(cache)Flanging

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Time-Varying Delay Effects

Doubling and Slap-Back

Flanger Speed and Excursion

The spectrum of a signal gives the distribution of signal energy as a function of frequency. — Click for http://ccrma.stanford.edu/~jos/mdft/Example_Applications_DFT.html

The spectrum of a signal gives the distribution of signal energy as a function of frequency. — Click for http://ccrma.stanford.edu/~jos/mdft/Example_Applications_DFT.html

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The sampling rate of a discrete-time signal is defined as the number of samples per second. Its units are thus in Hertz (Hz). Shannon's Sampling Theorem states that the original continuous-time signal can be recovered exactly from the samples if and only if the sampling rate is higher than twice the highest frequency present in the original signal. Any higher frequencies will alias to frequencies below half the sampling rate. — Click for https://ccrma.stanford.edu/~jos/mdft/Sampling_Theory.html

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The amplitude response of an LTI filter is simply the magnitude of the (complex) frequency response — Click for https://ccrma.stanford.edu/~jos/filters/Amplitude_Response_I_I.html

A feedback comb filter is made from a delay line by scaling its output signal by some coefficient and summing that with the delay-line input signal. — Click for https://ccrma.stanford.edu/~jos/pasp/Feedback_Comb_Filters.html

Spectrum analysis of sound is analogous to decomposing white light into its component colors by means of a prism — Click for https://ccrma.stanford.edu/~jos/mdft/Example_Applications_DFT.html

The frequency response is defined for LTI filters as the Fourier transform of the filter output signal divided by the Fourier transform of the filter input signal — Click for https://ccrma.stanford.edu/~jos/filters/Frequency_Response_I.html

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When displaced from its equilibrium state, a harmonic oscillator experiences a restoring force according to Hooke's law. — Click for http://ccrma.stanford.edu/~jos/filters/Mass_Spring_Oscillator_Analysis.html

A sinusoid is any function of the form A sin(ω t+φ), where t is the independent variable, and A, ω, φ are fixed parameters of the sinusoid called the amplitude, (radian) frequency, and phase, respectively. Sinusoidal motion is produced by any 'pure' vibration, such as that of an ideal tuning fork or mass-spring system. — Click for https://ccrma.stanford.edu/~jos/mdft/Sinusoids.html

A delay line is used to delay a signal in time. Delay lines for digital signals are typically implemented in software using a circular buffer. — Click for https://ccrma.stanford.edu/~jos/pasp/Delay_Lines.html

The feedforward comb filter is made by forming a linear combination of the input and output of a delay line. — Click for https://ccrma.stanford.edu/~jos/pasp/Feedforward_Comb_Filters.html

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A signal is typically a real-valued function of time. A discrete-time signal is typically a real-valued function of discrete time, and is therefore a time-ordered sequence of real numbers. — Click for http://ccrma.stanford.edu/~jos/filters/Definition_Signal.html

Flutists produce a jet of air by forcing air out of the mouth through a small opening in the lips. — Click for http://www.phys.unsw.edu.au/jw/fluteacoustics.html#airjet

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A delay effect is an audio effect implemented using a delay line. Nowadays, digital delay lines are most often used. Examples of digital audio delay effects include flanging, the Leslie effect, and artificial reverberation. Often the delay line simulates time delay associated with physical sound propagation. — Click for https://ccrma.stanford.edu/~jos/pasp/Acoustic_Modeling_Delay.html

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JOS Home Page

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Index of terms in JOS Website

Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Time-Varying Delay Effects

Doubling and Slap-Back

Flanger Speed and Excursion

Flanging

Flanging is a delay effect that has been available in recording studios since at least the 1960s. Surprisingly little literature exists, although there is some [32,433,59,17,104,244].^6.1

The ``flanging'' effect can be understood by considering two tape machines set up to play the same tape in unison, with their outputs added together (mixed equally), as shown in Fig.5.2. To create the flanging effect, the flange of one of the supply reels can touched lightly to make it play a littler slower. This causes a delay to develop between the two tape machines. The flange is released, and the flange of the other supply reel is touched lightly to slow it down. This causes the delay to gradually disappear and then begin to grow again in the opposite direction. The delay is kept below the threshold of echo perception (e.g., only a few milliseconds in each direction). The process is repeated as desired, pressing the flange of each supply reel in alternation. The flanging effect has been described as a kind of ``whoosh'' passing subtly through the sound.^6.2The effect is also compared to the sound of a jet passing overhead, in which the direct signal and ground reflection arrive at a varying relative delay [59]. If flanging is done rapidly enough, an audible Doppler shift is introduced which approximates the ``Leslie'' effect commonly used for organs (see §5.9).

**Figure 5.2:** Two tape machines configured to produce a *flanging effect*.
$\includegraphics{eps/twotapemachines}$

Flanging is modeled quite accurately as a feedforward comb filter, as discussed in §2.6.1, in which the delay is varied over time. Figure 5.3 depicts such a model. The input-output relation for a basic flanger can be written as

$\displaystyle y(n) = x(n) + g x[n-M(n)] \protect$

(6.1)

where

is the input signal amplitude at time $n=0,1,2,\dots$ ,

is the output at time

is the ``depth'' of the flanging effect, and

is the length of the delay-line at time

. The delay length

is typically varied according to a triangular or sinusoidal waveform. We may say that the delay length is modulated by an ``LFO'' (Low-Frequency Oscillator). Since

must vary smoothly over time, it is clearly necessary to use an interpolated delay line to provide non-integer values of

in a smooth fashion.

**Figure 5.3:** The basic flanger effect.
$\includegraphics{eps/flanger}$

As shown in Fig.2.25, the frequency response of Eq.(5.1) has a ``comb'' shaped structure. For , there are peaks in the frequency response, centered about frequencies

$\displaystyle \omega^{(p)}_k = k \frac{2\pi}{M}, \quad k=0,1,2,\dots,M-1.$

For

, the peaks are maximally pronounced, with

notches^6.3occurring between them at frequencies $\omega^{(n)}_k = \omega^{(p)}_k + \pi/M$ . As the delay length

is varied over time, these ``comb teeth'' squeeze in and out like the pleats of an accordion. As a result, the spectrum of any sound passing through the flanger is ``massaged'' by a variable comb filter.

As is evident from Fig.2.25, at any given time there are notches in the flanger's amplitude response (counting positive- and negative-frequency notches separately). The notches are thus spaced at intervals of Hz, where denotes the sampling rate. In particular, the notch spacing is inversely proportional to delay-line length.

The time variation of the delay-line length results in a ``sweeping'' of uniformly-spaced notches in the spectrum. The flanging effect is thus created by moving notches in the spectrum. Notch motion is essential for the flanging effect. Static notches provide some coloration to the sound, but an isolated notch may be inaudible [140]. Since the steady-state sound field inside an undamped acoustic tube has a similar set of uniformly spaced notches (except at the ends), a static row of notches tends to sound like being inside an acoustic tube.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2020-01-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Flanging

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4. Copyright © 2020-01-24 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2020-01-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University