Digitization - From Voltage to the Digital Word PDF

Digitization – from voltage to the digital word If we speaks of an analogue audio signal, it means an electrical (alternating) voltage. Its origin can be either a sound generator (synthesizer, organ) or a recording (microphone). Their electrical parameters behave continuously in time and value. They...

Digitization – from voltage to the digital word If we speaks of an analogue audio signal, it means an electrical (alternating) voltage. Its origin can be either a sound generator (synthesizer, organ) or a recording (microphone). Their electrical parameters behave continuously in time and value. They can be determined as accurately as possible at any time in their measured values. Signal parameters The most important signal parameters are already known. Added to this is the consideration of the spectrum. So the area between the highest and lowest usable frequency. It is defined by the bandwidth. Bandwidth The bandwidth (B) describes the difference between upper and lower limit frequency. Notice: The lower limit frequency does not always have to be 0 Hz! Examples: Bandwidth of (idealized) human hearing: 19980 Hz (20 Hz - 20 kHz) Bandwidth of the phone: 3700 Hz (300 - 4000 Hz) Amplitude The amplitude is the maximum deflection of a periodic oscillation. In audio technology, however, this term is also used for non-periodic signals. This refers to the maximum deflection of a signal. For complex signals, the amplitude is determined for the period of the fundamental oscillation. It does not have to be symmetrical. The measurement takes place without regard to the sign. The conversion in the digital level From the voltage to the coded word over many intermediate steps: Sample and hold Analog Signal During signal conversion, the input signal must not change in many conversion methods. Then the actual AD converter is preceded by a sample-and-hold circuit, which stores the signal value (sample) in such a way that it remains constant during digitization. Special capacitors are used for this. If a converter requires this sample-and-hold circuit, it is usually included Sampling today when implemented as an integrated circuit. Switch (Trigger In) Input Signal Digital Signal Sample and Hold Quantization Quantization is the second step after dissolution into discrete time periods. Here, the individual time segments are evaluated in their amplitude and rounded to the next valid value (quantized). The number of valid levels is defined by the word width. The bit significance runs from the Most Significant Bit (MSB) to the Least Significant Bit (LSB). This order must be followed for the digital word to keep its meaning. Typical resolutions in the audio domain: 8 bits = 256 levels 16 bits = 65536 levels 24 bits = 1677721 levels No matter how high the resolution has been chosen, there is always a difference between the real measured values and the values of the quantization table. This deviation manifests itself as a noise, the so-called quantization noise. The quantization noise represents one of the most important fault values of digital technology. It is important that the distance between the desired signal and noise is as high as possible. This can be done by several techniques: Increase the word width (bit depth) Displacement of the noise energy in the high frequency range (Noise shaping) Non-linear quantization characteristic Bitdepth Increasing the resolution improves the signal-to-noise ratio (SNR) according to the following rule of thumb: SNR = N x 6.02dB + 1.76dB Where N is the number of bits used. This formula applies to sinusoidal signals and can therefore only be used as a rule of thumb: 6 dB dynamic range per bit Nonlinear Quantization In non-linear quantization, larger signal amplitudes are combined in a larger value range and thus with a more coarsely resolution. Whereas small signal amplitudes are quantized at a higher resolution. The advantage is that less quantization noise can be achieved with fewer bits per sample than with linear quantization Noise Shaping In digital audio technology, noise shaping is also filtered according to psychoacoustic specifications in order to make it "quieter" and less intrusive in the overall impression. Thus, in audio technology, the noise energy can be shifted into frequency ranges in which the human ear is less sensitive. This is, for example, the range of 16 kHz to 20 kHz, which is also perceived only poor or not at all by older listeners. Moreover, there are not that much important signal components in this frequency range. In audio technology, Noise shaping is mostly used in conjunction with dithering - this achieves an optimization of the signal-to-noise ratio (SNR). Noise shaping occurs mainly in combination with oversampling, whereby both terms are mistakenly used mostly as a synonym. Especially with the delta-sigma converter noise shaping is essential, since in these systems, the quantization error is relatively large. By correspondingly high oversampling, the quantization noise can even be partially pushed into frequency ranges, which can then be completely separated from the useful signal by a digital filter. Aliasing Alias effects (also known as aliasing effects) are errors that occur when there are frequency components in the signal to be sampled which are higher than the Nyquist frequency (half the sampling frequency). Aliasing effects are noise sounds. The Nyquist-Shannon Sampling Theorem 0-8kHz Sweep 0-8kHz Sweep fSample > 2 * fmax fsampl=16kHz fsampl=8kHz In order for the original signal to be correctly restored, only frequency components smaller than the Nyquist frequency (half the sampling frequency) must be present in the signal to be sampled. However, if there are frequency components that are higher than the Nyquist frequency, these are interpreted as lower frequencies. The higher frequencies pretend to be different frequencies (lower) (see graphic), hence the name Alias. A continuous output signal (red line) is sampled with an inappropriate sampling frequency that is less than required by the sampling theorem. From the measured values obtained by interpolation, a distorted signal with a too large period (blue line). Disturbing frequency components that can lead to aliasing occur during sub-sampling (sampling theorem not complied with). But even if the sampling theorem is followed, aliasing may also occur if the signal to be sampled is superimposed by a noise signal containing frequency components higher than the Nyquist frequency. To avoid such aliasing effects, the input signal is filtered by a low-pass filter (anti-aliasing filter). The filtering effect of this cutting off of the high frequencies can also be described by the terms high cut and treble cut. This filtering must be done before the digitization - a subsequent correction of aliasing effects is not possible. Dither Since the quantization noise often (especially at very small signal levels) does not behave like noise, but is in a tonal context with the usable signal, it can be very noticeable. By adding so-called dither (special noise signal), this correlation between quantization noise and useable signal can be canceled out. The sound quality (especially in quiet passages) increases, despite the metrologically decreased signal-to-noise ratio. Dither should be used if the original bitrate is to be reduced. Space Requirement (PCM Audio): 44,100 measured values are recorded per second with 16 bits (2 bytes). If the signal is stored as a stereo track (2 channels), the space required for a 4 minute long Song is: 4 x 60sec x 44,100 Hz x 2 bytes x 2 channels = 42,336,000 bytes, which is 42,336 MB A commercial CD has a usable capacity of about 74 minutes. The real data capacity is greater, because also control characters for reading the data and information for error correction are stored. The specifications of the audio CD are laid down in the so-called Red-Book standard. Amongst other things: Number of channels: 2 channels Bit depth: 16bit Sampling frequency: 44.1kHz The Clock: Every digital process must be synchronized with the help of a clock. A transfer succeeds only if the clock can be reliably detected. Clock Errors: A fluctuation of the clock (Jitter) can lead to an irregular sampling (A to D, D to D or D to A) and thus to a signal distortion. In the case of severely disturbed clock signals, the edge can no longer be reliably detected and incorrectly interpreted bit patterns occur. To guarantee a correct connection of digital components, there must be a central clock generator. A digital system must have a clock master. Optionally, almost any number of clocks (slaves) can be used. A/D-Wandler DAW D/A-Wandler Notice: In a digital composite (unless a dedicated clock generator is used), the most important converter should always be used as master. When recording, this is the A/D converter, when mixing or digitally producing it is the D/A converter. Wordclock The word clock has exactly the period of a sample at a given sampling rate. Transmission is via a 75Ohm BNC cable. At the last device of the chain, the signal must be terminated via a 75Ohm resistor, otherwise the signal can be reflected back. Word Clock Inputs and Outputs are mostly found at more professional devices. Digital Interfaces and Connections The most important interfaces are: AES/EBU S/PDIF MADI ADAT Digital Interfaces and Connections Name Samplingrate Optical Electrical Channels Jack Clock Cable length AES/EBU 32 – 192 kHz - 110 Ohm, balanced 2 XLR Internal Up to ca. 100m (AES3) AES3id 32 – 192 kHz - 75 Ohm, 2 BNC Internal Up to ca. 300m unbalanced coaxial MADI 32 – 48 kHz FDDI 75 Ohm, Up to 64 FFDI Internal Electrical: (AES10) (96 kHz with unbalanced coaxial (less at BNC Up to ca. 100m Tricks) higher Optical: Samplera Up to ca. 2km tes) S/PDIF 32 – 48 kHz TOSLink 75 Ohm, 2 RCA Internal few meters unbalanced coaxial (coded TOSLink For short distances a up to 6) common RCA Cable is suficent ADAT 32 – 48 kHz TOSLink - 8 TOSLink Internal few meters (S/MUX (less at possible up S/MUX) to 96 kHz) Bildquellen: Friedemann Kootz, 2011 Handbuch der Tonstudiotechnik, Band 2 Dickreiter et.al., Saur 2008 Wikipedia, Artikel: Digitalsignal Friedemann Kootz, 2011 Handb. der Tonstudiot., Band 2 Dickreiter et.al., Saur 2008 Handb. der Tonstudiot., Band 2 Dickreiter et.al., Saur 2008 Wikipedia, Artikel: Nyquist-Shannon-Abtasttheorem Handbuch der Tonstudiot., Band 2 Dickreiter et.al., Saur 2008 Handbuch der Tonstudiot., Band 2 Dickreiter et.al., Saur 2008