Delta-Sigma Modulation. How Does It Work in Audio?

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Audio Basis - articles about audio

Delta-sigma modulation for high resolution audio it's 1-bit (digital) stream of 0 and 1. Thus coded audio signal. The format used for storing DSF, DFF and ISO [1-bit HD audio].

March 26, 2024 updated

Author: Yuri Korzunov,
Audiophile Inventory's developer with 25+ year experience in digital signal processing,
author of the articles that make audio easy for beginners

What is sigma-delta modulation in audio (DSD)?

Unlike multibit (16, 24, ... bit) modulation with "low" sampling frequencies (44, 48, ... kHz), sigma delta modulation (DSD audio) has super high sample rates:

1. 44 kHz x64(D64) = 2.8 MHz,

2. 44 kHz x128(D128) = 5.6 MHz.

Thus compensated for the loss of information due reducing of sample bit depth from 16 or 24 bit to 1.

How sigma-delta modulator works

We will consider the conversion of multibit audio PCM (CD audio, audio files WAV, FLAC, AIFF, ...) to 1-bit audio files (DSF, DFF) using sigma delta modulation.

Sigma delta modulator inside

1. Delta-sigma modulator first integrates a multibit (input) signal (passes through an integrator [Low Frequency Pass Filter - LF]).

2. Output multilevel signal from integrator output divided to 1 and 0 (more zero / less zero). This is delta sigma modulated signal.

3. For decreasing of error output signal, it converted back to multilevel (multibit PCM like "analog signal") signal into DAC. Multilevel PCM signal from DAC subtracts from input PCM signal. So corrected output (from delta sigma modulator) signal. It (when will demodulated) will more approach to input signal.

4. At output of demodulator appear 1 and 0 sequence.Its spectrum is useful audio signal (into band 0 ... 20 kHz) and noise with level -47 dB (for simplest modulator with sampling rate 44100 Hz x 64).

Thus, if pass the sequence of 1 and 0 through the low pass filter (0 ... 20 kHz), we distinguish the input signal. But in the spectral range of the useful signal (0 ... 20 kHz) will present the same noise with level -47 dB. Therefore impossible use this signal for high qualitative audio.

5. For reducing noise level into band 0 ... 20 kHz we can:

5.1. Increase sample rate. But it is not effective - increasing sample rate 2 times decrease noise level at 6 dB.

5.2. Apply noise shaping. Noise shaping extrudes noise energy out if band 0 ... 20 kHz. It decrease noise level to -145 дБ. It is compable for high resolution audio.

DAC for 1-bit sigma delta modulator is low frequency filter. It suppress concentrated by noise shaping energy out of band 0 ... 20 kHz. Thus we get high qualitative audio signal into band 0 ... 20 kHz.

For experiments with sigma delta modulation you can use free version of HD audio file converter AuI ConverteR 48x44 for convertation PCM to DSF and contrariwise.