Chorus/Flanger: LFO Modulated Delay

1. From Echo to Flanger: The Modulated Delay

The flanger is one of the most recognizable audio effects, creating a characteristic "swooshing" or "jet plane" sound. Its structure is a direct evolution of the delay effects we have already discussed. While an echo uses a feedback delay, a classic flanger uses a feedforward structure, mixing the original "dry" signal with a delayed "wet" signal. The crucial difference is that the delay time, $D$, is now a function of time, $D(t)$.

As you've read, the flanger's sound comes from its time-varying frequency response. It is a comb filter, but because the delay $D(t)$ is changing, the notches in the filter's spectrum are not static. They sweep through the frequency range, creating the distinctive "whoosh".

The delay time is typically modulated by a Low-Frequency Oscillator (LFO), often with a sinusoidal or triangular waveform. The modulation can be expressed as:

$D(t)=D_{avg}+D_{sweep}\cdot \sin (2\pi f_{LFO}t)$

where:

• $D_{avg}$ is the average delay length (e.g., 5 ms).
• $D_{sweep}$ is the sweep depth or excursion (e.g., ±4 ms).
• $f_{LFO}$ is the frequency of the LFO, also known as the "rate" or "speed" of the effect (e.g., 0.2 Hz).

For a flanger, the average delay $D_{avg}$ is kept very short, typically under 15 ms, so that we don't perceive the delay as a distinct echo.

2. The Physics of a Changing Delay: Doppler Shift

A key question arises: what is the perceptual effect of continuously changing the delay of a signal? Your background in signal processing and physics might suggest an answer: a change in frequency. This is precisely correct and is analogous to the Doppler effect.

When a sound source moves towards you, its sound waves are compressed, leading to a higher perceived pitch. When it moves away, the waves are stretched, leading to a lower pitch. A time-varying delay line simulates this phenomenon perfectly.

• Decreasing the delay is like moving the "listener" (the read-pointer) towards the "source" (the write-pointer), compressing the signal and increasing its pitch.
• Increasing the delay is like moving the listener away from the source, stretching the signal and decreasing its pitch.

Let's look at the mathematics behind this.

The key equation you saw is:

${\omega }_o(t)={\omega }_i\left(1-\frac{d\tau (t)}{dt}\right)$

Where:

• ${\omega }_o(t)$ is the instantaneous output frequency.
• ${\omega }_i$ is the input frequency.
• $\tau (t)$ is the delay in seconds.
• $\frac{d\tau (t)}{dt}$ is the rate of change of delay. This dimensionless quantity is the crucial factor.

This equation formalizes our intuition: the output frequency is shifted by a factor proportional to the negative derivative of the delay time. When the LFO is on its rising slope, the delay is increasing, $d\tau /dt>0$, and the pitch is shifted down. When the LFO is on its falling slope, the delay is decreasing, $d\tau /dt<0$, and the pitch is shifted up.

3. Implementation: The Need for Interpolation

In the previous lesson, our delay D was an integer number of samples. With LFO modulation, the delay D(t) will almost always be a floating-point number (e.g., 220.7 samples). We cannot simply access buffer[220.7]. We need a way to estimate the value of the signal between two samples. This technique is called fractional delay interpolation.

The simplest and most common method is linear interpolation. To find the value at a fractional position p (e.g., 220.7):

1. Find the integer sample index i before p (i.e., floor(p), which is 220).
2. Find the fractional part alpha (i.e., p - i, which is 0.7).
3. The interpolated value is a weighted average of the samples at i and i+1:
   value = (1 - alpha) * buffer[i] + alpha * buffer[i+1]

While more advanced interpolation methods exist (e.g., polynomial, all-pass, or windowed-sinc), linear interpolation is computationally cheap and often sufficient for these effects.

4. The Chorus Effect: Creating an Ensemble

The goal of a chorus effect is to make a single voice or instrument sound like a group of musicians playing in unison. Real musicians never play with perfect timing or tuning. The chorus effect simulates this by creating several copies of the original signal, each with its own slight, time-varying delay and pitch modulation.

The implementation is a direct extension of what we've learned. Instead of one modulated delay line, we use multiple.

To create a rich stereo chorus, one might use two or more modulated delay lines. Each line would have its own LFO, or a single LFO with different phase offsets for each line, to ensure the pitch variations are independent and decorrelated. The outputs of these delay lines are then panned to different positions in the stereo field and mixed with the dry signal.

Chorus vs. Flanger Parameters:

• Delay: Chorus uses longer average delays (typically 15-50 ms) to create a sense of distinct voices, while flangers use very short delays (< 15 ms) for a strong comb-filtering coloration.
• Feedback: Flangers often include a feedback or "regeneration" control to accentuate the resonant peaks of the comb filter. Choruses typically have no feedback.
• Modulation: Both use LFOs, but the modulation in a chorus is often subtler, aimed at creating a gentle shimmer rather than a dramatic sweep.

5. A Deeper Look: The Nuances of Modulation

So far, we've assumed a simple relationship: a sinusoidal LFO modulating delay creates a sinusoidal pitch variation (specifically, a cosine). However, the reality, especially in historical analog circuits, is more complex and interesting. This is a nuance your EE background will allow you to appreciate.

This article investigates the behavior of classic Bucket-Brigade Device (BBD) analog delay chips used in many famous chorus and flanger pedals. It uses simulation to show that the relationship between the LFO shape and the resulting pitch modulation is not linear.

This deep dive shows that the character of these beloved analog effects is partly due to these inherent non-linearities. While a modern digital implementation can create a "perfect" sinusoidal pitch vibrato, accurately modeling a vintage pedal might require emulating these very distortions. It's a perfect example of how limitations in analog technology created a unique and desirable sonic signature.

Conclusion

You have now extended your knowledge from fixed delays to time-varying delays, unlocking a new class of powerful modulation effects. You've seen how a simple concept—making the delay time dynamic—gives rise to the sweeping resonance of a flanger and the shimmering textures of a chorus.

Key Takeaways:

• Flanger and Chorus effects are built on delay lines where the delay time is modulated by a Low-Frequency Oscillator (LFO).
• The core mechanism for the pitch-shifting component is the Doppler effect: the output frequency is scaled by a factor related to the negative derivative of the delay time, $-\frac{d\tau (t)}{dt}$.
• A Flanger typically uses a short delay (<15ms), feedforward mixing, and often feedback to create a sweeping comb filter effect.
• A Chorus uses multiple, independent, longer-delay modulated lines (15-50ms) with no feedback to simulate an ensemble of performers.
• Implementing these effects requires fractional delay interpolation (e.g., linear interpolation) to read from the delay buffer at non-integer sample positions.

Preview of the Next Lesson:

We have just explored how to modulate pitch using a time-domain method based on the Doppler effect. This approach has its limits; large pitch shifts can introduce audible artifacts. The next lesson, "Analyze the phase vocoder method for time-stretching and pitch-shifting," will introduce you to a powerful frequency-domain technique. The phase vocoder analyzes, modifies, and resynthesizes the signal's spectrum, allowing for high-quality, independent control over pitch and time.