So you decide you want to use a particular type of filter…lets say a State Variable, but it’s not quite right, you need a steeper filter roll off…what to do to fix this? Fortunately you can just add another SV filter in series with the first one, and this turns a 12dB octave low/high pass into a 24dB octave filter and the bandpass/notch into 12dB octave. So far so good, but there’s one very important thing to watch out for…the resonance settings on the filters. If we have both filters with adjustable resonance then as soon as we start to approach any moderate level of resonance the second filter will be heavily overloaded at some frequencies. To avoid this we can use the structure below, where the resonance of the first filter is fixed at 0.
Be careful when cascading SV filters. Cascading too many band-pass or high-pass outputs is not a good idea. It can cause annoying high-frequency ringing, because state variable filters boost high frequencies even at low resonance settings. Another catch with filters cascaded in series is they do introduce phase shift, so beware if you are intending to mix them with the “dry” audio signal, you’ll quite probably get some unwanted peaks and notches occurring due to phase addition and cancellation effects. You can see below that there’s clearly a change in phase between oscillator and the output of the second filter that changes with frequency.
Parallel Filtering.
This is a good way of achieving a stereo effect, especially using two different models of filter, as shown below with a Moog filter for the left hand channel, and the SV filter for the right hand channel. By having two independently controlled filters (albeit with a common Keyboard Tracking CV (KB Track) you can get a really rich stereo effect, (especially when the Pitch is modulated by out of phase LFO’s, but that’s another topic for later) Note: When constructing a layout like this inside a container (as is good practice) it’s a really good idea to follow these steps: 1) Set the filter Pitch plugs to 0V (they are pre-programmed at 5V) 2) Put both of the Pitch CV’s through their own Level Adj module with the Input 1 plug set to 0 volts (again they are pre-programmed to 5V), and the Input 2 Plug set to 10V. This prevents our container inheriting any voltages from either the Filters, or the Level Adj and setting them as an unwanted voltage on the KB Track IO Module, leaving you with an odd 5V offset appearing on another module’s control voltage. I spent quite a time at one point tracking down why the controls on one of my synthesizer modules were not behaving as expected-due to this inherited voltage from inside a container!
State Variable Multifilter.
A multi-filter takes things a step further. I won’t show the frequency spectrum for any of the settings because you’ll get a far better idea of the sounds it will produce by building one, hooking up a white noise source and having a listen. What we are doing is taking separate outputs from each part of the filter, then mixing them to achieve a sound we like. Of course if you want to get really complex you could have four individual SV filters with individually controlled frequency and resonance settings… the world’s your oyster (or mollusk of choice)here, feel free to experiment.
The Oberheim Xpander multi-filter.
Oberheim took the concept of the multi-filter and ran with it. The Voltage Controlled filter (VCF). The available modes on the filter are: a) One-, two-, three- and four-pole low pass b) One-, two and three-pole high pass c) Two- and four-pole band pass d) Two-pole notch e) Three-pole phase shift f) Two- and three-pole high pass plus one-pole low pass g) Two-pole notch plus one-pole low pass h) Three-pole phase shift plus one-pole low pass The output from this filter could the be mixed and routed in a variety of ways. TD Panda filter. The nearest ready made SynthEdit module to this is the TD_Panda filter module However all the mixing and levels are handled internally so while there’s a huge variety of modes for the filter you’re stuck with the internally set mixing.
VA is short for Virtual Analogue. The difference between the VA and non-VA filters is a mixture of maths, physics, electronics and computer science. As simply explained as possible (by omitting some very technical bits) by taking a Moog filter as an example.
The Analogue filter. The real Moog low pass VCF is four single lowpass filters in series, with the output fed back to the input to create a resonance. In physical analogue circuits that output to input feedback loop is through copper tracks and wires and therefore happens almost instantly.
The problems with Digital Filters.
In the digital world, it’s not possible do that, if we think about it logically, how can you possible calculate the input and output of a filter at the same time? You really would need to calculate the input values to be able to begin to calculate the output signal, which really is like the old puzzle: “What came first? The chicken or the egg?”. You will be attempting to lift yourself by pulling on your shoelaces.
How this is fixed in SynthEdit.
To overcome this, the standard SE Moog filter will put a 1 sample delay in the feedback path. However that seriously messes with the phase response and therefore it messes with the high frequency response- it is just not at an accurate representation anymore. This problem also depends on the internal sample-rate, and when the filter modulates very fast, due to the time delays the input and output equations don’t match up in the time frame anymore. This can create anything from instability, to low frequency clicks, and more noise. Not only this, but if the filter signal also distorts the audio, the distortion would also not be accurate under heavy/fast modulation anymore.
Using Maths to fix it. The VA filters use maths on the problem to eliminate (as far as possible) that one sample delay that is causing problems. This why these types of filters are sometimes called “Zero Delay Feedback” or ZDF filters. There is actually is no technically agreed term for these filter designs so they are sometimes called “Virtual Analog” or “Topology Preserving Transform (TPT)”, and maybe other terms as well. Mathematicians can be really touchy about naming conventions.
Another Advantage. There is another advantage, by using VA techniques you can mimic the characteristics of an analogue circuit more accurately. This is because you can mimic the topology and layout of the filter, so it will behave in a closer approximation of the analogue filter. Now comes the tricky maths part, and it relates to the distortion of the filter.
A Mathematical note: There are two types of answers in math; explicit, and implicit. 1) Explicit is what most people think if they think about math like 1 divided by 2 equals 0.5 – that is explicit i.e. we can calculate the exact answer of 0.5, 2) Implicit means we cannot get an exact answer, but we are able to guess with relative certainly, and this guessing is usually iterative i.e. we guess and then use that guess to guess again ad infinitum. With every additional guess the result typically gets more accurate.
Factoring in non-linearity and distortion. Whether we like it or not there are no perfectly linear, or zero-distortion analogue circuits. Now, if a VA filter is linear in its response (no distortion modelled) we can get an explicit solution. However once you add distortion, we cannot get an explicit solution, so it becomes implicit and we have to use more math calculations. There are (sort of) three levels of adding distortion, and because you’re adding more calculations and complexity then CPU usage increases the higher you go in level. A 24dB/Oct filter can have nine separate distortions in it (think of it as 9 wave-shaper modules in a single filter).
Methods: 1) “Distort the states”:- This is a technically explicit method, but with the distortion at the wrong place (compared to the analogue model), but it uses the least CPU while retaining some of the VA benefits. 2) “Fixed step” solution:- This method is implicit, i.e. it always guesses a fixed number of times, the methods typically used are “Mystan’s Pivot“, where the Pivot is a fixed “One Best Guess” method. Note: Mystan is the DSP filter guru at KVR Audio, he suggested it. Naturally the mathematics people are still debating what the real name for this method should be – after all we know mathematicians are picky about the name used for a process. Another method would be fixed step solver would be the Runge-Kutta method. 3) Iterative (non-fixed step):- Another implicit method. This one might guess anything from once to an infinite number of times depending on filter settings and audio input. As you would expect, the more guesses made the more CPU is used. For practical purposes, this method will usually guess up to eight or nine times, and it is usually done with the Newton-Raphson method. Yes, by Newton we are referring to Sir Isaac Newton (mathematics is much older, and more advanced than PCs). As a practical example U-he’s Diva synthesizer uses this method of modelling.
First I’ll cover what a filter actually does, and the four modes of filtering: Low Pass, High Pass, Band Pass, and finally Notch filtering. Next will be the common types of VCF found in Synthesizers, such as Moog, Korg et al. A subtractive synthesizer without a filter is going to be very much lacking in the soundscapes you can generate – it will be like a curry without most of the spices missing. Filters lend sounds their flavour by boosting and cutting the oscillators’ frequencies.
Modulating a filter’s cut-off frequency.
Generally speaking any filter that has a cut-off pitch set by a float plug is not suitable changes in frequency during operation, they tend to respond badly, produce strange noises and crash unpredictably. Filters which have a dark blue voltage plug for pitch/frequency are safe for faster modulation speeds.
Filter characteristics.
So, let’s first review the different breeds of filter. In order of appearance: Low Pass, High Pass, Band Pass, and Notch (AKA Band Stop) filter frequency response curves are shown below.:
Resonance
Most Synthesiser voltage controlled filters have a resonance control. This alters the amount of internal feedback in the filter, which causes a boost to frequencies at the filters cut-off frequency, causing “ringing” and even self oscillation in the filter.
Low pass filter with a low resonance setting:
Low pass filter with a high resonance setting:
State Variable Filters.
The State Variable Filter (SVF) works in low-pass, high-pass, bandpass, and band-reject (also called notch and band-stop) modes. And all of these modes can operate at the same time, if you wish. Low-pass and high-pass modes cut-off slopes are 12 dB per octave, and the band-pass modes is 6 dB per octave. State variable filters are all-pole filters, meaning they boost high frequencies even when the resonance value is low. This affects band-pass and high-pass outputs more than the low-pass output, also mixing these outputs adds a touch more gain.
Moog Low Pass Filter.
The next type is the Moog ladder filter, which is a Low Pass filter. This is a digital emulation of Moog’s celebrated four-pole transistor ladder filter, the Moog Filter is a has a 24 dB/octave frequency attenuation slope. Its digital programming also simulates the analogue components’ natural non-linearities. As well as responding differently to different input levels, it also (like the original) self-oscillates when resonance is turned up high. It behaves very differently to an SV filter at high resonance levels. The Moog Filter features enhanced resonance levels for high frequencies, adding a natural high-end gloss, and moderate resonance levels for lower frequencies. Note: At extreme resonance settings, unlike the original analogue circuit the saturation in the digital filter may cause high frequency aliasing.
Sinc Filters.
SINC filters are linear phase “Brickwall” filters, Brickwall meaning that unlike normal filters where the frequencies above or below the cut-off frequency are attenuated more the further you pass the cut-off frequency these filters abruptly stop passing audio at the cut-off frequency. Linear phase meaning that across their frequency range there is as little change in phase shift as possible. These filters are an idealised design only possible in the world of DSP programming. Due to their nature SINC filters do not have a resonance control or any feedback High Pass SINC filter.
Low Pass SINC filter.
Korg Filter.
This is a digital emulation of the OTA Low Pass filter used in the Korg MS20. This filter had a characteristic “screaming” quality when high input levels were combined with high resonance control settings. In the SynthEdit emulation this saturation can be controlled, or turned off altogether. The effect of the saturator is shown below, as you can see the effect is to reduce slightly the main resonance peak, and introduce some new resonance peaks into the spectrum
Sallen Key (Steiner-Parker) filter.
For practical design purposes, the Sallen-Key filter is switchable from 12dB/octave lowpass to high-pass to band-pass – a versatile filter. Also, if you push a lot of volume through the Sallen-Key filter it starts to overdrive subtly and then more distinctly, which is another useful sonic option. On the Arturia Brute synths, Arturia arranges the “Steiner-Parker” style (Sallen-Key) and “Moog” style (transistor ladder) filters so they can be used either in series – one operating on the basic oscillator sound after the other – or in parallel, with the outputs from both equally audible. A Master Cut-off knob is also provided to change the basic setting of both simultaneously. Combining the various types of filter in these ways can give you a lot of options in your sonic palette.
TD Modules Sallen Key Filter
TD Modules Steiner-Parker filter Note that each filter mode has its own input, so you can have each mode set at it’s own level giving you all sorts of possibilities.
Diode V Ladder filters.
A type of voltage controlled filter, originally developed by EMS in order to work around the Moog patent for the VCF. The diode ladder works on a similar principle to the Moog transistor ladder; the diode, under the influence of an applied control voltage, permits or limits current flow to a filter capacitor, such that as the control voltage is varied, the filter’s cut-off frequency changes. A main difference between the transistor ladder and diode ladder is that in the transistor ladder circuit, each pole of the filter is electrically isolated or “buffered” from the others. In the diode ladder, this is not the case; all the poles interact electrically with each other. This makes the diode ladder much more difficult to analyze mathematically, and its distortion behaviour as resonance is increased is more non-linear and harder to predict. Performers often say that the diode ladder filter has a “dirtier” sound, which is probably the effect of the less predictable distortion behaviour. Besides the EMS synth models, the diode ladder was used by Roland in many older analogue models of Synthesizer. The famous TB-303 filter is a diode ladder filter.
VA Filters.
These are much like their ordinary counterparts in the SynthEdit filter selection, but are closer in sound and behaviour to their original counterpart Analogue filters. There are some comparisons below, see the difference in the frequency roll-off at the top end of the spectrum. SV Filter:- Top Spectrum is the ordinary SV Filter, the bottom one is the VA SV Filter. The “Normal” SV filter can start to distort at high resonance levels at the top end of the spectrum, and can start to sound distinctly “crunchy”
Comparison between the Standard (Top) Moog Filters, and the VA (bottom)
After doing some side by side testing (on a personal level) I prefer the sound and behaviour of the VA filters, as it’s closer to how the original analogue filters behaved. There is more to these filters than just that… if you want to go into the “geeky” stuff… read on, there’s more.
All Pass filters.
OK, so this sounds like a real contradiction in terms an ALL pass filter? What does it actually do? An all-pass filter is a signal processing filter that passes all frequencies equally in gain, but changes the phase relationship among various frequencies. Most types of filter reduce the amplitude (i.e. the magnitude) of the signal applied to it for some values of frequency, whereas the all-pass filter allows all frequencies through without changes in level, but changes the phase of the signal dependent on the frequency. A common application in electronic music is in the design of an effects unit known as a “phaser”, where a number of all-pass filters are connected in sequence and the output mixed with the input signal to produce a notch which can be swept back and forth in frequency by modulating frequency of the filter. Read more on All pass filters here
Bi-quad Filters
Bi-quad filters are commonly used in digital filter design. Bi-quad is short for Bi-quadratic, a second order filter comprising two poles and two zeros. A bi-quad filter’s transfer function is much like a state variable’s. What sets the former apart is that it contains so-called zeros. They do however eliminate the high-frequency ringing that State Variable filters are so well known for. A Bi-quad filters high-frequency performance is excellent, highly stable all the way up to Nyquist. Most are faster than state variables, and much faster than Moog filters, however for reasons outlined below they are not really useful as a VCF. Note: On the downside, a Bi-quad filter’s low frequency performance is not exactly a model of stability. At high resonance levels, low frequencies tend to destabilize with excessive gain. This can boost levels to extremes and cause clipping, especially during fast filter modulations. This makes Bi-quad filters unsuitable for fast modulation rates, as they can quickly become unstable, and prone to crashing or making strange clicking noises.
Butterworth Filters.
Butterworth filters are usually operated at fixed frequencies with variable gain levels for such designs as graphic or parametric equalizers, tone controls etc. Butterworth filters have no resonance control plugs, just peak or cut-off frequency, gain, number of poles, and for bandpass/notch filters an width setting (bandwidth).
High and Low Shelf filters.
These are often Butterworth filters that are used in equalizers or tone controls. The idea of a shelf filter is that it boosts or cuts frequencies above or below a set frequency. High shelf boosts or cuts audio above the set frequency, and Low shelf boosts or cuts audio below the set frequency (see chart below) the idea is just to cut or boost part of the spectrum without introducing any “colouration” of the audio (no resonances etc.) Much like the tone controls on a stereo.
Band Shelf filter.
A band shelf filter does much the same thing but will boost or cut a range of frequencies within a set pass-band, so you could set your mid-frequency to 1kHz, set the width of the filter to 400Hz then boost or cut the frequencies within the range of 800Hz to 1200Hz, again with no unwanted resonances or colouration of the audio.
