Linear Phase Equalizer

Linear Phase

In its essence, a linear phase is a filter property, where the filter's phase response is a linear function of frequency. The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the linear function's slope), referred to as the group delay. Consequently, there is no phase distortion due to the time delay of frequencies relative to one another.

Equalizers

When it comes to linear phase equalizers, we can say that they are one of the equalizers with the most transparent-sounding types of equalization. A significant downgrade of this type of equalizer is the tendency to create some undesirable side effects—for example, latency and pre-ringing. As mentioned above, a linear EQ is entirely transparent since, as its name implies, it is a filter property. The phase response of the filter is a linear function of frequency. The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the linear function's slope), referred to as the group delay.

Consequently, there is no phase distortion due to the time delay of frequencies relative to one another. In situations like live performances, linear phase EQ is not a suitable option since it produces a noticeable latency. We can safely say that the biggest drawback with the linear phase EQ is, without any doubt, the pre-ringing. The shape of the EQ curve governs the amount of pre-ringing (in fact, there is a precise mathematical relationship between the EQ curve and the amount of pre-ringing for linear phase EQ). This means pre-ringing can be controlled by changing the EQ curve. Some plugins attempt to suppress pre-ringing for you. But, as a result, you're not getting the curve (or phase) you think you are.

EQ Curves and Pre-Ringing

In the rest of this article, we'll give you some crucial information about the relationship between EQ curves and pre-ringing. After this, you can apply linear phase EQ like a seasoned pro. Pre-ringing is essentially a backward echo sound. It sounds like a strange sucking sound. You can hear it most noticeably on transients. Technically speaking, the only way to get a perfect linear phase is to apply an EQ twice: once forward in time and once backward in time. Applying an identical backward-in-time EQ cancels out any phase changes. The latency introduced in the linear phase EQ results from the backward in-time portion of the EQ nullifying the phase. As a side note, all EQ suffers from post-ringing, but our auditory senses don't notice it nearly as much. Linear phase EQ effectively halves the post-ringing and provides an equal and opposite amount of pre-ringing. Typically, the longer the pre-ringing, the more noticeable it is.

Examples

The following examples clearly show where you can use the linear phase EQ as a suitable option.

• Acoustic Instruments - Even in extreme settings, the sound of harmonically rich acoustic instruments such as guitars and pianos remains much more transparent with Linear Phase EQ than with regular EQ.
• Stereo sources: Linear Phase EQ is ideal for stereo-correlated sources such as left and right overheads or stereo-mic piano. With regular EQ, adjusting the frequency response on one of the stereo-correlated sources will introduce phase differences over parts of the frequency spectrum, which can cause the stereo coherence to collapse. This effect does not happen with Linear Phase EQ.
• Mastering: Linear Phase EQ is perfect for matching the sonic character of different songs on an album without adding the artifacts that non-linear phase EQs can add.