Signal Quantization

Consider an analog signal whose values from 0 to +10.let us assume that we whish to convert this signal to digital form and that the required output is a 4-bit digital signal .we know that a 4-bit binary number can represent 16 different values, 0 to15: it follows that the resolution of our conversion will be 10V/15=2/3V.thus an analog signal of 0V will be represented by 0000.2/3V will be represented by 0001, 6V will be represented by 1001, and 10V will be represented by 1111.

All these sample numbers are multiples of the basic increment (2/3V).A question now arises regarding the conversion of numbers that fall between these successive incremental levels. For instance, consider the case of a 6.2-V analog level. This process is called quantization. Obviously errors are inherent in this process; such errors are called quantization errors. Using more bits to represent(encode or, simply, errors code) an analog signal reduces quantization  errors but requires more complex circuitry.

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" Signal Quantization " !

Why Data Converters?

        Our environment is full of analog signals, such as sound, light, temperature, voltage, current, and electromagnetic waves. By the use of sensors, these signals are usually converted to electrical quantities, voltage or current, and processed to extract useful information. The processing can be carried out in analog or digital domain. During the last two decades, digital signal processing has become immensely powerful. Advances in technology of Integrated Circuits (IC) made it possible to implement digital signal processors with a reasonable amount of silicon wafer area, low power consumption, and affordable price for different applications. Digital signal processors (DSP) can easily be programmed for different algorithms. Many functions of analog circuits have been replaced by equivalent algorithms in DSPs. Another major advantage of DSP algorithms is that functionality is not subjected to fluctuations and variations with respect to time and temperature.

 In addition, there are some functions that can be performed by DSP, but are difficult to implement with analog circuits. One such function is a linear phase filter. The main advantages of DSP over analog processing are programmability, repeatability, stability, and flexibility.

 

         Although an increasing amount of signal processing is performed in digital domain, the interface between analog and digital domain will remain a fundamentally necessary element. The gates of DSPs to analog signals are Analog-to-digital (A/D) and Digital-to-Analog (D/A) converters. For example, an echo cancellation in an amphitheater makes use of a microphone that generates a voltage in the range of a few microvolts to a couple of milivolts. This analog voltage should be amplified and converted to a digital signal for extensive processing by DSP. After echo cancellation, it is converted to an analog signal, which can be applied to a power amplifier.

Fig 4.1

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" Why Data Converters? " !

Data Converter

Analog-to-digital (A/D) and digital-to-analog (D/A) converters are needed in all digital signal processing (DSP) applications and act as the interface between the analog and digital signal. As DSP continues to gain ground over analog signal processing, the importance of these converters increases correspondingly. The high-speed and high-resolution A/D converters are required in numerous applications, such as wireless communications, asymmetric digital subscriber line (ADSL), and very high-speed DSL (VDSL) systems.

       Sampling rate and precision or bit resolution greatly controls the performance of the data converters. In general case, we deal with a trade-off between these criteria. Different types of converter architectures offer system designers a wide range of choice in speed and resolution for optimal use in their applications. Among the choices in A/D architectures are flash, pipeline, successive-approximation register (SAR), and sigma-delta converters. D/A architectures include resistor-string converters, current-mode converters, and sigma-delta converters. Among these, sigma-delta converters are widely used in high-resolution applications.

         In addition, the test of the data converters is becoming even more important issue in mixed signal applications. The test of A/D and D/A converters can be carried out by using a DSP unit. In each case, some practical DSP solutions for the state-of-the-art-applications are given by using Texas Instruments (TI) data converters and DSP products.

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" Data Converter " !

How to Convert Analog Signal Into Digital One

In order to make analog to digital conversion we should convert the analog signal into digital by sampling and quantization processes ( Pulse Code Modulation) .

         Sampling of Analog Signals                    

       The principle underlying digital signal processing is that of sampling the analog signal Fig 4.2 illustrates in a conceptual form the process of obtaining samples of an analog signal. The switch shown closes periodically under the control of a periodic pulse signal (clock). The closure time of the switch, τ, is relatively short, and the samples obtained are stored (held) on the capacitor. The circuit of the following figure is known as a sample-and-hold (S/H) Circuit. As indicated, the S/H circuit consists of an analog switch that can be implemented by a MOSFET transmission gate. A storage capacitor, and (not shown) a buffer amplifier.

Between the sampling intervals-that is, during the hold intervals-the voltage level on the capacitor represents the signal sample we are after. Each of these voltage levels is then fed to the input of an A/D converter, which provides an N-bit binary number proportional to the value of signal sample. The fact that we can do our processing on a limited number of samples of an analog signal while ignoring the analog-signal details between samples is based on the shannon’s sampling theorem

Fig 4.2  The process of periodically sampling an analog signal (a) Sample-and-hold (S/H) circuit The switch closes for a small part of time of every clock period (T). (b) Input signal waveform. (c) Sampling signal (control signal for the switch). (d) Out put signal (to be fed to A/D converter).

References

" How to Convert Analog Signal Into Digital One " !