Analog signals. Fourier series. Fourier transform. Linear systems. Random processes. Discrete-time signals. Sampling. Z transform. LTI systems. DFT and FFT. Signal transmission: analog and digital systems. Applications.
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Learning Objectives
Providing tools and methods for the representation of deterministic and random processes for both analog and discrete-time signals. Introducing sampling and digital signal processing. Introducing basic concepts for the transmission of signals and of modern telecommunications systems. Introducing principal applications of digital signal processing.
At the end of the course, the student should be able to analyze and characterize signal and systems both in the time and in the frequency domain, know principal effects of sampling, design simple discrete-time systems and understand basic principles of the applications in the telecommunications field.
Prerequisites
Limits, series, integrals. Complex analysis. Linear algebra. Trigonometry. Probability theory. Random variables.
Teaching Methods
Lectures
Type of Assessment
Written and oral exams. The written exam may be substituted by a computer project (maximum two students per project).
Course program
Introduction and classification of signals (analog and discrete-time, random and deterministic).
Linear spaces of functions. Hilbert spaces, distance, norm, inner product, orthonormal bases. Approximations in Hilbert spaces.
Fourier series. Definition and properties. Complex form of the Fourier series. Spectrum of signals.
Fourier transform and its properties. Convolution of signals. Dirac's function.
Linear systems. Impulse and frequency response.
Random processes and their characterization.
Sampling. Discrete-time Fourier transform and its properties. Quantization.
Z transform and its properties.
Linear time-invariant (LTI) systems. Impulse response, transfer function, frequency response. Linear finite difference equations.
Discrete Fourier Transform. Circular convolution. Fast Fourier Transform (FFT). Fast convolution.
Examples and applications of digital signal processing. Modulation and transmission of signals.