## phaser1

phaser1 — First-order allpass filters arranged in a series.

## Description

An implementation of iord number of first-order allpass filters in series.

## Syntax

`ares phaser1 asig, kfreq, kord, kfeedback [, iskip]`

## Initialization

iskip (optional, default=0) -- used to control initial disposition of internal data space. Since filtering incorporates a feedback loop of previous output, the initial status of the storage space used is significant. A zero value will clear the space; a non-zero value will allow previous information to remain. The default value is 0.

## Performance

kfreq -- frequency (in Hz) of the filter(s). This is the frequency at which each filter in the series shifts its input by 90 degrees.

kord -- the number of allpass stages in series. These are first-order filters and can range from 1 to 4999.

Note Although kord is listed as k-rate, it is in fact accessed only at init-time. So if you are using a k-rate argument, it must be assigned with init.

kfeedback -- amount of the output which is fed back into the input of the allpass chain. With larger amounts of feedback, more prominent notches appear in the spectrum of the output. kfeedback must be between -1 and +1. for stability.

phaser1 implements iord number of first-order allpass sections, serially connected, all sharing the same coefficient. Each allpass section can be represented by the following difference equation:

y(n) = C * x(n) + x(n-1) - C * y(n-1)

where x(n) is the input, x(n-1) is the previous input, y(n) is the output, y(n-1) is the previous output, and C is a coefficient which is calculated from the value of kfreq, using the bilinear z-transform.

By slowly varying kfreq, and mixing the output of the allpass chain with the input, the classic "phase shifter" effect is created, with notches moving up and down in frequency. This works best with iord between 4 and 16. When the input to the allpass chain is mixed with the output, 1 notch is generated for every 2 allpass stages, so that with iord = 6, there will be 3 notches in the output. With higher values for iord, modulating kfreq will result in a form of nonlinear pitch modulation.

## Examples

Here is an example of the phaser1 opcode. It uses the file phaser1.csd.

Example 685. Example of the phaser1 opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

```<CsoundSynthesizer>
<CsOptions>
; Select audio/midi flags here according to platform
; Audio out   Audio in    No messages
-odac           -iadc     -d     ;;;RT audio I/O
; For Non-realtime ouput leave only the line below:
; -o phaser1.wav -W ;;; for file output any platform
</CsOptions>
<CsInstruments>

sr = 44100
kr = 4410
ksmps = 10
nchnls = 1

; demonstration of phase shifting abilities of phaser1.
instr 1
; Input mixed with output of phaser1 to generate notches.
; Shows the effects of different iorder values on the sound
idur   = p3
iamp   = p4 * .05
iorder = p5        ; number of 1st-order stages in phaser1 network.
; Divide iorder by 2 to get the number of notches.
ifreq  = p6        ; frequency of modulation of phaser1
ifeed  = p7        ; amount of feedback for phaser1

kamp   linseg 0, .2, iamp, idur - .2, iamp, .2, 0

iharms = (sr*.4) / 100

asig   gbuzz 1, 100, iharms, 1, .95, 2  ; "Sawtooth" waveform modulation oscillator for phaser1 ugen.
kfreq  oscili 5500, ifreq, 1
kmod   = kfreq + 5600

aphs   phaser1 asig, kmod, iorder, ifeed

out    (asig + aphs) * iamp
endin

</CsInstruments>
<CsScore>

; inverted half-sine, used for modulating phaser1 frequency
f1 0  16384 9 .5 -1 0
; cosine wave for gbuzz
f2 0  8192 9 1 1 .25

; phaser1
i1 0  5 7000 4  .2 .9
i1 6  5 7000 6  .2 .9
i1 12 5 7000 8  .2 .9
i1 18 5 7000 16 .2 .9
i1 24 5 7000 32 .2 .9
i1 30 5 7000 64 .2 .9
e

</CsScore>
</CsoundSynthesizer>
```

## Technical History

A general description of the differences between flanging and phasing can be found in Hartmann [1]. An early implementation of first-order allpass filters connected in series can be found in Beigel [2], where the bilinear z-transform is used for determining the phase shift frequency of each stage. Cronin [3] presents a similar implementation for a four-stage phase shifting network. Chamberlin [4] and Smith [5] both discuss using second-order allpass sections for greater control over notch depth, width, and frequency.

## References

1. Hartmann, W.M. "Flanging and Phasers." Journal of the Audio Engineering Society, Vol. 26, No. 6, pp. 439-443, June 1978.

2. Beigel, Michael I. "A Digital 'Phase Shifter' for Musical Applications, Using the Bell Labs (Alles-Fischer) Digital Filter Module." Journal of the Audio Engineering Society, Vol. 27, No. 9, pp. 673-676,September 1979.

3. Cronin, Dennis. "Examining Audio DSP Algorithms." Dr. Dobb's Journal, July 1994, p. 78-83.

4. Chamberlin, Hal. Musical Applications of Microprocessors. Second edition. Indianapolis, Indiana: Hayden Books, 1985.

5. Smith, Julius O. "An Allpass Approach to Digital Phasing and Flanging." Proceedings of the 1984 ICMC, p. 103-108.