The course focuses on statistical digital signal processing that makes an engineering usage of the estimation theory (=use of the statistics for solving engineering problems)
Statistical signal processing is the core of many electronic signal processing systems that are designed to extract some information from some observations or measurements or data.
In many situations these observations are multi-dimensional (e.g., images) and thus require 2D or multidimensional signal processing.
Examples from engineering systems:
- Location systems (radar, satellite GPS, sonar, video, audio): evaluation of the position of a target from observations collected by a set of sensors (radio transceivers, hydro-phones, cameras, micro-phones). Observations are typically measurements of distances (range) or angles (bearing) of the target location w.r.t. some reference points.
- Communication systems: evaluation of the transmitted information – usually bits – from the received signals; this requires at first the estimation of some parameters that characterize the radio signal, such as the channel impulse response, the carrier frequency/phase.
- Remote sensing: estimation of the the environment using the acoustic or electromagnetic waves such as in ultrasound (e.g., medical ultrasound), sonar (e.g., underwater and seafloor imaging) and (airborne or satellite) radar imaging.
- Seismic exploration: estimation of underground structure of the earth from data collected by sensors deployed over the surface (e.g., surface excitation emitting elastic waves and geophones measuring backscattered echos);
- Tomography: reconstruction of some physical properties (e.g., attenuation profile) inside an object from measurements gathered outside (e.g., computer assisted tomography or magnetic resonance).
- Speech recognition: recognition of a speech by a smart-phone (e.g., recognition of individual speech sounds – phonemes, vowels, consonants, etc. – by comparison to pre-registered speech sounds).
- Distributed system and social networks: consensus based on local observations, political parties, collective behaviors and synchronization (fireflies or flocks), marketing
In all these examples the problem to be solved is the estimation of a set of unknown parameters q (target location, transmitted data, channel response, carrier parameters, underground layered Earth structure, image of the object inside structure, phonemas, etc.) from a set of observations x (radio signals, elastic waves, audio/video signals, …).