 # Analysis II and signal theory

## Presentation

Program (detailed contents):

Analysis : functions of several real variables

• Differential calculus (differentiability, partial derivatives, local and global inversion theorems, implicit functions, extrema)
• Integral calculus (parameter, multiple)

Signal theory:

• Harmonic analysis (Fourier Transform)
• Invariant Linear Filters ; Sampling, Shannon theorem

Organisation:

Analysis lectures are required to begin harmonic analysis and therefore take place at the beginning of the semester. Lab work stands at the end of the course.

Main difficulties for students:

Students manipulate differential notion with difficulty and have problems with calculations (derivation and integration).

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

Analysis :

The fundamentals of differential calculus and the calculation of integrals with (multiple) parameters

Signal :

The main concepts, mathematical methods and tools used for signal processing

The student will be able to :

Analysis :

- define and calculate a differential

- define a condition of extremum

- calculate a change of variables (multiple)

- calculate an integral with parameters (multiple)

Signal :

- decompose periodic signals into Fourier series

- determine the spectrum of deterministic signals

- calculate the transfer function of a continuous, invariant linear filter and calculate the output signal of that filter for a given input

## Needed prerequisite

Lectures of mathematics of first year (I1ANIF11, I1ANMT11,  I1ANMT21).

Lectures of mathematics of first semester (I2MIMT11)

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...