# Category: Signals and Systems

### Signals and Systems: Preface

Aim of the study element:

To provide an introduction for signals and system analysis. The module includes discrete-time and variable-time signals, Fourier and Z transformations, and analysis of complex time invariant systems.

Learning outcome

Having successfully completed this element you will be able to:

• Understand and apply fundamentals of signal and sysem analysis.
• Calculate and analyse discrete- and continuous-time signals.
• Characterise periodic signals, to use Fourie, Laplace and Z transformations.
• Conduct time and frequency characterisation of systems and signals.

Covered topics

• Signals and systems introduction.
• Frequency and time characterisation of systems and signals.
• Linear-time-relevant systems.
• Periodic signals, Fourier model.
• Continuous- and discrete-time Fourier model.
• The Laplace and Z-transformations.
• System feedback.

The complete content for this module will be posted here soon.

Signals and Systems

## Fourier transform for discrete-time periodic function

Here we consider Fourier transform for discrete-time periodic function. Let's consider the discrete-time Fourier-representation of a function fn=1N∑-∞∞anejn2πnK, where an=1N∑-∞∞F(jw)e-jn2πNk and F(jw)=∑xne-jn2πNk-∞∞. The pair of…