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Index: Introduction to Digital Filters with Audio Applications

Introduction to Digital Filters with Audio Applications

Partial Fraction Expansion: residued.m

Parallel SOS to Transfer Function: psos2tf

Click for https://ccrma.stanford.edu/~jos/filters/Partial_Fraction_Expansion.html

In digital signal processing, FIR is an acronym for Finite Impulse Response — Click for https://ccrma.stanford.edu/~jos/filters/FIR_Digital_Filters.html

The impulse signal is the shortest pulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). The impulse is typically denoted by the Greek delta symbol δ and is often called the 'Dirac delta function', after Paul Dirac who pioneered its use (in addition to being a lead contributor in the development of Quantum Mechanics). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

The impulse response of a system is its output signal in response to the impulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

A resonator is a recursive filter that boosts signal amplitude at a particular frequency. The simplest resonator is made using a two-pole filter. The impulse response of the two-pole resonator is an exponentially decaying sinusoidal oscillation, where the zero-crossing rate is (twice) the resonance frequency. — Click for https://ccrma.stanford.edu/~jos/filters/Two_Pole.html

The Finite Impulse Response (FIR) part of a digital filter is the feedforward part, corresponding to the numerator polynomial of its transfer function. — Click for https://ccrma.stanford.edu/~jos/filters/FIR_Digital_Filters.html

Search JOS Website

JOS Home Page

JOS Online Publications

Index of terms in JOS Website

Index: Introduction to Digital Filters with Audio Applications

Introduction to Digital Filters with Audio Applications

Partial Fraction Expansion: residued.m

Parallel SOS to Transfer Function: psos2tf

Method

The FIR part is first extracted, and the (strictly proper) remainder is passed to residuez for expansion of the IIR part (into a sum of complex resonators). One must remember that, in this case, the impulse-response of the IIR part begins after the impulse-response of the FIR part has finished, i.e.,

$\displaystyle H(z) = F(z) + z^{-{N_f}}R(z)$

where

is the length of the FIR part (order of

plus 1).

See §6.8.8 for an example usage of residued (with a comparison to residuez).

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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2024-09-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Method

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition) Copyright © 2024-09-03 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2024-09-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University