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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.

Flanging is modeled quite accurately as a feedforward comb filter, as discussed in §2.6.1, in which the delay $ M$ 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 $ x(n)$ is the input signal amplitude at time $ n=0,1,2,\dots$ , $ y(n)$ is the output at time $ n$ , $ g$ is the ``depth'' of the flanging effect, and $ M(n)$ is the length of the delay-line at time $ n$ . The delay length $ M(n)$ 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 $ M(n)$ must vary smoothly over time, it is clearly necessary to use an interpolated delay line to provide non-integer values of $ M$ in a smooth fashion.

Figure 5.3: The basic flanger effect.

As shown in Fig.2.25, the frequency response of Eq.(5.1) has a ``comb'' shaped structure. For $ g>0$ , there are $ M$ 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 $ g=1$ , the peaks are maximally pronounced, with $ M$ notches6.3occurring between them at frequencies $ \omega^{(n)}_k = \omega^{(p)}_k
+ \pi/M$ . As the delay length $ M$ 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 $ M(n)$ notches in the flanger's amplitude response (counting positive- and negative-frequency notches separately). The notches are thus spaced at intervals of $ f_s/M$ Hz, where $ f_s$ denotes the sampling rate. In particular, the notch spacing is inversely proportional to delay-line length.

The time variation of the delay-line length $ M(n)$ 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 © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University