Signal Sampling: General Theorem

This lecture covers the general theorem of signal sampling, emphasizing the concept that any signal can be represented as a sum of sinusoids. It delves into topics such as bandwidth, spectrum, ideal filters, and interpolation techniques. The instructor explains the complexities of reconstructing a signal from its sampled version, highlighting the challenges and limitations of interpolation formulas. The lecture also explores the role of sinc functions, aliasing effects, and the importance of sampling frequency in signal reconstruction. Through practical examples and illustrations, students gain insights into the sampling theorem and the critical relationship between sampling frequency and signal bandwidth.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (45)

Related concepts (42)

CS-119(c): Information, Computation, Communication

L'objectif de ce cours est d'introduire les étudiants à la pensée algorithmique, de les familiariser avec les fondamentaux de l'Informatique et de développer une première compétence en programmation (

Nyquist–Shannon sampling theorem

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing distortion. In practice, it is used to select band-limiting filters to keep aliasing distortion below an acceptable amount when an analog signal is sampled or when sample rates are changed within a digital signal processing function.

Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Digital signal

A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values. Simple digital signals represent information in discrete bands of analog levels. All levels within a band of values represent the same information state.

Trigonometric interpolation

In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods. This form is especially suited for interpolation of periodic functions. An important special case is when the given data points are equally spaced, in which case the solution is given by the discrete Fourier transform.

Signals, Instruments, and Systems ENG-366: Signals, instruments and systems

Explores signals, instruments, and systems, covering ADC, Fourier Transform, sampling, signal reconstruction, aliasing, and anti-alias filters.

Sampling Theorem: Illustration CS-119(c): Information, Computation, Communication

Explores the sampling theorem through sinusoid reconstruction, under-sampling effects, and signal filtering importance.

LTI Systems: Analysis and Properties COM-202: Signal processing

Covers the analysis and properties of Linear Time-Invariant (LTI) systems.

Sampling Theorem and Control Systems ME-326: Control systems and discrete-time control

Explores the Sampling Theorem, digital control, signal reconstruction, and anti-aliasing filters.

Sampling Theorem: Illustration CS-119(c): Information, Computation, Communication

Explores the sampling theorem, illustrating the importance of sampling frequency for accurate signal reconstruction and addressing under-sampling effects.