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How does a limiter work?

For the answer, we’ll turn to our friends at Universal Audio, who practically invented compression and limiting as we know it today:

For a limiter to keep its output signal absolutely below a given level, it has to have two features: look-ahead, and a finite attack time. Look-ahead allows the limiter to do level detection on a signal that is advanced relative to the audio path. This gives the detector time to react to an incoming transient. Once the signal appears in the look-ahead buffer, the detected level must then converge to the incoming level within the look-ahead window. This can be achieved by using a FIR follower for the detected estimate. To understand what this means, let’s review the process of detection:

For dynamic range control applications, signal detection should result in an estimate of the incoming signal’s envelope. The detector should be relatively insensitive to modulation at audio rates, but should react quickly enough to accurately detect the short-term dynamics of the signal. Generically speaking, the detector should behave as a lowpass filter operating on the absolute value or square of the incoming signal. For proper signal tracking, the filter should be normalized to have a DC response of unity.

Traditionally, the lowpass filter used for detection is a first- or second- order IIR filter with different time constants for upward-tracking (attack) or downward-tracking (release) behavior. The historical reason for implementation as an IIR filter is that many detection algorithms are motivated by analog circuit designs. For peak limiting with look-ahead, it is necessary to use an FIR filter for tracking signal level if the detected output is to reach the signal level by the time the look-ahead period expires. Lowpass FIR filters can be designed using the window method, and normalized for unity gain at DC. The goal of the tracking filter is to have as short a length as possible (to minimize necessary look-ahead time), while having as small a bandwidth as possible to prevent excessive modulation on the audio path. In digital-domain applications, it is especially important to minimize modulation, because of aliasing concerns. Because of the many applications that demand time-limited, low-bandwidth windows, there is a vast array of window designs appropriate for detection in this situation. Choice of a reasonable window results in the ability to have true limiting of peaks while preventing the large amounts of distortion that can accompany fast changes in gain.

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