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Hans Mikelson

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Filters are used to separate mixtures into different components. A complex sound can be considered a mixture of sounds of different frequencies. Audio filters can be used to separate high frequency sounds from low frequency sounds. Usually this means allowing sounds of certain frequencies to pass unaltered while blocking sounds of other frequencies. Certain filters can be used to amplify or boost certain frequencies. This article will only describe a few of the most commonly used filters: the low pass filter, the high pass filter and the band pass filter.

The low pass filter

A low pass filter is designed to allow all frequencies below a cut off frequency to pass while preventing all frequencies above the cut off frequency from passing. Figure 1 shows a frequency response from a low pass filter. Notice that the transition is not an abrupt vertical line but instead a sloping line which is rounded at the top and bottom. This means that the filter allows some high frequencies through and reduces some of the frequencies below the filter cut off frequency. The cut off frequency is defined as the point where the curve has dropped to about .707 or 1/sqrt(2).

Figure 1.
Frequency response of a low pass filter.

A good way to understand the effect of a filter is to apply the filter to white noise and listen to the result. The following Csound code implements this:

arnd   rand      1                          ; White noise
aout   butterlp  arnd, kfco                 ; Low pass filter
;    Sta   Dur  Amp    Fco1  Fco2
i10  0     10   30000  5000  100

In the above example the filter is swept from 5000 Hz to 100 Hz. Instrument 20 applies a low pass filter to a spoken phrase.

The high pass filter

The high pass filter is the opposite of the low pass filter blocking low frequencies but allowing high frequencies to pass.

Figure 2.
Frequency response of a high pass filter.

High pass filters have many different uses. A high pass filter with a very low cut off frequency (~20 Hz) can be used to remove DC from a signal. A high pass filter with a moderately high cut off frequency (~1500 Hz) can be used to simulate the flared end of a clarinet or horn in a waveguide model. A high pass filter can create a sort of "radio voice" sound effect when applied to vocals as in the following example.

asig   diskin    isamp, 1                   ; Read sample from disk
aout   butterhp  asig, ifc                  ; High pass filter
aout   =         aout*iamp*kdclk            ; Amplify
;    Sta   Dur   Amp  Sample       Fc
i21  5     4.63  1    "limit.wav"  2000

High pass filters can be used to isolate the high's for additional processing as in a de-esser. High pass filters are useful when synthesizing certain percussion instruments such as cymbals.

The band pass filter

The band pass filter only allows frequencies within a certain range of the center frequency to pass. Band pass filters are useful for creating formants or simulating the resonances of acoustic resonators like a guitar or violin body. The following example processes the sound as if it had been produced inside a particular resonating body

af1    butterbp  asig, if1, if1/8           ; Band pass filter
af2    butterbp  asig, if2, if2/8           ; Band pass filter
af3    butterbp  asig, if3, if3/8           ; Band pass filter

aout   =         (af1+af2+af3)*iamp*kdclk   ; Amplify
;    Sta   Dur   Amp  Sample       F1  F2  F3
i22  10    4.63  1    "limit.wav"  116 422 849

Band pass filters are used to isolate certain frequency bands for further processing.

Filter types

Csound has many different types of filters. Below is a table listing most of Csounds filters categorized by the type of frequency response:

Filter Name Description Opcodes Example
Low pass filter Allows low frequencies to pass. Attenuates high frequencies. tone, tonek, tonex, butterlp, rezzy, moogvcf, svfilter, lowres, lowresx, vlowres, lowpass2, port, portk Hiss reduction, most common synthesizer filter, darkness
High pass filter Allows high frequencies to pass. Attenuates low frequencies. atone, atonek, atonex, butterhp, rezzy, svfilter, dcblock Cross-over, some synthesizer filters, radio voice
Band pass filter A center frequency and a bandwidth is specified. Frequencies within a frequency band of the center frequency are allowed to pass. Other frequencies are blocked. reson, resonk, resonx, resonr, resonz, butterbp, svfilter Fomants, acoustic body simulations
Band reject filter or notch filter The opposite of the band pass filter. A center frequency and band width are specified. Frequencies within the specified bandwidth are blocked while higher and lower frequencies are allowed to pass. areson, aresonk, butterbr 60 Hz hum eliminator
Parametric boost/cut filter Similar to both band pass and band reject filters. Able to boost or cut a certain frequency band. pareq Parametric equalizer
High shelf filter Can amplify or attenuate high frequencies. pareq Home stereo treble control, mixing console high shelf filter.
Low shelf filter Can amplify or attenuate low frequencies. pareq Home stereo bass control, mixing console low shelf filter.
General digital filters Can be used to construct many different types of filters. biquad, filter2, zfilter2, nlfilt  
Other filters These typically involve delay lines with feedback. comb, alpass, nestedap, streson Reverbs and digital waveguides.
If I want a simple solid filter solution I usually use the butterworth filters: butterlp, butterhp, butterbr and butterbp. These are very reliable over a wide range of conditions. If I want a musical analog sounding filter I usually use rezzy or moogvcf. Svfilter has been recommended to me as well. For an equalizer or a shelf filter pareq is the only choice. Experiment with different filters until you find some that work for you. Sometimes I will try one filter while I am working on a sound and then substitute different one to see if it sounds better.

Links Yehar's sound DSP tutorial for the braindead. This is an excellent introduction to digital filter theory. Frequency Response of Discreet Systems. Some lecture notes on filters.