SPFBU36

UE Signal and image analysis

Unité d'enseignement (UE) de 3 crédits

^En UE enseignée en Anglais

Contenu

Part A : Signals : Presents the essential tools commonly used to describe continuous-time (analog) and discrete-time signals, images and noise, mostly from a deterministic waveform point of view. Continuous-time waveforms are represented by direct mathematical expressions or by the use of orthogonal series representations such as the Fourier series. Properties of these waveforms, such as their DC value, root-mean-square (RMS) value, energy and power, magnitude and phase spectrum (through the Fourier transform), power spectral density, and bandwidth, are recalled or established. In the frequency-domain, analog and digital signals are represented by their Fourier transform. The Discrete Fourier Transform (DFT), when properly applied, allows the computation of spectra.

Part B : Systems : Used to manipulate analog or digital waveforms, exploiting various operations like scalar product, convolution and correlation. In addition, effects of linear filtering is introduced. Actual systems used in signal storage, transmission and modulation, multiplexing, video signal coding, lossy signal compression (principle of JPEG standard) will be explained.

Lab Sessions (practicals) :

Lab 1 : Signal representation using GNU-Octave: Introduction to Octave scripts and functions, application to the sinc signal.
Lab 2 : Representation of analog signals by discrete-time signals: Introduction to discrete sinusoids, discrete frequency and sampling, empirical discovery of the Shannon-Nyquist theorem.
Lab 3 : Signal Parameter Estimation – Part A: Estimation of the parameters of a sinusoidal signal (of known frequency f0) using the scalar product; dependence on S/N ratio and on the precise knowledge of f0.
Lab 4 : Signal Parameter Estimation – Part B: Estimation of the parameters of a sinusoidal signal (of unknown frequency), an empirical introduction to the Discrete Fourier Transform (DFT).
Lab 5 : Signal recognition through Correlation: Retrieve the occurrence of replicas of a reference signal hidden in a noisy signal using sliding scalar product and “running” (“real-time”) correlation; application to Radar/Sonar signals.
Lab 6 : FIR Filtering: From running correlation to convolution, to implement various digital filters, used e.g. to extract a sinusoid of known frequency in a composite signal.
Lab 7 : Discrete Fourier Transform: Empirical and extensive self-paced exploration of the DFT tool, supported by a complete and specifically-designed “active” reference (a Jupyter notebook).
Lab 8 : Image Processing and Filtering: Generalizes the convolution to 2D signals (images), digital filtering of images.

UE Signal and image analysis

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