AR Envelope Follower

Overview

AR Envelope Follower, where "AR" stands for Attack-Release, is similar to the Peak Envelope Follower but allows you to specify the attack duration. During the attack phase of an audio signal, the AR envelope follower attempts to follow the signal but is constrained by the attack duration. A longer attack period gives a softer response, exponentially increasing. When the signal level drops below the peak, the follower gradually releases the peak level with an exponential decay.

AR Envelope DetectorThe AR envelope follower models the behavior of two resistors, one for attack, and one for release, each connected in series with an ideal diode —with no voltage drop—, tied together and connected to a capacitor. During attacks, the capacitor charges through the attack resistor, exponentially increasing. The capacitor discharges through the release resistor as the audio signal falls below the peak charge, causing the output voltage to progressively decay with an exponential curve.

Response

AR Envelope Follower
Figure 1. AR envelope follower response

The plot in Figure 1 depicts the response of the AR envelope follower, which was obtained by picking the guitar’s low-E string and using a 2-milliseconds attack duration and 2-second release duration (envelope: magenta, signal: blue, absolute value of the signal: dark blue).

It is worth noting that we use the absolute value of the signal to capture both the positive and negative sides of the waveform, as indicated by the dark blue plot. The AR envelope follower does not perform this operation automatically, allowing you to perform any necessary preprocessing before computing the envelope. This flexibility enables you, for example, to capture only the positive or negative peaks, or perhaps the square of the signal, depending on your application needs.

Like the Peak Envelope Follower, the AR Peak Detector is susceptible to having ripples in the envelope with the short release durations. See Envelope Ripples for details.

Include

#include <q/fx/envelope.hpp>

Declaration

struct ar_envelope_follower
{
                           ar_envelope_follower(
                              duration attack
                            , duration release
                            , float sps
                           );

    float                  operator()(float s);
    float                  operator()() const;
    ar_envelope_follower&  operator=(float y);
    void                   config(duration attack, duration release, float sps);
    void                   attack(float attack_, float sps);
    void                   release(float release_, float sps);
};

Expressions

Notation

env, a, b

Objects of type ar_envelope_follower

atk, rel

Objects of type duration

sps

Floating point value for samples per second.

s

Floating point value for the latest input sample.

y

Floating point value from 0.0 to 1.0.

Constructors and Assignment

Expression Semantics

ar_envelope_follower(atk, rel, sps)

Construct a ar_envelope_follower given atk (attack duration), rel (release duration) and sps (samples per second).

ar_envelope_follower(env)

Copy construct from ar_envelope_follower env.

a = b

Assign b to a.

a = y

Reset the latest held value of the ar_envelope_follower to y.
C++ brace initialization may also be used.

Function Call

Expression Semantics Return Type

env(s)

Process the input sample s and return the detected envelope.

float

env()

Get the latest held value of the ar_envelope_follower

float

Mutators

Expression Semantics Return Type

env.config(atk, rel, sps)

Set the attack duration given atk (attack duration), rel (release duration) and sps (samples per second).

void

env.attack(atk, sps)

Set the attack duration given atk (attack duration) and sps (samples per second)

void

env.release(rel, sps)

Set the release duration given rel (release duration) and sps (samples per second)

void