Digital Audio Recording

Firstly lets have a whole picture of Record System.

The analog waveform is filtered and time sampled and its amplitude is quantized by an analog-to-digital (A/D) converter.
Binary numbers are represented as a series of modulated code pulses representing waveform amplitudes and sample times.
If two channels are sampled, the data can be multiplexed to form one data stream.
Data can be manipulated to provide synchronization and error correction, and auxiliary data can be added as well.
Upon playback, the data is demodulated, decoded and error-corrected to recover the original amplitudes at sample times, and the analog waveform is reconstructed by a digital-to-analog (D/A) converter and lowpass filter.

Dither

Dither is added to the input audio signal to decorrelate the quantization error form the signal.
Although it reduces distortion, dither adds noise to the audio signal.
- Distortion does not mean noise.
- Here, noise means white noise and distortion means color noise (with harmonic content).
Perceptually, dither is beneficial because noise is more readily tolerated by the ear than distortion.

Input lowpass filter (LPF)

To bandlimit the signal and its entire harmonic content to frequencies below the half-sampling Nyquist frequency.
To avoid aliasing problem, we will use anti-aliasing filter.

Higher order filter

Approximates ideal brick-wall frequency response more closely
Results in more significant phase shift as compared with low order filter

Problem with analog filters

Sensitive to temperature and humidity
Aging problem
Noise-prone
Not reliable
Expensive (calibration for precision)
Not flexible

In practice, analog filters are replaced by digital filters if possible.

Digital filters can only be used in Digital signals. To meet this requirement, we need to meet nyqiust sampling rate and quite often we do oversampling to let there are enough room for digital system to filter.

S/H circuit

The sample-and-hold circuit performs two simple yet critical operations:

It time samples the analog waveform at a periodic rate, putting the sampling theorem into practice.
It holds the analog value of the sample while the analog-to-digital converter outputs the corresponding digital word.

We basically sample the inputs and hold it as a buffer (because the signal keeps changing). ADC need time to work with the input.

Conceptually, an S/H circuit is a capacitor and a switch.

When it samples, switch to the ‘Sample’ point, charge up the capacitor. -> It takes time

When it holds the value, switch to the ‘Hold’ point, the capacitor maintains the voltage level for the ADC to operate.

It will discharge and the voltage level drops. -> droop

Acquisition time is the time between the initiation of the sample command and the taking of the sample.
- Should be 0
- Is a function of the analog signal amplitude
Droop is the decrease in hold voltage as the capacitor leaks between sample times.
Variations in absolute timing, called phase jitter, added noise to the sampled signal, and
- must be limited in the clock switching the S/H circuit.
- especially critical for high amplitude, high frequency input signal.

A/D converter

The analog-to-digital converter is the single most critical component in a PCM audio digitization system

Concerns: Conversion time, Accuracy.

The conversion time is the time required for an A/D converter to output a digital word.
- conversion time must be < the sampling period
- Otherwise overrun occurs

Integral linearity

An n-bit converter is not a true n-bit converter unless it guarantees at least $\pm1/2$ $\pm 1/2$ LSB integral linearity.
- In measurement systems, integral linearity is a measure of the device’s deviation from an ideal behaviour.
  - For ADC, the analog-input levels that trigger any two successive output codes should differ by one LSB.
  - The max deviation from this ideal situation in the operation range should be within +/-0.5

Successive approximation A/D converter

Example: Successive approximation in Comparator

Record-processing

After the analog signal is converted to binary numbers, several operations must occur prior to storage or transmission.

PCM systems generally
- multiplex the data,
- add redundancy for error correction,
- perform interleaving (noise protection), and
- provide channel coding (data protection, embedding extra data).
Multiplexing is used to form a single serial bit stream.
Coded parity data is added to provide necessary error protection and correction.

Interleaving

Interleaving is employed to scatter data through the bit stream such that the effect of an error is scattered when data is de-interleaved during play back.

Channel modulation

Channel modulation modulates data prior to storage and transmission.

Extra information is entered into the data stream as subcodes:

specification of sampling frequency,
use of pre-emphasis,
table of contents,
timing and track information, and even
copyright information

Digital Audio Reproduction

Reproduction processing comprises a signal chain that

accepts a degraded coded signal in digital format and
ultimately converts it to a high-fidelity analog waveform.

The modulated audio data, whether it is EFM, MFM, or another code, is typically demodulated to NRZ code, which use amplitude level to represent the binary information.

Modulation coding is used in storage and transmission channels to
- improve coding efficiency and
- make the data self-clocking.
Successful recovery of data is limited by the timebase accuracy of the received clock. Otherwise, jitter (noise) occurs.
Demultiplexing is performed to restore parallel structure to the audio data.
The audio data and coded error-correction data are identified and separated.
Reassemble the data properly in time by de-interleaving and scatter the errors through the bit stream for easier correction.
Correct error samples if it is possible.
Concealment technique is used to hide the error if it cannot be corrected.

Digital-to-analog converter (DAC)

The digital-to-analog (D/A) converter is one of the most critical elements in the reproduction system.

Critical parameters: Linearity & Settling time

Linearity errors in converters generally result in a stochastic deviation
The linearity of a D/A converter, and not the number of bits it uses, measures its accuracy.
Settling time for a D/A converter is the elapsed time between a new input code and the time when the analog output is settled.
D/A converter must have fast settling time.
- Settle time must less than the sampling time, otherwise, there will be overrun.

Output sample and hold (S/H)

Usage:

Remove switching glitches form the D/A converter’s output voltage.
Correct aperture error, an attenuation of high frequencies.
Not all bits change simultaneously when the input to the D/A converter switches, which creates transient glitches.
The output S/H circuit acquires a voltage from the D/A converter only when that circuit has reached a stable output condition so as to deglitch the D/A converter’s output signal.

In ideal case, the output of the D/A converter (after S/H circuit) should be an impulse train.
- Impulse train : all pulse with same amplitude
In practice, it is a pulse train instead.
- pulse train : not all pulse with same amplitude
The difference results in an attenuation of high frequencies (called aperture error).
The narrower the pulse width, the less the aperture error.

Output Lowpass filter

Function of the input LPF:

Remove all frequency content above the half-sampling frequency to prevent aliasing.

Function of the output LPF:

Remove all frequency content above the half-sampling frequency to reconstruct the original analog waveform with the D/A converter’s output pulse amplitude modulation.

Question: Why bother if the frequency content lies above the presumed limit of human audibility?

Ans: It could cause modulation in other downstream equipments through which the signal passes.

LPF Design criteria

Flat passband 一
highly attenuated stop band |
steep cutoff slope

With brick-wall anti-aliasing filters, group delay (due to phase distortion) occurs and cause audible artifacts.

Use of oversampling in ADC

Analog LPFs suffer from problems such as noise, distortion, group delay, and passband ripple, and it is difficult for multibit A/D converters to achieve resolution beyond 18 bits.

In order to overcome this,

analog input (anti-aliasing) filters and multibit A/D converters have been replaced by oversampling A/D converters with digital filters.
- Oversampling A/D converters: modulate their analog inputs into short digital words at very high sampling rate.

The input signal is first passed through a simple analog anti-aliasing filter, which provides sufficient attenuation, but only at a high frequency.

The filtered signal is sampled at a high frequency to extend the Nyquist frequency, and quantized.

After quantization, a digital lowpass filter uses decimation to
- reduce the sampling frequency and
- prevent aliasing at the new, lower sampling frequency.
Noise shaping technique can also be used to shape the noise spectrum to improve the signal-to-noise performance.

Advantages of oversampling A/D converter over conventional A/D converters:

It eliminates brick-wall analog filters.
It achieves increased resolution compared to SAR (successive-approximation) methods by extending the spectrum of the quantization error between analog input and digital output far outside the audio band.