simulateDSM

Simulate delta-sigma modulator with given input

Since R2026a

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Syntax

[v,xn,xmax,y] = simulateDSM(u,ABCD,ntf,nlev,x0)

Description

[v,xn,xmax,y] = simulateDSM(u,ABCD,ntf,nlev,x0) simulates a delta-sigma modulator with a given input.

Examples

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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

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Input sequence to the delta-sigma modulator, specified as an m×N matrix. m is the number of inputs. Full scale corresponds to an input of magnitude nlev − 1, where nlev is the number of quantizer levels.

Data Types: double

State space description of the loop filter of the delta-sigma modulator, specified as a matrix.

Data Types: double

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

Note

The function assumes the modulator STF is unity.

Number of levels in the quantizer, specified as a real scalar for a single quantizer or real-valued vector for multiple quantizers.

Initial state of the modulator, specified as a real scalar.

Data Types: double

Output Arguments

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Samples of the output of the modulator, one for each input sample, returned as a matrix.

Internal states of the modulator, one for each input sample, returned as an n×N matrix.

Maximum absolute state of each state variable, returned as a vector.

Samples of quantizer input, one per input sample, returned as a matrix.

Version History

Introduced in R2026a

See Also

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