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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 [32,429,59,17,104,242].6.1

The term ``flanging'' is said to have arisen from the way the effect was originally achieved by 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 achieve the flanging effect, the flange of one of the supply reels is 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 $ 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.
\includegraphics{eps/flanger}

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 [139]. 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.

Flanger Speed and Excursion

As mentioned above, the delay-line length $ M(n)$ in a digital flanger is typically modulated by a low-frequency oscillator (LFO). The oscillator waveform is usually triangular, sinusoidal, or exponential (triangular on a log-frequency scale). In the sinusoidal case, we have the following delay variation:

$\displaystyle M(n) = M_0 \cdot \left[1 + A\sin(2\pi f n T)\right]
$

where $ f$ is the ``speed'' (or ``rate'') of the flanger in cycles per second, $ A$ is the ``excursion'' or ``sweep'' (maximum delay swing) which is often not brought out as a user-controllable parameter, and $ M_0$ is the average delay length controlling the average notch density (also not normally brought out as a user-controllable parameter).


Flanger Depth Control

To obtain a maximum effect, the depth control, $ g$ in Fig.5.3, should be set to 1. A depth of $ g=0$ gives no effect.


Flanger Inverted Mode

A different type of maximum depth is obtained for $ g=-1$. In this case, the peaks and notches of the $ g=1$ case trade places. In practice, the depth control $ g$ is usually constrained to the interval $ [0,1]$, and a sign inversion for $ g$ is controlled separately using a ``phase inversion'' switch.

In inverted mode, unless the delay $ M$ is very large, the bass response will be weak, since the first notch is at dc. This case usually sounds high-pass filtered relative to the ``in-phase'' case ($ g>0$).

As the notch spacing grows very large ($ M$ shrinks), the amplitude response approaches that of a first-order difference $ y(n) = x(n) -
x(n-1)$, which approximates a differentiator $ y(t) =
\frac{d}{dt}x(t)$. An ideal differentiator eliminates dc and provides a progressive high-frequency boost rising 6 dB per octave (specifically, the amplitude response is $ \left\vert H(\omega)\right\vert =
\left\vert\omega\right\vert$).


Flanger Feedback Control

Many modern commercial flangers have a control knob labeled ``feedback'' or ``regen.'' This control sets the level of feedback from the output to the input of the delay line, thereby creating a feedback comb filter in addition to the feedforward comb filter, in the same manner as in the creation of a Schroeder allpass filter in §2.8.1 (see Fig.2.30).


Summary of Flanging

In view of the above, we may define a flanger in general as any filter which modulates the frequencies of a set of uniformly spaced notches and/or peaks in the frequency response. The main parameters are

  • Depth $ g\in[0,1]$ -- controlling notch depth
  • Speed $ f$ -- speed of notch movement
  • Phase -- switch to subtract instead of adding the direct signal with the delayed signal
Possible additional parameters include
  • Average Delay $ M_0$
  • Excursion or Sweep $ A$ -- amount by which the delay-line grows or shrinks
  • Feedback or Regeneration $ a_M \in(-1,1)$ -- feedback coefficient from output to input

Note that flanging provides only uniformly spaced notches. This can be considered non-ideal for several reasons. First, the ear processes sound over a frequency scale that is more nearly logarithmic than linear [459]. Therefore, exponentially spaced notches (uniformly spaced on a log frequency scale) should sound more uniform perceptually. Secondly, the uniform peaks and notches of the flanger can impose a discernible ``resonant pitch'' on the program material, giving the impression of being inside a resonant tube. Third, when $ g<0$ (inverted flanging), it is possible for a periodic tone to be completely annihilated by harmonically spaced notches if the harmonics of the tone are unlucky enough to land exactly on a subset of the harmonic notches. In practice, exact alignment is unlikely; however, the signal loudness can be modulated to a possibly undesirable degree as the notches move through alignment with the signal spectrum. For this reason, flangers are best used with noise-like or inharmonic sounds. For harmonic signals, it makes sense to consider methods for creating non-uniform moving notches.

A Faust software implementation of flanging may be found in the file effect.lib within the Faust distribution [154,170]. The Faust programming example phaser_flanger.dsp may be run to hear the effect on a test signal and experiment with its parameters in real time.


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