Category: Audio and video

Noise – Part 4

To summarize and simplify, something like the following happens. A PCM data stream is fed to the DAC input through the I2S connector, oversampling is added, dithering, and then the stream is sent to a noise shaping decoder. At the end, a one-bit stream is formed, it passes through an analog low-pass filter, where the final audio signal that we hear is already obtained.

A multi-bit DAC is more complex: in addition to the above, it also uses DEM technology.

WWW
If you want to understand the details, please read the materials in the links, there is information not only about sigma-delta-DAC, but also about sigma-delta-ADC.

Article on delta-sigma modulation on microsin.net
Notes from E. I. Vologdin’s lecture on sigma-delta modulation
Modern digital-to-analog converters are complex devices. But the use of these technologies is necessary to artificially expand the dynamic range, and they are generally used to overcome the limitations of CDDA and MP3 formats. If the recordings were originally published in high resolution PCM (192 × 24), or better in DSD format, then there would not be as many technologies and complex digital transformations. In the case of DSD, interference with the quantized signal is not necessary at all, at least during playback.

Conclution
The development of recording and playback in the digital age has been challenging and arduous. With the invention of the compact disc, analog audio practically ceased to exist in just a couple of decades. Good or bad: everyone decides for themselves, but I would like the possibility to choose to remain. If it is not between digital and analog, at least how and with what quality to listen to your favorite music. Unfortunately, now there is hardly any other option. Few people are releasing high definition music these days, aside from crawler enthusiasts. The only fault for this is the recording studios, who decided to limit themselves to a single format: CDDA.

All that’s left is to sympathize with the musicians! How much effort and time they put into creating music, but their work isn’t even preserved in decent quality. The solution would be to record on the master tape or at least on DSD. But the recording studios will not waste extra effort, because they are satisfied with the current situation (PDM).

Noise – Part 3

In addition to those considered, other technologies are used, as well as their combinations and variations.

Manufacturers especially love experimenting with digital filters and modulators, inventing more and more digital filters that affect the signal for both better and worse. Modern DAC digital signal processing algorithms are often complex and include all of the above, as well as manufacturers’ own developments. Of course, manufacturers do not publish algorithms for filters and modulators; at best, they provide a rough block diagram. Therefore, it remains only to assume what actually happens with the audio signal inside one or another digital-to-analog converter.

Sigma delta converters
Sigma-delta digital-to-analog converters have evolved apart from multi-bit DACs. The base was taken, as its name indicates, sigma-delta modulation, in the literature it is usually denoted by the abbreviation SDM. In sigma-delta modulation, the absolute value of the signal amplitude is not transmitted per unit time, as in multi-bit DACs, but the signal changes from the previous value. So if the amplitude increases, 1 is transmitted, and if it falls – 0. A similar principle was already described in the section on DSD.

Early sigma-delta DACs were completely 1-bit, but due to the high sample rate, they provided a dynamic range of approximately 129 dB. The sampling frequency is 44.1 kHz. The chosen frequency probably saved hardware resources due to simplification of calculations during interpolation.

At the beginning, a frequency of 2.8 MHz was used, this is 44.1 kHz, increased 64 times. Now the frequency can be different, it is determined by the internal architecture of the DAC itself. It is generally based on frequency grids in multiples of 44.1 kHz and 48 kHz, with a multiplier of 64, 128, 256, 512, 1024.

Over time, delta-sigma DACs have almost completely supplanted multibit, simply for economic reasons. First, its component quality and precision requirements are much lower than multi-bit DACs, and consequently the cost price is lower. Second, in the 1980s and 1990s, the cost of implementing interpolation and noise shaping for a one-bit modulator was significantly less than for 16-bit. Now, with the development of technology, this is not that critical, and many sigma-delta DACs, like multibits, have multiple levels of output. But due to the multiple increase in frequency, the requirements for the components are not still very high, so the first advantage continues to this day.

Modern sigma-delta DACs are complex and include almost all of the technologies listed in the previous chapter. I will give an example of the internal structure of one of the simple sigma-delta-DACs from the Vologdin lectures.

Input 16-bit digital samples with a sampling frequency of 44.1 kHz are fed into the digital oversampling filter. The scheme uses a non-recursive quadruple oversampling FIR (finite impulse response) interpolation filter with a linear phase response. In the first modulation stage, as a result of requantization, the number of bits in the samples is reduced from 16 to 14 and first-order SDM is used. Then a further resampling is performed using two steps (Kos = 32 and 2). A noise signal is introduced on the path between these stages, performing the “Dithering” operation with a noise level equal to minus 20 dB. It reduces the non-linearity of the transfer function due to quantization errors. The overall oversampling factor is 256 and the sampling frequency increases to 11.29 MHz. In the second modulation stage, second-order SDM is used and a one-bit digital stream is formed. The DAC output is connected to a digital time pulse modulator, which converts the digital data into a density modulated pulse sequence (PDM).

Noise – Part 3

Recording audio

To record and mix the audio signal, they started using decimation, this is the reverse process, oversampling with downsampling and quantization bit depth. The signal is recorded at a high sample rate and quantization bit depth, for example 176.4 or 192 kHz with a 24 bit bit depth, and removing some of the samples using a digital filter is “compressed” to the CDDA standard – 44.1 kHz, 16 bits. This approach can slightly reduce quantization noise.

Below is an illustration of the algorithm for decimating a discrete signal with a factor of 2. Red dots indicate samples, solid lines – a continuous signal, representing these samples. Above is the original signal. In the middle, the same signal after filtering on a digital low pass filter. Below is the decimated signal.

Dithering
Dithering (dithering) – A method of mixing pseudo-random noise when digitizing or playing a sound signal. This technology has two purposes:

linearization of the quantizer / requantizer transfer function;
decorrelation of quantization errors.
Quantization noise has a correlation, that is, a relationship with the main signal. This creates parasitic harmonics that follow the waveform. They affect perception creating a “diffuse” sound. Correlation can be removed by adding specially patterned noise to the main signal, thus converting the correlated quantization noise to ordinary white noise. This increases the overall noise level a bit, but is good for perception.

Dithering in the image processing example: before and after
Dithering in the image processing example: before and after
Noise modeling
Noise Shaping (NS) technology can significantly reduce noise introduced during quantization, re-entrapment, and dithering.

Noise modeling works like this: the quantized signal at the input is compared to the signal at the output of the requantizer, a difference (error) is formed, which is subtracted from the main signal. This compensates for distortions introduced by the requantizer and during the dithering process. A so-called feedback is formed, which seeks to compensate for the error in the input and output of the requanter. This technology works like negative feedback in an op amp, except that all conversions are done digitally.

Here’s a diagram of a first-order requantizer, but as a rule, requanters are used up to order 9-12.
Here’s a diagram of a first-order requantizer, but as a rule, requanters are used up to order 9-12.
This technology has its drawbacks. Using NS introduces a large amount of noise in the high frequency region, making it necessary to apply a low pass filter, with a cutoff frequency close to the upper cutoff frequency. In practice, together with NS, dithering is also always used, the result of their joint work is much better by ear.

Dynamic item matching
Dynamic Element Matching (DEM) is a technology that generates various signal levels at the DAC output. It looks like a cross between a single bit and multi-bit DAC. DEM is used to reduce deterministic errors when using sigma-delta modulation (SDM). These errors, like quantization noise, are highly correlated with the signal at the one-bit modulator output and therefore significantly affect the perception of the audio signal.

This technology also reduces the requirements for the analog filter, because the waveform is close to the reproduced waveform even before filtering. DEM is implemented with several pins connected to a common bus, which form the output signal of the DAC.

Noise – Part 2

Also, poor sound engineers love to shake and level everything using limiters and compressors, the principle of which is based on reducing the dynamic range.

Almost all samples go through all this torture. Even when using a simple EQ, the signal passes through a digital filter, which introduces rounding noise by at least half a quantization step. During final mixing, all samples are collected in a sequence, respectively, the noise from each being added to the noise from another resampling. But that’s not all: during playback, the DAC adds its own noise and rounding noise. Can you imagine what really remains of the useful signal?

Noise control techniques
To remedy this unfortunate situation, special noise reduction technologies have been developed. Let’s see the most basic.

Oversampling
Oversampling technology has been used since the days of multi-bit DACs to compensate for losses caused by noise. The principle of oversampling is that intermediate samples are added to existing discrete samples, repeating the approximate waveform. Intermediate samples are calculated by mathematical interpolation or filled with zero values ​​and transmitted to a digital filter. Generally, both approaches are called interpolation and the digital filter is called interpolation. The simplest interpolation method is linear interpolation, and the simplest digital filter can be a low-pass filter.

Below is an illustration of an interpolation algorithm for a discrete signal with a factor of 2. Red dots indicate the original signal samples, solid lines – a continuous signal, representing these samples. Above is the original signal. In the middle is the same signal with inserted zero counts (green dots). Bottom: interpolated signal (blue dots: interpolated sample values).

At first they started using only oversampling with an increase in frequency, for example from 44.1 to 176.4 kHz. Subsequently, oversampling was used with an increase in the sampling frequency and an increase in the quantization bit depth; This process is called recantization.

Although oversampling introduces rounding noise, it also reduces overall noise density by expanding the dynamic range of the signal, and post-processing of the signal will have less impact. Each doubling of the sample rate expands the dynamic range by approximately one quantization step (6 dB) minus the rounding noise.

Just to be able to use oversampling, they began to produce multi-bit DAC chips that supported up to 192×24 digital stream on input. DSP (digital signal processor) -based hardware upsamplers also appeared.

Of course, the use of oversampling technology improved the characteristics of the audio signal, but the situation did not change drastically: the noise level remained high. Therefore, other technologies began to be applied.