EQ and filtering are some of the most fundamental aspects of the recording and mixing processes. Best practice is always to be thoughtful about microphone selection and placement within the recording space, and to use the natural characteristics of the mic’s frequency response and polar pattern to get the best possible sound.
However, there are often times when it is not possible to get the ‘perfect’ sound – seemingly more often than not in the project studio – and it becomes necessary to reach for the EQ as a corrective tool. The art of notch filtering is something that should be understood, as it can be one of the most useful tools for audio correction and restoration – and when done well, it can often sound transparent.
Cutting A Notch
A notch filter reduces the gain of a narrow band of the frequency spectrum while (theoretically at least) leaving the surrounding audio unaffected. It has three main parameters that go some way to defining its operation: cut-off frequency (the frequency around which the notch is centred and more accurately called the centre frequency); Q (the steepness of the roll-off of the filter itself); and gain – the overall ‘depth’ of the filter (the amount of gain reduction within the frequency band –although, strictly speaking, this is relevant only when the notch filter is being used as part of a parametric equaliser). These parameters define the shape of the filter and the frequencies it will operate over.
Notch filters are most commonly found within a parametric EQ, where it is possible to select a specific centre frequency, then tighten the Q sufficiently to be able to act on a tight range of frequencies. This makes it possible to remove very specific elements of a sound that are problematic to a recording, and it is always quite surprising just how much can be taken out by good notch filtering and still leave the body of the recording in very good shape – frequency-dependent, obviously. It is the steepness of the Q that is key.
A sine sweep that has been notched at 2kHz by an analogue emulation (upper plot) and a linear-phase filter (lower plot).
Quality Control
Q is regularly seen as a parameter on filters and EQs that is used to provide a numeric value describing the steepness of the cut-off slope of the filter/EQ in question. The problem is that in many cases the way in which the Q value is calculated does not appear to be consistent and so becomes confusing. Q refers to ‘quality factor’ and is a dimensionless measurement of the amount of damping within any physical system that displays resonance.
To keep things simple: for notch filters, Q is most commonly defined as a ratio between the centre cut-off frequency and the frequency bandwidth at which there is a 3dB drop. So, for filters with a high Q, the frequency at which 3dB of attenuation is achieved would be nearer the centre frequency; conversely, for a low value of Q, 3dB of attenuation would be achieved further away from the centre frequency.
To give this some real figures: for a 1kHz centre frequency with a Q value of 1, the 3dB drop-off curves would be at 500Hz and 1.5kHz, giving a bandwidth of 1,000Hz. If Q is increased to 10, then the 3dB points would be at 950 and 1,050Hz, a bandwidth of 100Hz. For a final example, if the centre frequency is at 5kHz but with the same value for Q (10), the 3dB points become 4,750Hz and 5,250Hz – a bandwidth of 500Hz. The point is that even though the Q factor of the filter has remained the same, the bandwidth of the filter has changed purely because the centre frequency has changed.
It would be far more meaningful, then, to regard the bandwidth in terms of octaves instead of purely in terms of frequency. When we go up an octave, in frequency terms the value is doubled – so the scale is a simple logarithmic function. This can then be applied to the bandwidth when measured in Hertz, such that the bandwidth in octaves can be calculated just from the Q value. So a Q factor of 10 gives a value of bandwidth (in octaves) of 0.144 wherever the centre frequency is located. Working backwards through this, if the notch filter was to have a very wide bandwidth of one octave, the Q setting would be 1.414.
The Remove Hum tool in iZotope’s RX2 can automatically calculate the harmonics from the fundamental – and have very high Q values.
Swingeing Cuts
The anatomy of a notch filter is similar to the combination of two filters working together: a low-pass filter and a high-pass filter. However, this combination of filters is more often called a band-rejection (or band-stop) filter as it generally has a much wider frequency range than a notch filter.
A problem that can present itself with both notch and band-rejection filters is the effect of the filter on the phase of the audio signal. Part of the inherent operation of analogue filters is the phase shift – and this is resolved in the digital world only by using linear-phase filters, which can incur significant latency issues when used as plug-ins (not withstanding latency compensation within the DAW). By using the sum of a low-pass and high-pass filter on the same source audio to create a band-rejection filter, it can be possible to introduce phase issues, especially around the ‘slope’ region of the filter. It is quite rare that audio is parallel-processed through different filter elements and subsequently summed together – yet this is exactly what is happening here, so phase shift can become a problem.
The horizontal region at around 720Hz is a prime candidate for notch filtering – this source was possibly a shoe squeak.
In The Loop
What makes narrow notch filters so useful is their ability to pinpoint specific elements within a sound and reduce (if not remove) their presence. This is done all the time with EQ when broad frequency band manipulation is necessary, but for some reason, notch filtering with an EQ is often not thought of when trying to remove extraneous elements. The most obvious/regular requirement for notch filtering is mains hum. This is a low-frequency drone that is generated by earth loops and can be picked up by the microphone within the live room just as easily as it can be created at the patchbay. In the UK the fundamental frequency is at 50Hz (in the USA it is 60Hz), but the key thing is that, like most sounds that are recorded, the mains hum has overtones and harmonics that make up the ‘full’ sound.
In Pro Tools it is useful to save notch filters as presets – this one is a good starting point for reducing the ‘whine’ from a Red Camera.
Solving this problem requires a series of notch filters to be built up that each has a related centre frequency that is part of the harmonic series. The Q of each filter still needs to be quite steep so as to filter only the specific harmonic content relating to the fundamental, but also the depth (gain) of the filter can often be reduced on each successive harmonic, as the relative amplitudes of each harmonic will decrease by comparison to the fundamental.
DIY band-stop filters can be made in Logic by parallel processing and using low-pass and high-pass filters on each channel.
Tags: Cubase, EQ and Filtering, Home, Music Mixing, Music Production, Notch Filtering, Pro Tools Tutorials, Ten Minute Masters, Tutorials
