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Linear phase? Natural phase?
If you’ve worked with plugins, you’ve likely come across the terms “Linear Phase” and “Natural Phase.”
As the name suggests, a linear phase implies that the phase response is linear. This means there’s a consistent time delay applied to all frequency components.
Link to Phase and Waveform document
When processing related to frequency, not all frequencies receive the same time delay, leading to phase distortion. This is typically referred to as the “Natural Phase.” However, if we apply the same delay based on the longest delay time across all frequencies, every frequency is processed uniformly without any phase distortion. This approach is called the “Linear Phase.”
To delve deeper into this concept, it’s essential to understand some terms and principles. Let’s now explore the two major classifications of digital filters: the FIR filter and the IIR filter.
FIR filter(Finite Impulse Response filter)
An FIR (Finite Impulse Response) filter has an impulse response that converges to zero within a finite duration. This means that the filter’s response to an input occurs only for a limited time and then becomes zero. This property implies that by appropriately designing the filter coefficients (or taps), any phase response can be achieved. As a result, FIR filters are often used in linear phase designs.
However, to achieve a given frequency response, an FIR filter might require more coefficients than an IIR filter. This can lead to an increased computational load and inevitable latency. Additionally, the need for many coefficients can result in higher implementation costs.
IIR Filter(Infiite Impulse Response filter)
Literally speaking, it refers to a filter with an infinite impulse response.
Wait a second, an infinite impulse response? Does that make sense?
An impulse signal is a signal that has a value of 1 for a very short duration and a value of 0 before and after that period. When plotted on a graph, it appears as a single sharp peak surrounded by zeros. So, how can it be infinite?
Indeed, an impulse signal exists only for a brief moment in time and is zero everywhere else. It doesn’t sustain for long. However, one of the defining characteristics of an IIR (Infinite Impulse Response) filter is its feedback mechanism. This feedback allows its impulse response to theoretically continue indefinitely. (Of course, in practice, the value will diminish over time, approaching but never truly reaching zero.)
To put it simply, in an IIR filter, a portion of the output is repeatedly fed back as an input. Because some of the output is recycled as input through feedback, the output signal can theoretically continue forever. This is why nonlinear phase responses can occur, making linear phase design challenging.
However, because of this characteristic, IIR filters can achieve the same filtering properties as FIR filters with fewer coefficients. This reduces memory usage and enhances computational efficiency (with less latency). As a result, they are often used in the design of typical digital equalizers.
Pre – ringing
Isn’t the sound of linear phase always superior? Not necessarily. One drawback of the linear phase is the phenomenon called pre-ringing.
When pre-ringing occurs, it sounds as if the transient front part is reversed, somewhat reminiscent of an echo or reflected sound. The principle behind this phenomenon is as follows:
Due to the characteristics of FIR filters, they possess a symmetrical impulse response, meaning they have symmetrical phase characteristics. This symmetry imparts an identical delay to all frequency components of the filter, thus avoiding phase distortion. When a signal passes through an FIR filter, each sample of the signal convolves with the filter’s coefficients. Due to the symmetrical nature of the impulse response, this convolution operation initiates a response even before a rapid signal change, leading to what is known as pre-ringing.
In simpler terms, because of this symmetry, there’s a premature reaction even before a significant sound change or peak occurs.
Pre-ringing tends to be more prominent in lower frequencies rather than higher ones, and it is more evident during boosting than cutting, especially when the Q value is narrow and precise. Therefore, caution is needed when processing low frequencies(typically where phase issues arise). It’s worth noting that some believe that natural phase sounds more organic and pleasant than linear phase, primarily because phase variations are natural in our environment.