# Signal processing (05_XDSIG)

**Coefficient :**3**Hourly Volume:**90h (including 36h supervised)- CTD : 27h supervised (and 4.5h unsupervised)
- Labo : 9h supervised (and 1.5h unsupervised)
- Out-of-schedule personal work : 48h

### AATs Lists

## Description

- General information on signals and systems - Signals and systems - Classification, Energy, Power - Common models
- Harmonic analysis of periodic signals - Principle of decomposition - Calculation of Fourier coefficients - Amplitude and phase spectra - Harmonic synthesis - Parseval identity
- Spectral analysis of non-periodic signals - Principle of decomposition - Properties of the TF - Amplitude and phase spectra - TF of some usual signals - Parseval identity
- Convolution - Definition - Physical interpretation - Convolution/filtering relationship - Properties of convolution - Generalization of TF to periodic signals
- Linear filtering of analog signals - System, continuous, linear and stationary - Concept of frequency filtering - Amplitude response and phase response - Physically realizable linear filters - Analysis of elementary transfer functions - Filter properties, notions of phase delay and group delay

## Learning Outcomes AAv (AAv)

AAv1 [heures: 4, B2, B3, B4] : At the end of the semester, the student must be able to recognize usual continuous signals (gate, triangle, step, ramp, harmonic, exponential, impulse) and model them using an analytical expression.

AAv2 [heures: 4, B2, B3, B4] : At the end of the semester, the student must be able to apply and identify transformations on the temporal representation of analog continuous signals (superposition, shift, scale transformation and amplitude).

AAv3 [heures: 50, B2, B3, B4, E1] : At the end of the semester, the student must be able to analyze the frequency content of continuous signals, composed of usual signals, using the Fourier transformation. This spectral analysis consists in particular of: (1) Manipulating the complex formalism of the Fourier transformation (positive and negative frequencies) and finding the real, physically interpretable form of the decomposition (amplitude, phase, energy spectra and power); (2) Identify whether the signal is more or less rich in low and high frequencies and make the connection with its temporal form; (3) Determine the decay rate of the spectrum; (4) Identify particular frequencies according to the nature of the spectrum (discrete/continuous); (5) Determine spectrally (and temporally) the mean value, rms value, energy and power of the signal; (6) Determine the percentage of signal energy or power located in a given frequency band; (7) Synthesize a real signal by imposing a percentage of its total average power. The student will have consulted and assimilated the scientific resources necessary to complete the work to be carried out.

AAv4 [heures: 8, B2, B3, B4, E1] : At the end of the semester, the student must be able to analyze using a spectrum analyzer the frequency content of usual signals and real signals in sensor output. The student will have consulted and assimilated the scientific resources necessary to complete the work to be carried out.

AAv5 [heures: 12, B2, B3, B4] : At the end of the semester, the student must be able to predict the response of a SLIT system (continuous, linear and time invariant system) to a model input ( combination of usual signals) using temporal convolution, or frequency filtering.

AAv6 [heures: 12, B2, B3, B4] : At the end of the semester, the student must be able to carry out the temporal and frequency analysis of signals at the input and output of a continuous system of convolution-filtering (SLIT) and make the link with the frequency response and the amplitude and phase distortions of such a system. Analyzing here means in particular: (1) Making the link between the impulse response of a SLIT and its bandwidth; (2) Determine the amplitude and phase distortion, phase delay and group delay of classical transfer functions of order 1 and 2.

## Assessment methods

A long evaluation (coefficient 1) and the average of several short evaluations in CTD (coefficient 1) and in Lab (coefficient 1)

## Key Words

signals, time, frequency, energy, power, Fourier series, Fourier transform (TF), convolution, filtering

## Mots prérequis

signals, time, frequency, energy, power, Fourier series, Fourier transform (TF), convolution, filtering

## Resources

Course handouts, tutorial and LAB texts