Finite impulse response

FIRFIR filterFinite Impulse Response (FIR)FIR filtersArbitrary Finite Impulse Response FilterFeed-forward filterfinite impulseFinite impulse response (FIR) filterfinite impulse response filter chipfinite-impulse response (FIR)
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.wikipedia
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Filter (signal processing)

filterfiltersfiltering
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.
The delayed outputs are recombined to produce a direct analog implementation of a finite impulse response filter.

Infinite impulse response

IIRIIR filterinfinite-impulse-response
This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
This is in contrast to a finite impulse response (FIR) in which the impulse response h(t) does become exactly zero at times t > T for some finite T, thus being of finite duration.

Signal processing

signal analysissignalsignal processor
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.
Examples of algorithms are the fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters.

Discrete-time Fourier transform

convolution theoremDFTDTFT § Properties
where operators \mathcal{F} and respectively denote the discrete-time Fourier transform (DTFT) and its inverse.
So multi-block windows are created using FIR filter design tools.

Parks–McClellan filter design algorithm

an influential paperMcClellan transformationParks-McClellan filter design algorithm
The Parks–McClellan algorithm, published by James McClellan and Thomas Parks in 1972, is an iterative algorithm for finding the optimal Chebyshev finite impulse response (FIR) filter.

Window function

Hamming windowwindow functionswindowing
In the window design method, one first designs an ideal IIR filter and then truncates the infinite impulse response by multiplying it with a finite length window function.
Window functions are used in spectral analysis/modification/resynthesis, the design of finite impulse response filters, as well as beamforming and antenna design.

Convolution

convolvedconvolvingconvolution kernel
This computation is also known as discrete convolution.
Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.

Moving average

exponential moving averagesimple moving averageWeighted moving average
A moving average filter is a very simple FIR filter.
It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter.

Audio crossover

crossoveractive crossovercrossover filter
They either use digital approximations to traditional analog circuits, known as IIR filters (Bessel, Butterworth, Linkwitz-Riley etc.), or they use Finite impulse response (FIR) filters.

Downsampling (signal processing)

downsamplingdecimationdownsampled
It is sometimes called a boxcar filter, especially when followed by decimation.
With FIR filtering, it is an easy matter to compute only every M th output.

Cascaded integrator–comb filter

CICCascaded integrator-combCascaded integrator-comb filter
In digital signal processing, a cascaded integrator–comb (CIC) is an optimized class of finite impulse response (FIR) filter combined with an interpolator or decimator.

Z-transform

Z transformZ domainz''-plane
In signal processing, this definition can be used to evaluate the Z-transform of the unit impulse response of a discrete-time causal system.

Low-pass filter

low-passlow pass filterlowpass filter
The magnitude plot indicates that the moving-average filter passes low frequencies with a gain near 1 and attenuates high frequencies, and is thus a crude low-pass filter.
Real filters for real-time applications approximate the ideal filter by truncating and windowing the infinite impulse response to make a finite impulse response; applying that filter requires delaying the signal for a moderate period of time, allowing the computation to "see" a little bit into the future.

FIR transfer function

In digital processing, an FIR filter is a time-continuous filter that is invariant with time.

Half-band filter

The window design method is also advantageous for creating efficient half-band filters, because the corresponding sinc function is zero at every other sample point (except the center one).
That makes it possible to design a FIR filter whose every other coefficient is zero, and whose non-zero coefficients are symmetrical about the center of the impulse response.

Impulse response

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

Kronecker delta

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

Discrete time and continuous time

discrete timediscrete-timecontinuous-time
FIR filters can be discrete-time or continuous-time, and digital or analog. For a causal discrete-time FIR filter of order N, each value of the output sequence is a weighted sum of the most recent input values:

Digital data

digitaldigital informationdigitally
FIR filters can be discrete-time or continuous-time, and digital or analog.

Analogue electronics

analoganalog circuitanalogue
FIR filters can be discrete-time or continuous-time, and digital or analog.

Causal filter

causalnon-causal filteranti-causal
For a causal discrete-time FIR filter of order N, each value of the output sequence is a weighted sum of the most recent input values: