Digital signal processing (06POESIN)

• Coefficient : 2
• Hourly Volume: 60h (including 24h supervised)
  CTD : 16.5h supervised
  Labo : 7.5h supervised (and 3h unsupervised)
  Out-of-schedule personal work : 33h

AATs Lists

Description

1. Digital signals
2. Discrete Fourier Transform
3. z-transform
4. Numerical Convolution
5. Numerical filtering

Learning Outcomes AAv (AAv)

• AAv1 [heures: 3, B2, B3, B4] : At the end of the semester, the student should be able to establish the analytical expression of discrete-time signals and systems (this course is limited to the case of regular sampling).

• AAv2 [heures: 9, B2, B3, B4] : At the end of the semester, the student should be able to perform the spectral analysis of sampled signals and systems (discrete-time and continuous-frequency analysis) based on the concept of the Fourier transform in the sense of distributions.

• AAv3 [heures: 9, B2, B3, B4, C1, C2, C4] : At the end of the semester, students should be able to analyse and design a digitisation-reconstruction chain for continuous analogue signals. The digital signal processing concepts to be put into practice are in particular: (1) Shannon's theorem on the choice of sampling frequency (oversampling and undersampling) and the spectral properties derived from it; (2) The issues involved in choosing the parameters of the anti-aliasing filter to be able to minimise the overlapping noise; (3) The issues involved in choosing the parameters of the low-pass reconstruction filter (interpolator filter) to correctly reconstruct the analogue DC signal.

• AAv4 [heures: 10, C1, C2, C4] : At the end of the semester, the student must be able to know and master the determining factors (maximum frequency, frequency resolution and separation dynamics) in a digital spectral analysis (FFT digital tool: discrete-time and discrete-frequency spectral calculation). The use of digital spectral analysis requires appropriate choices to be made regarding sampling frequency, signal observation time and the addition of zeros to the signal (zero-padding technique).

• AAv5 [heures: 12, B2, B3, B4, C1, C2, C4] : At the end of the semester, the student must be able to carry out a complete analysis (time response, frequency response, stability study, number of coefficients in the recurrence equation, number of delay elements, fluence graph, digital sensitivity and calculation noise) of a digital filter of the RIF or RII type using discrete convolution and the Z transfer function. This analysis should lead to an appropriate and argued choice with regard to the signal to be filtered.

• AAv6 [heures: 17, D1, D2, D3, D4] : At the end of the semester, the student must be able to implement these basic digital signal processing techniques in an interpreted language such as python, matlab or octave, and implement them on a hardware target (digital processing unit). The student will have consulted and assimilated the scientific resources required for the work to be carried out.

Assessment methods

One long continuous assessment (coefficient 1) and the average of several short continuous assessments in CTD (coefficient 1) and Lab (coefficient 1).

Key Words

Digital signals, discrete values of time and frequency, discrete Fourier transform Fourier transform, z-transform, convolution filtering, digital systems.

Prerequisites

S5O semester signal programme.

Resources

Course handouts, tutorials and lab texts