Signal Flow Graph

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Index: Introduction to Digital Filters with Audio Applications

Introduction to Digital Filters with Audio Applications

Analysis of a Digital Comb Filter

Difference Equation

Software Implementation in Matlab

The difference equation is a recipe for computing samples of the output signal of a digital filter based on samples of the input signal and the filter coefficients. In an Infinite-Impulse-Response (IIR) digital filter, there are typically both feedforward and feedback coefficients in the difference equation. — Click for https://ccrma.stanford.edu/~jos/filters/Difference_Equation_I.html

The transfer function is defined for LTI filters as the z transform of the filter output signal, divided by the z transform of the filter input signal — Click for https://ccrma.stanford.edu/~jos/filters/Transfer_Function_Analysis.html

A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html

A comb filter is made from a delay line using a linear combination of its input and output signals. — Click for https://ccrma.stanford.edu/~jos/pasp/Comb_Filters.html

A digital filter can be visualized as a 'black box' that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. — Click for https://ccrma.stanford.edu/~jos/filters/

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

Analysis of a Digital Comb Filter

Difference Equation

Software Implementation in Matlab

Signal Flow Graph

Figure 3.1 shows the signal flow graph (or system diagram) for the class of digital filters we are considering (digital comb filters). The symbol `` $z^{-M}$ '' means a delay of samples (always an integer here). This notation for a pure delay will make more sense after we derive the filter transfer function in §3.7.

**Figure 3.1:** signal flow graph for digital filters having difference equations of the form $y(n) = x(n) + g_1\, x(n-M_1) - g_2\, y(n-M_2)$ (digital comb filters).
$\includegraphics[width=\twidth]{eps/esd}$

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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

Signal Flow Graph

``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