Impulse response in the context of "Linear filter"

In speech science and phonetics, a formant is the broad spectral maximum that results from an acoustic resonance of the human vocal tract. In acoustics, a formant is usually defined as a broad peak, or local maximum, in the spectrum. For harmonic sounds, with this definition, the formant frequency is sometimes taken as that of the harmonic that is most augmented by a resonance. The difference between these two definitions resides in whether "formants" characterise the production mechanisms of a sound or the produced sound itself. In practice, the frequency of a spectral peak differs slightly from the associated resonance frequency, except when, by luck, harmonics are aligned with the resonance frequency, or when the sound source is mostly non-harmonic, as in whispering and vocal fry.

A room can be said to have formants characteristic of that particular room, due to its resonances, i.e., to the way sound reflects from its walls and objects. Room formants of this nature reinforce themselves by emphasizing specific frequencies and absorbing others, as exploited, for example, by Alvin Lucier in his piece I Am Sitting in a Room. In acoustic digital signal processing, the way a collection of formants (such as a room) affects a signal can be represented by an impulse response.

Studio monitors are loudspeakers in speaker enclosures specifically designed for professional audio production applications, such as recording studios, filmmaking, television studios, radio studios and project or home studios, where accurate audio reproduction is crucial. Among audio engineers, the term monitor implies that the speaker is designed to produce relatively flat (linear) phase and frequency responses. In other words, it exhibits minimal emphasis or de-emphasis of particular frequencies, the loudspeaker gives an accurate reproduction of the tonal qualities of the source audio ("uncolored" and "transparent" are synonyms), and there will be no relative phase shift of particular frequencies—meaning no distortion in sound-stage perspective for stereo recordings. Beyond stereo sound-stage requirements, a linear phase response helps impulse response remain true to source without encountering "smearing". An unqualified reference to a monitor often refers to a near-field (compact or close-field) design. This is a speaker small enough to sit on a stand or desk in proximity to the listener, so that most of the sound that the listener hears is coming directly from the speaker, rather than reflecting off walls and ceilings (and thus picking up coloration and reverberation from the room). Monitor speakers may include more than one type of driver (e.g., a tweeter and a woofer) or, for monitoring low-frequency sounds, such as bass drum, additional subwoofer cabinets may be used.

There are studio monitors designed for mid-field or far-field use as well. These are larger monitors with approximately 12 inch or larger woofers, suited to the bigger studio environment. They extend the width of the sweet spot, allowing "accurate stereo imaging for multiple persons". They tend to be used in film scoring environments, where simulation of larger sized areas like theaters is important.

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio equipment and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations. In an audio system, it may be used to minimize audible distortion by designing components (such as microphones, amplifiers and loudspeakers) so that the overall response is as flat (uniform) as possible across the system's bandwidth. In control systems, such as a vehicle's cruise control, it may be used to assess system stability, often through the use of Bode plots. Systems with a specific frequency response can be designed using analog and digital filters.

The frequency response characterizes systems in the frequency domain, just as the impulse response characterizes systems in the time domain. In linear systems (or as an approximation to a real system neglecting second order non-linear properties), either response completely describes the system and thus there is a one-to-one correspondence: the frequency response is the Fourier transform of the impulse response. The frequency response allows simpler analysis of cascaded systems such as multistage amplifiers, as the response of the overall system can be found through multiplication of the individual stages' frequency responses (as opposed to convolution of the impulse response in the time domain). The frequency response is closely related to the transfer function in linear systems, which is the Laplace transform of the impulse response. They are equivalent when the real part ${\displaystyle \sigma }$ of the transfer function's complex variable ${\displaystyle s=\sigma +j\omega }$ is zero.

A reverb effect, or reverb, is an audio effect applied to simulate reverberation. It may be created through physical means, such as echo chambers, or electronically through audio signal processing. The American producer Bill Putnam is credited for the first artistic use of artificial reverb in music, on the 1947 song "Peg o' My Heart" by the Harmonicats.

Spring reverb, created with a series of mounted springs, is popular in surf music and dub reggae. Plate reverb uses electromechanical transducers to create vibrations in large plates of sheet metal. Convolution reverb uses impulse responses to record the reverberation of physical spaces and recreate them digitally. Gated reverb became a staple of 1980s pop music, used by drummers including Phil Collins. Shimmer reverb, which alters the pitch of the reverberated sound, is often used in ambient music.

The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector is a scale-dependent description of their imaging contrast. Its magnitude is the image contrast of the harmonic intensity pattern, ${\displaystyle 1+\cos(2\pi \nu \cdot x)}$, as a function of the spatial frequency, ${\displaystyle \nu }$, while its complex argument indicates a phase shift in the periodic pattern. The optical transfer function is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain.

Formally, the optical transfer function is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is generally complex-valued; however, it is real-valued in the common case of a PSF that is symmetric about its center. In practice, the imaging contrast, as given by the magnitude or modulus of the optical-transfer function, is of primary importance. This derived function is commonly referred to as the modulation transfer function (MTF).

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).

The impulse response (that is, the output in response to a Kronecker delta input) of an N-order discrete-time FIR filter lasts exactly ${\displaystyle N+1}$ samples (from first nonzero element through last nonzero element) before it then settles to zero.

In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant, A. The function is named after its graph's resemblance to a boxcar, a type of railroad car. The boxcar function can be expressed in terms of the uniform distribution as$${\displaystyle \operatorname {boxcar} (x)=(b-a)A\,f(a,b;x)=A(H(x-a)-H(x-b)),}$$where f(a,b;x) is the uniform distribution of x for the interval [a, b] and ${\displaystyle H(x)}$ is the Heaviside step function. As with most such discontinuous functions, there is a question of the value at the transition points, which are usually best chosen depending on the individual application.

When a boxcar function is selected as the impulse response of a filter, the result is a simple moving average filter, whose frequency response is a sinc-in-frequency, a type of low-pass filter.

In 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 in the overview 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). What's more, there are systematic methods for solving any such system (determining h(t)), whereas systems not meeting both properties are generally more difficult (or impossible) to solve analytically. A good example of an LTI system is any electrical circuit consisting of resistors, capacitors, inductors and linear amplifiers.

Linear time-invariant system theory is also used in image processing, where the systems have spatial dimensions instead of, or in addition to, a temporal dimension. These systems may be referred to as linear translation-invariant to give the terminology the most general reach. In the case of generic discrete-time (i.e., sampled) systems, linear shift-invariant is the corresponding term. LTI system theory is an area of applied mathematics which has direct applications in electrical circuit analysis and design, signal processing and filter design, control theory, mechanical engineering, image processing, the design of measuring instruments of many sorts, NMR spectroscopy, and many other technical areas where systems of ordinary differential equations present themselves.