predictSNR

Predict SNR for different input amplitudes

Since R2026a

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Syntax

[snr,amp,k0,k1,sigma_e2] = predictSNR(ntf,osr,amp,f0)

Description

[snr,amp,k0,k1,sigma_e2] = predictSNR(ntf,osr,amp,f0) predicts the signal-to-noise ratio (SNR) versus the input amplitude curve of a binary delta-sigma modulator using the describing function method [1].

The describing function method assumes that the quantizer processes signal and noise components separately. The method models the quantizer as two linear gains, k0 and k1 and an additive white Gaussian noise source of power sigma_e2. The function assumes nearly infinite gain at the loop filter of the modulator at the test frequency.

Examples

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Open Live Script

Define a second-order delta-sigma modulator and the system parameters for the simulation.

order = 2;              % The "Order" of the modulator
OSR = 64;               % Oversampling Ratio (fs / 2*BW)
nlev = 2;               % Number of quantizer levels (2 = Binary: +1 or -1)
N = 2^14;               % Number of points for the FFT simulation (16,384)
test_freq = 5;          % The bin index for our test sine wave (must be an integer)

Determine the in-band frequency range for SNR calculation.

fB = floor(N/(2*OSR));

Synthesize the noise transfer function (NTF). This creates a mathematical filter that pushes noise to high frequencies.

ntf = synthesizeNTF(order, OSR);

Realize the NTF as a CIFB circuit topology.

[a, g, b, c] = realizeNTF(ntf, 'CIFB');

Create the state-space matrix for the simulator.

abcd = stuffABCD(a, g, b, c, 'CIFB');

Scale the ABCD matrix so that the internal voltages stay within the range of the quantizer.

[abcd_scaled, umax] = scaleABCD(abcd, nlev);

To set up the simulation, define a range of input amplitudes to test, from very quiet to loud. Run simulation.

amp_db = -110:10:-10;        % Decibels relative to Full Scale (dBFS)
amp_lin = 10.^(amp_db/20);   % Convert dB to linear voltage
snr_sim = zeros(size(amp_db)); % Pre-allocate space for results
for i = 1:length(amp_db)
    % Generate a test sine wave at the current amplitude
    t = 0:N-1;
    u = amp_lin(i) * sin(2*pi*test_freq/N * t);

    % Run the Delta-Sigma Modulator Simulation
    % Returns 'v', which is the high-speed 1-bit output bitstream.
    v = simulateDSM(u, abcd_scaled, nlev);

    % Spectral Analysis:
    % 1. Apply a Hann window to prevent spectral leakage
    w = ds_hann(N);
    % 2. Perform the FFT
    V = fft(v .* w);
    % 3. Calculate SNR of the in-band portion
    % calculateSNR sums signal power at 'test_freq' and noise in remaining bins.
    snr_sim(i) = calculateSNR(V(1:fB), test_freq);
end

Predict the theoretical SNR. Calculate a peak value to anchor the predicted SNR curve.

peak_snr_theory = 10*log10( ((2*order+1)/(2*pi^(2*order))) * (OSR^(2*order+1)) );
snr_pred = peak_snr_theory + amp_db;

Plot the predicted and simulated SNR.

figure('Color', 'w', 'Name', 'Delta-Sigma Performance');

% Plot the Theoretical Limit (The Blue Line)
plot(amp_db, snr_pred, 'b-', 'LineWidth', 2); hold on;

% Plot the Actual Simulated Results (The Red Dots)
plot(amp_db, snr_sim, 'ro', 'MarkerFaceColor', 'r', 'MarkerSize', 8);

% Formatting the plot
grid on;
axis([-125 5 -20 120]); % Set fixed view for comparison
xlabel('Input Amplitude (dBFS)');
ylabel('SNR (dB)');
title(sprintf('Order %d Delta-Sigma Modulator (OSR=%d)', order, OSR));
legend('Predicted Theory (Ideal)', 'Simulated Bitstream', 'Location', 'SouthEast');

Figure Delta-Sigma Performance contains an axes object. The axes object with title Order 2 Delta-Sigma Modulator (OSR=64), xlabel Input Amplitude (dBFS), ylabel SNR (dB) contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted Theory (Ideal), Simulated Bitstream.

Input Arguments

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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.

Oversampling ratio of the delta-sigma modulator, specified as a real scalar. It is the ratio of the delta-sigma modulator sampling rate to the Nyquist rate.

Data Types: double

Input amplitude against which the function predicts SNR, specified as a row vector in dB. 0 dB means full-scale (peak value 1) sine wave.

Note

The function assumes the amplitudes are sorted in increasing order. Once the function detects instability, it sets the remaining SNR values to -Inf.

Data Types: double

Center frequency of the binary delta-sigma modulator, specified as a real scalar.

Data Types: double

Output Arguments

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Calculated SNR values, returned as a row vector in dB.

Amplitudes used to calculate SNR, returned as a row vector in dB.

Signal gain of the quantizer model, returned as a row vector.

Noise gain of the quantizer model, returned as a row vector.

Mean square value of the noise in the quantizer model, returned as a row vector.

References

[1] Ardalan, S., and J. Paulos. “An Analysis of Nonlinear Behavior in Delta - Sigma Modulators.” IEEE Transactions on Circuits and Systems 34, no. 6 (1987): 593–603. https://doi.org/10.1109/TCS.1987.1086187.

Version History

Introduced in R2026a

See Also

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