# The Signal processing Chair

Incumbent: Prof. Anthony Weiss

**Typical operations and applications**

Processing of signals includes the following operations and algorithms with application examples:

- Filtering(for example in tone controls andequalizers)
- Smoothing, deblurring (for example inimage enhancement)
- Adaptive filtering(for example forecho-cancellationin a conference telephone, ordenoisingfor aircraft identification by radar)
- Spectrum analysis(for example inmagnetic resonance imaging,tomographic reconstructionandOFDMmodulation)
- Digitization, reconstruction andcompression(for example,image compression, sound coding and othersource coding)
- Storage (indigital delay linesandreverb)
- Feature extraction(for examplespeech-to-textconversion)
- Modulation(inmodems)
- Prediction
- System identificationand classification
- A variety of other operations

In communication systems, signal processing may occur at OSI layer 1, the Physical Layer (modulation, equalization, multiplexing, etc) in the seven layer OSI model, as well as at OSI layer 6, the Presentation Layer (source coding, including analog-to-digital conversion and data compression).

**Mathematical topics embraced by signal processing**

- Linear signals and systems, andtransform theory
- Calculus
- Vector spacesandLinear algebra
- Functional analysis
- Probabilityandstochastic processes
- Detection theory
- Estimation theory
- Optimization
- Programming
- Numerical methods
- Iterative methods

**Categories of signal processing**

*Analog signal processing*

Analog signal processing is for signals that have not been digitized, as in classical radio, telephone, radar, and television systems. This involves linear electronic circuits such as passive filters, active filters, additive mixers, integrators and delay lines. It also involves non-linear circuits such as compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.

*Discrete time signal processing*

Discrete time signal processing is for sampled signals that are considered as defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.

The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.

*Digital signal processing*

Digital signal processing is for signals that have been digitized. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and look-up tables. Examples of algorithms are the Fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, Wiener filter, Adaptive filter and Kalman filter.

**Fields of signal processing**

*Statistical signal processing* - analyzing and extracting information from signals and noise based on their stochastic properties

*Audio signal processing* - for electrical signals representing sound, such as speech or music

*Speech signal processing* - for processing and interpreting spoken words

*Image processing* - in digital cameras, computers, and various imaging systems

*Video processing* - for interpreting moving pictures

*Array processing* - for processing signals from arrays of sensors

*Time-frequency signal processing* - for processing non-stationary signals[3].

*Filtering* - used in many fields to process signals

*Seismic signal processing*

*Data mining*