Impulse responseIn signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (δ(t)). More generally, an impulse response is the reaction of any dynamic system in response to some external change.
Step responseThe step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter.
Dirac delta functionGeneralized function whose value is zero everywhere except at zero Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually meant to specify the value of any multiplicative constant, which will give the area under the function. The other convention is to write the area next to the arrowhead.
Heaviside step functionThe Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.
Fourier transformMathematical transform that expresses a function of time as a function of frequencyThe Fourier transform applied to the waveform of a C majorpianochord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G).
Time domainIn mathematics and signal processing, the time domain is a representation of how a signal, function, or data set varies with time. It is used for the analysis of mathematical functions, physical signals or time series of economic or environmental data. In the time domain, the independent variable is time, and the dependent variable is the value of the signal. This contrasts with the frequency domain, where the signal is represented by its constituent frequencies.
EngineeringEngineering is the practice of systematically applying natural science and mathematics to design and improve systems, devices, or processes that solve problems under constraints. It is typically motivated by satisfying human needs, resulting in creations such as bridges, engines, smartphones, pacemakers, the internet, spacecraft, and washing machines.
Linear time-invariant systemMathematical model which is both linear and time-invariantBlock diagram illustrating the superposition principle and time invariance for a deterministic continuous-time single-input single-output system. The system satisfies the superposition principle and is time-invariant if and only if y3(t) = a1y1(t – t0) + a2y2(t – t0) for all time t, for all real constants a1, a2, t0 and for all inputs x1(t), x2(t).
ParameterA parameter (from Ancient Greek (pará)'beside, subsidiary' and (métron)'measure'), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.).
Greek languageIndo-European languageGreek (Modern Greek: ελληνικά, romanized: elliniká; Ancient Greek: ἑλληνική, romanized: hellēnikḗ) is an Indo-European language, constituting an independent Hellenic branch within the Indo-European language family.PhysicsPhysics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. It is one of the most fundamental scientific disciplines. A scientist who specializes in the field of physics is called a physicist. Physics is one of the oldest academic disciplines.NondimensionalizationNondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis.*As an Amazon Associate I earn from qualifying purchases.