ANALOG DATA AND CONVERSION BETWEENANALOG AND DIGITAL FORMS

Analog Representation of Data

Numerical data can be represented in electronic circuits by analog form instead of dig-ital form by a voltage or voltage pulse whose amplitude is proportional to the num-ber being represented, as shown in Fig. 4-2A. An example of analog representation is a voltage pulse produced by a photomultiplier tube attached to a scintillation detec-tor. The amplitude (peak voltage) of the pulse is proportional to the amount of energy deposited in the detector by an x- or gamma ray. Another example is the signal from the video camera attached to the image intensifier tube of a fluoroscopy system; the voltage at each point in time is proportional to the intensity of the x-rays incident on a portion of the input phosphor of the image intensifier tube (Fig. 4-2C).

Advantages and Disadvantages of the Analog and Digital Forms

There is a major disadvantage to the electronic transmission of data in analog form-the signals become distorted. Causes of this distortion include inaccuracies

Chapter 4:Computers in Medical Imaging 67

(0 decimal) (5 decimal) (10 decimal)

000 0 o 1 0 1 1 0 1 0

FIGURE 4-2. Analog and digi-tal representation of numerical data. A: Three analog voltage pulses, similar to those pro-duced by a photomultiplier tube attached to a scintillator.

The height of each pulse repre-sents a number. B: These same numbers represented in digital form. C:A continuously varying analog signal, such as that from the video camera in a flu-oroscopy system. The height of the signal at each point in time represents a number. 0: The values of this signal, sampled at three points, represented in digital form.

when signals are amplified, attenuation losses, and electronic noise-small stray voltages that exist on circuits and become superimposed on the data. The more the data are transferred, the more distorted they become. On the other hand, data stored or transferred in digital form are remarkably immune to the accumulation of error because of signal distortion. These distortions are seldom of sufficient ampli-tude to cause a 0 to be mistaken for a 1 or vice versa. Furthermore, most digital cir-cuits do not amplify the incoming data, but make a fresh copy of it, thus prevent-ing distortions from accumulatprevent-ing durprevent-ing multiple transfers.

The digital form facilitates other safeguards. When information integrity is critical, additional redundant information can be sent with each group of bits to permit the receiving device to detect errors or even correct them. A simple error detection method uses parity bits. An additional bit is transmitted with each group of bits, typically with each byte. The bit value designates whether an even or an odd number of bits were in the" 1" state. The receiving device determines the parity and compares it with the received parity bit. If the parity of the data and the parity bit do not match, an odd number of bits in the group have errors.

Data can often be transferred in less time using the analog form. However, dig-ital circuits are likely to be less expensive.

The transducers, sensors, or detectors of most electronic measuring equipment, including medical imaging devices, produce analog data. If such data are to be ana-lyzed by a computer or other digital equipment, they must be converted into digi-tal form. Devices that perform this function are called analog-to-digital converters (ADCs). ADCs are essential components of multichannel analyzers, modern nuclear medicine scintillation cameras, computed radiography systems, modern ultrasound systems, MRI scanners, and CT scanners.

Most analog signals are continuous in time, meaning that at every point in time the signal has a value. However, it is not possible to convert the analog signal to a digital signal at every point in time. Instead, certain points in time must be selected at which the conversion is to be performed. This process is called sampling. Each analog sample is then converted into a digital signal. This conversion is called digi-tization or quandigi-tization.

An ADC is characterized by its sampling rate and the number of bits of output it provides. The sampling rate is the number of times a second that it can sample and digitize the input signal. Most radiologic applications require very high sampling rates. An ADC produces a digital signal of a fixed number of bits. For example, one may purchase an 8-bit ADC, a lO-bit ADC, or a 12-bit ADC. The number of bits of output is just the number of bits in the digital number produced each time the ADC samples and quantizes the input analog signal.

The digital representation of data is superior to analog representation in its resistance to the accumulation of errors. However, there are also disadvantages to digital representation, an important one being that the conversion of an analog signal to digital form causes a loss of information. This loss is due to both sampling and quantization. Because an ADC samples the input signal, the values of the analog signal between the moments of sampling are lost. If the sampling rate of the ADC is sufficiently rapid that the analog signal being digitized varies only slightly during the intervals between sampling, the sampling error will be small. There is a mini-mum sampling rate requirement, the Nyquist limit (discussed in Chapter 10) that ensures the accurate representation of a signal.

Quantization also causes a loss of information. An analog signal is continuous in magnitude, meaning that it may have any value between a minimum and maxi-mum. For example, an analog voltage signal may be 1.0,2.5, or 1.7893 V. In con-trast, a digital signal is limited to a finite number of possible values, determined by the number of bits used for the signal. As was shown earlier in this chapter, a I-bit digital signal is limited to two values, a 2-bit signal is limited to fout values, and an

TABLE 4-5. MAXIMAL ERRORS WHEN DIFFERENT