realizeNTF

Modulator topology coefficients from NTF

Since R2026a

collapse all in page

Syntax

[a,g,b,c] = realizeNTF(ntf,form,stf)

Description

[a,g,b,c] = realizeNTF(ntf,form,stf) converts an NTF into a set of coefficients for a particular modulator topology.

Examples

collapse all

Open Live Script

Define delta-sigma modulator parameters.

order = 5;      % Modulator order
OSR = 32;       % Oversampling ratio
N = 8192;       % Number of simulation points
f = 85;         % Input signal frequency bin
amp = 0.5;      % Input signal amplitude (should be less than 1)
fB = ceil(N/(2*OSR));

Create a sinusoidal input signal.

u = amp * sin(2*pi*f/N * (0:N-1)) % Create a sine wave input
u = 1×8192

         0    0.0326    0.0650    0.0972    0.1289    0.1601    0.1906    0.2203    0.2491    0.2768    0.3034    0.3286    0.3525    0.3748    0.3956    0.4147    0.4320    0.4475    0.4611    0.4727    0.4823    0.4899    0.4953    0.4987    0.5000    0.4991    0.4961    0.4911    0.4839    0.4746    0.4634    0.4502    0.4350    0.4181    0.3993    0.3789    0.3568    0.3332    0.3082    0.2819    0.2544    0.2258    0.1963    0.1659    0.1348    0.1032    0.0711    0.0387    0.0061   -0.0264

Synthesize the noise transfer function (NTF).

H = synthesizeNTF(order, OSR, 1)
H =
 
         (z-1) (z^2 - 1.997z + 1) (z^2 - 1.992z + 1)
  ----------------------------------------------------------
  (z-0.7778) (z^2 - 1.613z + 0.6649) (z^2 - 1.796z + 0.8549)
 
Sample time: 1 seconds
Discrete-time zero/pole/gain model.
Model Properties

Realize the NTF into coefficients for a CRFB modulator structure.

[a, g, b, c] = realizeNTF(H, 'CRFB')
a = 1×5

    0.0007    0.0084    0.0550    0.2443    0.5579


g = 1×2

    0.0028    0.0079


b = 1×6

    0.0007    0.0084    0.0550    0.2443    0.5579    1.0000


c = 1×5

     1     1     1     1     1

Assemble the final ABCD matrix.

ABCD = stuffABCD(a, g, b, c, 'CRFB')
ABCD = 6×7

    1.0000         0         0         0         0    0.0007   -0.0007
    1.0000    1.0000   -0.0028         0         0    0.0084   -0.0084
    1.0000    1.0000    0.9972         0         0    0.0633   -0.0633
         0         0    1.0000    1.0000   -0.0079    0.2443   -0.2443
         0         0    1.0000    1.0000    0.9921    0.8023   -0.8023
         0         0         0         0    1.0000    1.0000         0

Run the simulation.

[v,xn,xmax,y] = simulateDSM(u, ABCD)
v = 1×8192

     1    -1    -1     1     1    -1     1    -1     1     1    -1     1     1     1    -1     1     1    -1     1    -1     1     1     1     1     1    -1     1    -1     1     1     1     1     1    -1     1     1    -1     1    -1     1    -1     1     1     1    -1    -1     1     1    -1     1


xn = 5×8192

   -0.0007    0.0000    0.0007    0.0001   -0.0005    0.0003   -0.0002    0.0006    0.0001   -0.0004    0.0005    0.0000   -0.0004   -0.0008    0.0001   -0.0003   -0.0007    0.0003   -0.0000    0.0009    0.0006    0.0003   -0.0001   -0.0004   -0.0008    0.0002   -0.0001    0.0009    0.0006    0.0002   -0.0002   -0.0005   -0.0009    0.0001   -0.0004   -0.0008    0.0001   -0.0003    0.0006    0.0001    0.0009    0.0004   -0.0001   -0.0007    0.0001    0.0008    0.0002   -0.0005    0.0002   -0.0005
   -0.0084   -0.0002    0.0087    0.0017   -0.0055    0.0039   -0.0026    0.0075    0.0016   -0.0044    0.0062    0.0010   -0.0045   -0.0100    0.0010   -0.0038   -0.0087    0.0029   -0.0013    0.0111    0.0075    0.0036   -0.0004   -0.0047   -0.0092    0.0028   -0.0013    0.0112    0.0075    0.0035   -0.0008   -0.0056   -0.0108    0.0004   -0.0046   -0.0100    0.0008   -0.0047    0.0061    0.0006    0.0112    0.0054   -0.0010   -0.0081    0.0009    0.0102    0.0031   -0.0049    0.0032   -0.0053
   -0.0633   -0.0068    0.0604    0.0126   -0.0407    0.0269   -0.0202    0.0544    0.0147   -0.0294    0.0484    0.0125   -0.0276   -0.0720    0.0058   -0.0302   -0.0701    0.0124   -0.0185    0.0735    0.0525    0.0281   -0.0001   -0.0323   -0.0690    0.0161   -0.0128    0.0803    0.0595    0.0341    0.0038   -0.0320   -0.0738    0.0046   -0.0330   -0.0772   -0.0019   -0.0431    0.0349   -0.0040    0.0761    0.0390   -0.0061   -0.0600    0.0032    0.0741    0.0261   -0.0316    0.0269   -0.0348
   -0.2443   -0.0490    0.2066    0.0423   -0.1585    0.0888   -0.0833    0.1978    0.0647   -0.0984    0.1934    0.0734   -0.0745   -0.2534    0.0218   -0.1157   -0.2814    0.0102   -0.1075    0.2386    0.1820    0.1070    0.0104   -0.1113   -0.2619    0.0435   -0.0623    0.2931    0.2423    0.1688    0.0682   -0.0641   -0.2330    0.0452   -0.0982   -0.2807   -0.0191   -0.1825    0.0998   -0.0416    0.2637    0.1457   -0.0142   -0.2231    0.0006    0.2749    0.1164   -0.0948    0.1221   -0.1046
   -0.8023   -0.2752    0.5256    0.0641   -0.5804    0.1557   -0.3792    0.4995    0.1453   -0.3567    0.5640    0.2627   -0.1730   -0.7752    0.0252   -0.4171   -1.0153   -0.1975   -0.6057    0.4545    0.3477    0.1701   -0.1011   -0.4921   -1.0330   -0.1531   -0.4965    0.6285    0.5829    0.4586    0.2274   -0.1435   -0.6917    0.1447   -0.2887   -0.9159   -0.1781   -0.7326    0.0971   -0.3451    0.6185    0.3323   -0.1304   -0.8189   -0.1851    0.7052    0.3034   -0.3277    0.3557   -0.3216


xmax = 5×1

    0.0014
    0.0167
    0.1147
    0.3735
    1.1084


y = 1×8192

         0   -0.7697   -0.2102    0.6227    0.1930   -0.4203    0.3463   -0.1588    0.7486    0.4221   -0.0533    0.8926    0.6152    0.2018   -0.3796    0.4399    0.0149   -0.5679    0.2635   -0.1330    0.9368    0.8375    0.6654    0.3977    0.0079   -0.5338    0.3431   -0.0054    1.1124    1.0575    0.9220    0.6776    0.2916   -0.2736    0.5440    0.0902   -0.5591    0.1551   -0.4244    0.3790   -0.0907    0.8443    0.5286    0.0355   -0.6841   -0.0820    0.7763    0.3421   -0.3216    0.3293

Analyze the output.

figure;
spec = fft(v .* ds_hann(N)) / (N/4);
plot(dbv(spec));
axis([0 N/2 -120 0]);
title('Spectrum of Modulator Output');
xlabel('Frequency Bin');
ylabel('dBV');
grid on;

Figure contains an axes object. The axes object with title Spectrum of Modulator Output, xlabel Frequency Bin, ylabel dBV contains an object of type line.

Calculate SNR.

snr = calculateSNR(spec(1:fB),f)
snr = 
82.5313

Calculate the NTF and STF of the modulator.

[ntf,stf] = calculateTF(ABCD,1)
ntf =
 
         (z-1) (z^2 - 1.997z + 1) (z^2 - 1.992z + 1)
  ----------------------------------------------------------
  (z-0.7778) (z^2 - 1.613z + 0.6649) (z^2 - 1.796z + 0.8549)
 
Sample time: 1 seconds
Discrete-time zero/pole/gain model.
Model Properties

stf =
 
  1
 
Static gain.
Model Properties

Map the ABCD matrix back to coefficients of the CRFB topology.

[a,g,b,c] = mapABCD(ABCD,'CRFB')
a = 1×5

    0.0007    0.0084    0.0550    0.2443    0.5579


g = 1×2

    0.0028    0.0079


b = 1×6

    0.0007    0.0084    0.0550    0.2443    0.5579    1.0000


c = 1×5

     1     1     1     1     1

Dynamically scale the ABCD matrix so that the state maxima are less than specified limit 1.

nlev = 2;
xlim = 1;
ymax = nlev+5;
[ABCDs,umax]=scaleABCD(ABCD,nlev,f,xlim,ymax,N)
ABCDs = 6×7

    1.0000         0         0         0         0   -0.0007    0.0007
    1.0000    1.0000   -0.0028         0         0   -0.0084    0.0084
    1.0000    1.0000    0.9972         0         0   -0.0633    0.0633
         0         0    1.0000    1.0000   -0.0079   -0.2443    0.2443
         0         0    1.0000    1.0000    0.9921   -0.8023    0.8023
         0         0         0         0   -1.0000    1.0000         0


umax = 
8192

Input Arguments

collapse all

Noise transfer function of the delta-sigma modulator in pole zero form, specified as a zpk object.

Note

Poles of NTF must match those of STF to realize STF without the addition of extra state variables.

String specifying the modulator topology. The supported topologies are:

formModulator Topologu
CRFBCascade of resonators, feedback form
CRFBDCascade of resonators, feedback form, with quantizer delay
CRFFCascade of resonators, feedforward form
CRFFDCascade of resonators, feedforward form, with quantizer delay
CIFBCascade of integrators, feedback form
CIFBDCascade of integrators, feedback form, with quantizer delay
CIFFCascade of integrators, feedforward form
CIFFDCascade of integrators, feedforward form, with quantizer delay

Data Types: double

Signal transfer function of the delta-sigma modulator in pole zero form, specified as a zpk object.

Note

Poles of NTF must match those of STF to realize STF without the addition of extra state variables.

Output Arguments

collapse all

Feedback coefficients from the quantizer or feedforward coefficients to the quantizer, returned as a real-valued vector.

Resonator coefficients, returned as a real-valued vector.

Feed-in coefficients from the modulator input to each integrator, returned as a real-valued vector.

Integrator inter-stage coefficients, returned as a real-valued vector. In unscaled modulators, c is all ones.

Version History

Introduced in R2026a

See Also

| | | | | | | |