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How work sigma delta modulation in audio

Educational line

Sigma delta 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].

Unlike multibit (16, 24, ... bit) modulation with "low" sampling frequencies (44, 48, ... kHz), sigma delta modulation 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 work sigmadelta modulator

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

Устройство дельта сигма модулятора аудио

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).

Noise shaping

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.

Author: Yuri Korzunov, 2014 September 11.

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Released new studio audio converter AuI ConverteR 48x44 v. 6.2.2 CD ripper, ISO, DFF, DSF, WAV, FLAC, AIFF, ALAC. Fixed some bugs of displaying output formats and some minor bugs.

Released new studio audio converter AuI ConverteR 48x44 v. 6.2 CD ripper, ISO, DFF, DSF, WAV, FLAC, AIFF, ALAC. Apllied downmix multichannel to stereo (5.1 to 2.0) and translation of user interface to Russian and German (partitially yet).

Final of the article about click matter into DSF and PCM (FLAC, WAV, AIFF, etc.) files after ISO (1-bit audio) extraction. Clicks inside audio stuff.

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