de.quippy.sidplay.resid_builder.resid

Class Filter

java.lang.Object

de.quippy.sidplay.resid_builder.resid.Filter

public class Filter
extends Object

The SID filter is modeled with a two-integrator-loop biquadratic filter, which has been confirmed by Bob Yannes to be the actual circuit used in the SID chip.

Measurements show that excellent emulation of the SID filter is achieved, except when high resonance is combined with high sustain levels. In this case the SID op-amps are performing less than ideally and are causing some peculiar behavior of the SID filter. This however seems to have more effect on the overall amplitude than on the color of the sound.

The theory for the filter circuit can be found in "Microelectric Circuits" by Adel S. Sedra and Kenneth C. Smith. The circuit is modeled based on the explanation found there except that an additional inverter is used in the feedback from the bandpass output, allowing the summer op-amp to operate in single-ended mode. This yields inverted filter outputs with levels independent of Q, which corresponds with the results obtained from a real SID.

We have been able to model the summer and the two integrators of the circuit to form components of an IIR filter. vhp is the output of the summer, vbp is the output of the first integrator, and vlp is the output of the second integrator in the filter circuit.

According to Bob Yannes, the active stages of the SID filter are not really op-amps. Rather, simple NMOS inverters are used. By biasing an inverter into its region of quasi-linear operation using a feedback resistor from input to output, a MOS inverter can be made to act like an op-amp for small signals centered around the switching threshold.

Qualified guesses at SID filter schematics are depicted below.

 SID filter
 ----------
 
     -----------------------------------------------
    |                                               |
    |            ---Rq--                            |
    |           |       |                           |
    |  ------------<A]-----R1---------              |
    | |                               |             |
    | |                        ---C---|      ---C---|
    | |                       |       |     |       |
    |  --R1--    ---R1--      |---Rs--|     |---Rs--| 
    |        |  |       |     |       |     |       |
     ----R1--|-----[A>--|--R-----[A>--|--R-----[A>--|
             |          |             |             |
 vi -----R1--           |             |             |
 
                       vhp           vbp           vlp
 
 
 vi  - input voltage
 vhp - highpass output
 vbp - bandpass output
 vlp - lowpass output
 [A> - op-amp
 R1  - summer resistor
 Rq  - resistor array controlling resonance (4 resistors)
 R   - NMOS FET voltage controlled resistor controlling cutoff frequency
 Rs  - shunt resitor
 C   - capacitor
 
 
 
 SID integrator
 --------------
 
                                   V+
 
                                   |
                                   |
                              -----|
                             |     |
                             | ||--
                              -||
                   ---C---     ||->
                  |       |        |
                  |---Rs-----------|---- vo
                  |                |
                  |            ||--
 vi ----     -----|------------||
        |   ˆ     |            ||->
        |___|     |                |
        -----     |                |
          |       |                |
          |---R2--                 |
          |
          R1                       V-
          |
          |
 
          Vw
 ----------------------------------------------------------------------------
 

Author:

Ken Händel

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Filter.Coefficients

Field Summary

Fields

Modifier and Type	Field and Description
protected int	_1024_div_Q
protected boolean	enabled Filter enabled.
protected int[]	f0
protected int[]	f0_6581 Cutoff frequency tables.
protected int[]	f0_8580 Cutoff frequency tables.
protected int	f0_count
protected int[][]	f0_points
protected static int[][]	f0_points_6581 Maximum cutoff frequency is specified as FCmax = 2.6e-5/C = 2.6e-5/2200e-12 = 11818.
protected static int[][]	f0_points_8580 Maximum cutoff frequency is specified as FCmax = 2.6e-5/C = 2.6e-5/2200e-12 = 11818.
protected int	fc Filter cutoff frequency.
protected int	filt Selects which inputs to route through filter.
protected int	hp_bp_lp Highpass, bandpass, and lowpass filter modes.
protected int	mixer_DC Mixer DC offset.
protected int	res Filter resonance.
static boolean	SPLINE_BRUTE_FORCE #define SPLINE_BRUTE_FORCE false
protected int	vbp State of filter. bandpass
protected int	vhp State of filter. highpass
protected int	vlp State of filter. lowpass
protected int	vnf State of filter. not filtered
protected int	voice3off Switch voice 3 off.
protected int	vol Output master volume.
protected int	w0 Cutoff frequency, resonance.
protected int	w0_ceil_1 Cutoff frequency, resonance.
protected int	w0_ceil_dt Cutoff frequency, resonance.

Constructor Summary

Constructors

Constructor and Description
Filter() Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
void	clock(int voice1, int voice2, int voice3, int ext_in) SID clocking - 1 cycle
void	clock(int delta_t, int voice1, int voice2, int voice3, int ext_in) SID clocking - delta_t cycles.
protected void	cubic_coefficients(double x1, double y1, double x2, double y2, double k1, double k2, Filter.Coefficients coeff) Calculation of coefficients.
void	enable_filter(boolean enable) Enable filter.
void	fc_default(SID.FCPoints fcp) Return the array of spline interpolation points used to map the FC register to filter cutoff frequency.
PointPlotter	fc_plotter()
protected void	interpolate_brute_force(double x1, double y1, double x2, double y2, double k1, double k2, PointPlotter plotter, double res) Evaluation of cubic polynomial by brute force.
protected void	interpolate_forward_difference(double x1, double y1, double x2, double y2, double k1, double k2, PointPlotter plotter, double res) Evaluation of cubic polynomial by forward differencing.
void	interpolate(int[][] f0_base, int p0, int pn, PointPlotter plotter, double res) Evaluation of complete interpolating function.
int	output() SID audio output (16 bits).
void	reset() SID reset.
void	set_chip_model(ISIDDefs.chip_model model) Set chip model.
protected void	set_Q() Set filter resonance.
protected void	set_w0()
void	writeFC_HI(int fc_hi) Register functions.
void	writeFC_LO(int fc_lo) Register functions.
void	writeMODE_VOL(int mode_vol) Register functions.
void	writeRES_FILT(int res_filt) Register functions.
protected double	x(int[][] f0_base, int p)
protected double	y(int[][] f0_base, int p)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

SPLINE_BRUTE_FORCE

public static final boolean SPLINE_BRUTE_FORCE

#define SPLINE_BRUTE_FORCE false

See Also:

Constant Field Values

enabled

protected boolean enabled

Filter enabled.

fc

protected int fc

Filter cutoff frequency.

res

protected int res

Filter resonance.

filt

protected int filt

Selects which inputs to route through filter.

voice3off

protected int voice3off

Switch voice 3 off.

hp_bp_lp

protected int hp_bp_lp

Highpass, bandpass, and lowpass filter modes.

vol

protected int vol

Output master volume.

mixer_DC

protected int mixer_DC

Mixer DC offset.

vhp

protected int vhp

State of filter. highpass

vbp

protected int vbp

State of filter. bandpass

vlp

protected int vlp

State of filter. lowpass

vnf

protected int vnf

State of filter. not filtered

w0

protected int w0

Cutoff frequency, resonance.

w0_ceil_1

protected int w0_ceil_1

Cutoff frequency, resonance.

w0_ceil_dt

protected int w0_ceil_dt

Cutoff frequency, resonance.

_1024_div_Q

protected int _1024_div_Q

f0_6581

protected int[] f0_6581

Cutoff frequency tables. FC is an 11 bit register.

f0_8580

protected int[] f0_8580

Cutoff frequency tables. FC is an 11 bit register.

f0

protected int[] f0

f0_points_6581

protected static int[][] f0_points_6581

Maximum cutoff frequency is specified as FCmax = 2.6e-5/C = 2.6e-5/2200e-12 = 11818.

Measurements indicate a cutoff frequency range of approximately 220Hz - 18kHz on a MOS6581 fitted with 470pF capacitors. The function mapping FC to cutoff frequency has the shape of the tanh function, with a discontinuity at FCHI = 0x80. In contrast, the MOS8580 almost perfectly corresponds with the specification of a linear mapping from 30Hz to 12kHz.

The mappings have been measured by feeding the SID with an external signal since the chip itself is incapable of generating waveforms of higher fundamental frequency than 4kHz. It is best to use the bandpass output at full resonance to pick out the cutoff frequency at any given FC setting.

The mapping function is specified with spline interpolation points and the function values are retrieved via table lookup.

NB! Cutoff frequency characteristics may vary, we have modeled two particular Commodore 64s.

f0_points_8580

protected static int[][] f0_points_8580

Maximum cutoff frequency is specified as FCmax = 2.6e-5/C = 2.6e-5/2200e-12 = 11818. Measurements indicate a cutoff frequency range of approximately 220Hz - 18kHz on a MOS6581 fitted with 470pF capacitors. The function mapping FC to cutoff frequency has the shape of the tanh function, with a discontinuity at FCHI = 0x80. In contrast, the MOS8580 almost perfectly corresponds with the specification of a linear mapping from 30Hz to 12kHz. The mappings have been measured by feeding the SID with an external signal since the chip itself is incapable of generating waveforms of higher fundamental frequency than 4kHz. It is best to use the bandpass output at full resonance to pick out the cutoff frequency at any given FC setting. The mapping function is specified with spline interpolation points and the function values are retrieved via table lookup. NB! Cutoff frequency characteristics may vary, we have modeled two particular Commodore 64s.

f0_points

protected int[][] f0_points

f0_count

protected int f0_count

Constructor Detail

Filter

public Filter()

Constructor.

Method Detail

clock

public void clock(int voice1,
         int voice2,
         int voice3,
         int ext_in)

SID clocking - 1 cycle

Parameters:

voice1 -

voice2 -

voice3 -

ext_in -

clock

public void clock(int delta_t,
         int voice1,
         int voice2,
         int voice3,
         int ext_in)

SID clocking - delta_t cycles.

Parameters:

delta_t -

voice1 -

voice2 -

voice3 -

ext_in -

output

public int output()

SID audio output (16 bits). SID audio output (20 bits).

Returns:

enable_filter

public void enable_filter(boolean enable)

Enable filter.

Parameters:

enable -

set_chip_model

public void set_chip_model(ISIDDefs.chip_model model)

Set chip model.

Parameters:

model -

reset

public void reset()

SID reset.

writeFC_LO

public void writeFC_LO(int fc_lo)

Register functions.

Parameters:

fc_lo -

writeFC_HI

public void writeFC_HI(int fc_hi)

Register functions.

Parameters:

fc_hi -

writeRES_FILT

public void writeRES_FILT(int res_filt)

Register functions.

Parameters:

res_filt -

writeMODE_VOL

public void writeMODE_VOL(int mode_vol)

Register functions.

Parameters:

mode_vol -

set_w0

protected void set_w0()

set_Q

protected void set_Q()

Set filter resonance.

fc_default

public void fc_default(SID.FCPoints fcp)

Return the array of spline interpolation points used to map the FC register to filter cutoff frequency.

Parameters:

fcp - IN/OUT parameter points and count

fc_plotter

public PointPlotter fc_plotter()

cubic_coefficients

protected void cubic_coefficients(double x1,
                      double y1,
                      double x2,
                      double y2,
                      double k1,
                      double k2,
                      Filter.Coefficients coeff)

Calculation of coefficients.

Parameters:

x1 -

y1 -

x2 -

y2 -

k1 -

k2 -

coeff -

interpolate_brute_force

protected void interpolate_brute_force(double x1,
                           double y1,
                           double x2,
                           double y2,
                           double k1,
                           double k2,
                           PointPlotter plotter,
                           double res)

Evaluation of cubic polynomial by brute force.

Parameters:

x1 -

y1 -

x2 -

y2 -

k1 -

k2 -

plotter -

res -

interpolate_forward_difference

protected void interpolate_forward_difference(double x1,
                                  double y1,
                                  double x2,
                                  double y2,
                                  double k1,
                                  double k2,
                                  PointPlotter plotter,
                                  double res)

Evaluation of cubic polynomial by forward differencing.

Parameters:

x1 -

y1 -

x2 -

y2 -

k1 -

k2 -

plotter -

res -

x

protected double x(int[][] f0_base,
       int p)

y

protected double y(int[][] f0_base,
       int p)

interpolate

public void interpolate(int[][] f0_base,
               int p0,
               int pn,
               PointPlotter plotter,
               double res)

Evaluation of complete interpolating function. Note that since each curve segment is controlled by four points, the end points will not be interpolated. If extra control points are not desirable, the end points can simply be repeated to ensure interpolation. Note also that points of non-differentiability and discontinuity can be introduced by repeating points.

Parameters:

p0 -

pn -

plotter -

res -