Delta sigma modulator PSD simulation

Hi everyone. I built a first-order delta-sigma modulator, as shown in the figure, using Fourier transform to simulate PSD, but it is not the same as the simulation I saw in related papers, please help check where the problem is

attach my code and simulink module

https://lurl.cc/6eYHF

Answer 1

[Pragati]

Your DSM implementation is likely fine—the mismatch is coming from how the PSD is being computed.

Key things to fix

• Don’t use raw FFT directlyA simple FFT → |·|² → log will give inaccurate PSD. Use:
• Windowing (e.g., Hann)
• Averaging (e.g., Welch)
• Use long simulationsDSM noise shaping requires large sample sizes. Short runs produce noisy and misleading PSD.
• Discard transientsThe initial portion of the simulation distorts the spectrum—remove it before computing PSD.
• Average multiple segmentsA single FFT realization is not sufficient. Averaging is necessary to match published results.
• Normalize correctlyEnsure proper scaling for:
• Sampling frequency
• One-sided spectrum
• Check expected slopeFor a first-order DSM, the noise floor should rise (~20 dB/dec). If not, the issue is in PSD estimation.

Recommended approach

Instead of building everything manually, you can validate your results using Mixed-Signal Blockset:

• Use the Delta-Sigma Modulator block / ADC examples

https://www.mathworks.com/help/msblks/ref/deltasigmamodulator.html

https://www.mathworks.com/help/msblks/examples.html?s_tid=CRUX_topnav&category=data-converters

• Run long simulations and use consistent analysis workflows for PSD/SNR
• These examples already capture correct NTF-based noise shaping and avoid common PSD pitfalls