Fast RMS Envelope Follower

Overview

The Fast RMS Envelope Follower is a variation of the Fast Envelope Follower. It is a simple composite class that contains a Fast Averaging Envelope Follower member.

RMSThe signal path is as follows:

  1. Square the signal.

  2. Apply the fast averaging envelope follower. The moving average filter in the fast averaging envelope follower returns the arithmetic mean of the squared values over its hold period.

  3. Return the square root the result.

This is embodied in the fast_rms_envelope_follower class. Following the fast envelope follower API, the function call operator accepts a floating point sample, transforms it, and returns an envelope, also a floating point.

The fast_rms_envelope_follower_db variant works in the dB domain, making it easy to use as an envelope follower for dynamic range effects (compressor, expander, and agc) that already work in the dB domain, so we eliminate a linear to decibel conversion and optimize computation by using division by 2 instead of sqrt as an added bonus.

Response

The plot in Figure 1 below shows the fast RMS envelope follower’s response (envelope: green, signal: blue, absolute value of the signal: dark blue). It may look indistinguishable from the Fast Averaging Envelope Follower's output, but this detector returns true RMS results.

Fast RMS envelope follower response
Figure 1. Fast RMS envelope follower response

Include

#include <q/fx/envelope.hpp>

Declaration

struct fast_rms_envelope_follower
{
            fast_rms_envelope_follower(duration hold, float sps);
    float   operator()(float s);
};

struct fast_rms_envelope_follower_db : fast_rms_envelope_follower
{
    using fast_rms_envelope_follower::fast_rms_envelope_follower;

    decibel operator()(float s);
};

fast_rms_envelope_follower essentially follows the same API as Fast Envelope Follower. The fast_rms_envelope_follower_db variant works in the dB domain and returns decibel instead of float.

Expressions

Notation

env_t

A fast_rms_envelope_follower or fast_rms_envelope_follower_db.

env, a, b

Objects of type fast_rms_envelope_follower or fast_rms_envelope_follower_db.

hold

Object of type duration

sps

Floating point value for samples per second.

s

Floating point value for the latest input sample.

Constructors and Assignment

Expression Semantics

env_t(hold, sps)

Construct a basic_fast_ave_envelope_follower<div> given hold (hold duration) and sps (samples per second).

env_t(env)

Copy construct from basic_fast_ave_envelope_follower<div> env.

a = b

Assign b to a.
C++ brace initialization may also be used.

env_t is just a shortcut notation for any type or alias to a template instantiation of fast_rms_envelope_follower or fast_rms_envelope_follower_db.

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 basic_fast_ave_envelope_follower<div>

float