Answers to All Your Signal Processing Questions

Editor’s Note: This article was originally featured in a previous edition of our Webzine. It has been selected for a reprint because of its ongoing relevance. With the variety of great sounding EQs our Online Store has to offer, it’s not surprising the following question is asked so frequently.

Q: How are digital mastering EQs different from digital tracking/mixing EQs?

A: Historically, in terms of application, the mastering EQ is required to achieve high fidelity, offer a wide range of center frequencies for EQ features, provide good agreement between left and right channels, and allow for easy recall of exact settings. The particular curves picked for the EQ should be designed to work well for program material. The tracking/mixing EQ has a different set of requirements: It should have a wider gain selection for boost/cut, but doesn't need quite as wide a range of center frequencies for EQ features. More choices for cut filters are useful, and all stages of EQ and filtering should be able to be adjusted smoothly while passing audio. The tracking/mixing EQ should also be able to perform parametric cut with a narrow bandwidth.

"Mastering applications call for very high fidelity in all respects"

Over the years, these considerations have influenced the design of a number of popular "benchmark" analog EQs, which in turn influence the design of modern digital EQs. A good example of this chain of influence is as follows: The desire for good left-to-right agreement, as well as easy recall of settings, led to analog mastering EQ designs that feature "stepped" or discrete controls. With stepped controls, the gain, center frequency, and Q controls each offer a discrete collection of settings. In a DSP-based EQ, the ability to save presets and to use exactly the same DSP parameters for left and right channels eliminates the original motivation for using stepped controls. However, designs implemented with discrete controls do not require smooth parameterization of filter response over control ranges, because the controls are not designed to be moved in a continuous way. This means that many popular analog mastering EQs have responses for their discrete settings that can not be readily parameterized for use with continuous controls.

Therefore, design of digital mastering EQs may favor stepped controls, if desired, to approximate the behavior of an analog device. Of course, for users who are used to working with analog equipment, discrete controls may seem more familiar, which is another factor favoring them for the DSP-based design. And because automation is not commonly used during application of mastering EQ, the down side of having discrete controls is negligible. Consequently, it may be desirable to use discrete controls for a DSP-based mastering EQ, even though the original factors that called for discrete controls on analog units are not relevant to DSP-based designs. And, because response curves for mastering EQs tend to lack sharp features, it is not difficult to find a manageable number of discrete settings for controls that effectively span the working space for the EQ, with adequate range and density of accessible settings.

Because of the wide range of center frequencies required for mastering, it is simplest to employ up-sampling in order to carry out the design. To the extent that equalization is a linear process, it would be possible to develop an equivalent design without using up-sampling, and no aliasing would occur. However, designing filters whose features lie beyond the Nyquist limit is difficult when systems must be controlled parametrically. The up-sampled design may or may not require more computation to produce an equivalent result, but the ease of parametric-based design makes up-sampling a good choice for mastering EQs.

The Q ranges for parametric mastering EQs tend to be significantly lower than for tracking/mixing EQs. Broad curves are preferred. For shelving filters, it is also desirable to have gradual transitions that are gradual compared to shelving filters found in tracking/mixing EQs.

Mastering applications call for very high fidelity in all respects. Good digital mastering EQs can be designed in either fixed- or floating-point number systems, provided adequate bit depth is used. Filter structure becomes important for keeping distortion to a minimum. Because plug-in count can be expected to be lower in mastering applications, more DSP can be spent, if necessary, in order to ensure good numerics. For precise control over filter responses, especially at low frequencies, it is imperative to use adequate bit depth for filter coefficients as well as filter states.

For tracking/mixing EQs, since automation may be used frequently, it is imperative to employ a robust method for making smooth transitions between different EQ settings. Considerations include stability of intermediate filters, as well as sonic artifacts caused by different coefficient trajectories. Filter structure interacts with transitional behavior of the filters, so properties of a structure in time-varying conditions must be taken into account as well as distortion figures for picking a DSP filter structure for tracking/mixing EQs.

— Dr. Dave Berners & Dr. Jonathan Abel