# Digital video noise

Digitizing an analog video signal involves two operations: sampling and quantization. Sampling means the periodical measurement of the amplitude of the video signal.

The significant parameter is the sampling frequency (fS). Quantizing means assigning a binary value to the measured amplitude at each sampling instant. The significant parameter is the number of bits per sample (n).

Figure 1. Quantizing errors introduced by a 3-bit codec. Click here to see an enlarged diagram.

Sampling at constant time intervals, T=1/fS, results in an amplitude modulation of the sampling pulses or PAM. According to Nyquist, the sampling frequency has to be equal to or higher than twice the maximum frequency of interest to avoid aliasing. It also has to be high enough to allow for the design of realizable anti-aliasing low-pass filters with minimum ripple and group delay. Another video sampling requirement is for fS to be a multiple of a basic video frequency, such as the horizontal scanning frequency (fH) or the chrominance subcarrier frequency (fSC).

Quantizing converts each of the amplitude levels of a continuously varying analog video signal to one of a finite number of discrete levels, 2n, where “n” is the number of bits per sample.

### The quantizing error

Video signal amplitudes vary in time and can assume an infinite number of levels ranging from 0V (black) to 0.7V (white). Because the digital signal can assume only a limited number of discrete levels, it is an approximation of the original analog signal. The quantized values may be in error by as much as ±1/2Q, where Q is the amplitude of the quantizing step. This process generates a unique impairment in digital systems: the quantizing error.

In studio-type digital video equipment, all quantizing steps are of equal amplitude, and the process is called uniform quantization. The number of quantizing steps and, consequently, the magnitude of the quanitizing error, depends on the number of bits per sample.

Figure 2. Oscilloscope display of 8-bit quanitizing error Horizontal display: 0.5 microsecond/cm Vertical display: 5 millivolt/cm S/QRMS: 58.3dB theoretical S/QRMS: 57.9dB measured

Click here to see an enlarged diagram.

Figure 1 shows the quantizing errors introduced by a 3-bit codec. In this idealized case, all the steps have a constant width and a constant height (Q). Early technology used seven or eight bits per sample, depending on the class of equipment. This resulted in 128 or 256 quantizing steps, respectively. With few exceptions, contemporary studio-type equipment uses 10 bits per sample, resulting in 1024 quantizing steps.

With eight bits or more per sample, the quantizing error is perceived by the human visual system as random noise. Figure 2 shows the oscilloscope display of quantizing errors generated by an 8-bit system. Below eight bits per sample, the quantizing error results in a severe distortion of the waveform and gives rise to contouring effects. Figure 3 shows the oscilloscope display of quantizing errors generated by a 7-bit system.

Video signal to random noise specifications are usually expressed as p-p signal to RMS noise ratio. The p-p video signal value at the output of the D/A is (2n-1) × Q simplified to 2n × Q. An ideal A/D transfer process as shown in Figure 1 results in peak values of ±Q/2. The RMS value of this type of signal is equal to Q/12. Therefore, the peak-to-peak signal to RMS quanitizing noise is:

Sp-p/QRMS (dB) = 20 log10[p-p Video/RMS noise] = 20 log10[2nQ/(Q/√12)] = 6.02n + 10.8

Figure 3. Oscilloscope display of 7-bit quantizing error Horizontal display: 1 microsecond/cm Vertical display: 5 millivolts/cm S/QRMS:52.2dB theoretical S/QRMS: 51.9dB measured

Click here to see an enlarged diagram.

It is evident that the higher the value of n, the better the signal-to-noise ratio. This simplified formula does not take into consideration the bandwidth of the quanitizing noise nor the fact that the video signal does not occupy the whole quantizing range. In all standards, the maximum analog video frequency is lower than half of the sampling frequency, and analog video signals have a well-defined peak-to-peak amplitude.

The amplitude reference is the component analog 100-percent color bars signal, which assumes a peak-to-peak luminance value of 0.7V. It is important that these signals be handled by the A/D converter without clipping. Consequently, a certain amount of headroom is provided to avoid A/D converter overloading and is specified in current digital television standards. Taking these facts into consideration, the p-p video to RMS quantizing noise ratio becomes:

Sp-p/QRMS (dB) = 6.02 n + 10.8 + 10 log10 (fS/2fmax) - 20 log10 [Vq/Vp-p]

where

n: The number of bits per sample

fS: The sampling frequency (e.g. 13.5MHz for Rec. 601 luminance)

fmax: The maximum video frequency (e.g. 5.75MHz for Rec. 601 luminance)

Vq: Signal voltage that occupies the whole quantizing range (0.8174 Vp-p)

Vp-p: Active video signal (0.7 Vp-p)

This formula takes into account the headroom, which is the difference between the whole quantizing range (Vq) and the p-p active video signal (Vp-p).

### The measurement of Sp-p/QRMS

The calculated theoretical value of Sp-p/QRMS for a 10-bit codec is ≈ 70.35dB. The calculated theoretical value of Sp-p/QRMS for an 8-bit codec is ≈ 58.3dB.

Figure 4. Conceptual block diagram of measurement of signal-to-quantizing noise ratio. Click here to see an enlarged diagram.

Figure 4 shows a conceptual block diagram of a test setup. The codec consists of an input (anti-aliasing) LPF, an A/D converter, a processor, a D/A converter and an output (reconstruction) LPF. The codec is fed a ramp signal, which activates all quanitizing levels. The input is subtracted from the output of the codec, leaving only the quantizing errors, which are fed to a high-gain wideband oscilloscope. The p-p amplitude of quantizing error is carefully measured, and the Sp-p/QRMS is calculated using the formula:

Sp-p/QRMS (dB) = 20 log10[p-p video/RMS quantizing noise] = 20 log10 [p-p video/p-p quantizing noise] + 15

The Sp-p/QRMS ratio is obtained by adding a constant (15). This is a correction factor that takes into account the fact that the oscilloscope displays p-p quantizing noise instead of RMS quantizing noise. This measurement, when carefully carried-out, gives results correlated with the calculated value within 2dB.

Table 1. Theoretical and measured Rec. 601 4:2:2 luminance Sp-p/QRMS. Click here to see an enlarged diagram.

The disadvantage of this simple method lies essentially in the difficulty in measuring the quasi p-p amplitude in a consistent and reliable manner, since the judgment of the observer and many other factors, such as the chosen value of the correction factor, affect the accuracy of the measurement. Table 1 lists theoretical and measured Rec 601 4:2:2 luminance S p-p/Q RMS values for several values of n, all other parameters being kept constant.

Specialized automatic video testing equipment, such as the Tektronix VM700, has the capability of normalizing the luminance ramp test signal to a horizontal line and give direct readings of Sp-p/QRMS at the output of the digital black box.

A comparison of theoretical and measured Sp-p/QRMS provides a useful guide in the performance of video A/D and D/A converters.

*Michael Robin, a fellow of the SMPTE and former engineer with the Canadian Broadcasting Corp.'s engineering headquarters, is an independent broadcast consultant located in Montreal, Canada. He is co-author of “Digital Television Fundamentals,” published by McGraw-Hill and translated into Chinese and Japanese*.

**Send questions and comments to:**michael_robin@primediabusiness.com