the range migration correction. The wavenumber algorithm (omega-k) and the Stolt interpolation. Exemplification with real synthetic aperture sonar data.

Design and implementation of a synthetic aperture radar complete experiment: from signal definition to data capture. Full processing of the acquired data. Receiver-transmitter synchronisation, including frequency and phase correction. Range and azimuth compression in the scope of the range-doppler algorithm (including range migration) and comparison with omega-k algorithm. Analysis of motion error induced image defocusing.

Presentation by the students of OFDM, SONAR and SAS home assignments. Discussion of methods, implementation details and impact on results.