BandlimitingBandlimiting refers to a process which reduces the energy of a signal to an acceptably low level outside of a desired frequency range. Bandlimiting is an essential part of many applications in signal processing and communications. Examples include controlling interference between radio frequency communications signals, and managing aliasing distortion associated with sampling for digital signal processing. A bandlimited signal is, strictly speaking, a signal with zero energy outside of a defined frequency range.
Nonlinear filterIn signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage R(t) at any moment is the square of the input voltage r(t); or which is the input clipped to a fixed range [a,b], namely R(t) = max(a, min(b, r(t))).
Linear time-invariant systemIn system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).
Méthode de la transformée inverseLa méthode de la transformée inverse est une méthode permettant d'échantillonner une variable aléatoire X de loi donnée à partir de l'expression de sa fonction de répartition F et d'une variable uniforme sur . Cette méthode repose sur le principe suivant, parfois connu sous le nom de théorème de la réciproque : soient F une fonction de répartition, Q la fonction quantile associée, et U une variable uniforme sur . Alors, la variable aléatoire X = Q(U) a pour fonction de répartition F.
Échantillonnage (statistiques)thumb|Exemple d'échantillonnage aléatoire En statistique, l'échantillonnage désigne les méthodes de sélection d'un sous-ensemble d'individus (un échantillon) à l'intérieur d'une population pour estimer les caractéristiques de l'ensemble de la population. Cette méthode présente plusieurs avantages : une étude restreinte sur une partie de la population, un moindre coût, une collecte des données plus rapide que si l'étude avait été réalisé sur l'ensemble de la population, la réalisation de contrôles destructifs Les résultats obtenus constituent un échantillon.
Network synthesisNetwork synthesis is a design technique for linear electrical circuits. Synthesis starts from a prescribed impedance function of frequency or frequency response and then determines the possible networks that will produce the required response. The technique is to be compared to network analysis in which the response (or other behaviour) of a given circuit is calculated. Prior to network synthesis, only network analysis was available, but this requires that one already knows what form of circuit is to be analysed.
Retard de groupe et retard de phaseEn traitement du signal, le temps de propagation de groupe ou retard de groupe est le retard infligé par un filtre, en secondes, de l'enveloppe en amplitude pour un signal à bande étroite. Le retard de phase est le retard (en secondes) de chaque composante fréquentielle calculé à partir de la réponse en phase du filtre. Le temps de propagation de groupe et le retard de phase dépendent en général de la fréquence, à l'exception d'un filtre à phase linéaire dont le retard de groupe et de phase sont constants et sont tous deux égaux.
Overshoot (signal)In signal processing, control theory, electronics, and mathematics, overshoot is the occurrence of a signal or function exceeding its target. Undershoot is the same phenomenon in the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters. It is often followed by ringing, and at times conflated with the latter. Maximum overshoot is defined in Katsuhiko Ogata's Discrete-time control systems as "the maximum peak value of the response curve measured from the desired response of the system.
Convenience samplingConvenience sampling (also known as grab sampling, accidental sampling, or opportunity sampling) is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand. This type of sampling is most useful for pilot testing. Convenience sampling is not often recommended for research due to the possibility of sampling error and lack of representation of the population. But it can be handy depending on the situation. In some situations, convenience sampling is the only possible option.
Nyquist rateIn signal processing, the Nyquist rate, named after Harry Nyquist, is a value (in units of samples per second or hertz, Hz) equal to twice the highest frequency (bandwidth) of a given function or signal. When the function is digitized at a higher sample rate (see ), the resulting discrete-time sequence is said to be free of the distortion known as aliasing. Conversely, for a given sample-rate the corresponding Nyquist frequency in Hz is one-half the sample-rate.
