Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Signal Sampling and Reconstruction: Fundamentals

In course

MICRO-310(a): Signals and systems I (for MT)

Présentation des concepts et des outils de base pour la caractérisation des signaux ainsi que pour l'analyse et la synthèse des systèmes linéaires (filtres ou canaux de transmission). Application de ces techniques au traitement du signal et aux télécommuni ...

Description

This lecture covers the fundamentals of signal sampling and reconstruction, including the reconstruction of an analog signal, the sampling theorem (Shannon), multiplication with a Dirac comb, ideal sampling, and the duality with Fourier series. It also discusses the characteristics of sampled analog signals, periodic functions, sub-sampling, the Fish formula, and practical reconstruction systems.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Michaël Unser

Official source

Related concepts (32)

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.

Analog signal

An analog signal is any continuous-time signal representing some other quantity, i.e., analogous to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies continuously with the pressure of the sound waves. In contrast, a digital signal represents the original time-varying quantity as a sampled sequence of quantized values. Digital sampling imposes some bandwidth and dynamic range constraints on the representation and adds quantization error.

Signal

In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.

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.

Dirac comb

In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula for some given period . Here t is a real variable and the sum extends over all integers k. The Dirac delta function and the Dirac comb are tempered distributions. The graph of the function resembles a comb (with the s as the comb's teeth), hence its name and the use of the comb-like Cyrillic letter sha (Ш) to denote the function. The symbol , where the period is omitted, represents a Dirac comb of unit period.

Related lectures (52)

Sampling and Reconstruction Theory

Covers the concepts of analog, discrete, and digital signals, sampling times, frequencies, and pulses.

Discrete Fourier Transform: Sampling and Interpretation

Explores discrete Fourier transform, signal reconstruction, sampling interpretation, and periodic signal repetition.

Discrete Fourier Transform: Frequency Periodicity and Reconstruction

Explores frequency periodicity in the discrete Fourier transform for signal reconstruction.

Signals & Systems I: Sampling and Reconstruction Log in to Mediaspace to watch this video

Explores ideal sampling, Fourier transformation, spectral repetition, and analog signal reconstruction.

Signals, Instruments, and Systems Log in to Mediaspace to watch this video