Quantization in GNU Radio

2015

Quantization

Author: Rakesh Rakesh Email id: [email protected]

What is Gnu radio?

GNU Radio is a software library, which can be used to develop complete applications for radio engineering and signal processing. Introduction

GNU Radio is a free and open-source software development toolkit that provides signal processing blocks to implement software radios. It can be used with readilyavailable low-cost external RF hardware to create software-defined radios, or without hardware in a simulation-like environment. GNU Radio is licensed under the GNU General Public License (GPL) version 3. All of the code is copyright of the Free Software Foundation. While all the applications are implemented using python language while critical signal processing path is done using C++ language. Idea behind GNURADIO

The goal is to give ordinary software people the ability to 'hack' the electromagnetic spectrum, i.e. to understand the radio spectrum and think of clever wa ys to use it. Why GNURADIO

Instead of purchasing multiple expensive radios, a single generic radio can be implemented using GNU Radio software and with support of minimal hardware to receive and transmit processed signal at required frequencies and any data type can be passed from one block to another i.e.it can be in bits, bytes, vectors, bursts or more complex data types Since the performance critical blocks are implemented in C++ using processor floating point extensions the developers are able to implement real-time, high-throughput radio systems in a simple-to-use, rapid-application-development environment.

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One can use it to write applications to receive data out of digital streams or to send data into digital streams, which is then transmitted using hardware. GNU Radio has filters, channel codes, synchronisation elements, equalizers, demodulators, vocoders, decoders, and many other elements which are called as blocks that are typically found in radio systems. Features The main features of GNU Radio are flexibility and configurability. Extending GNU Radio is also quite easy, if you find a specific block that is missing you can quickly create and add it.


What do you mean by quantization?

Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a (countable) smaller set – such such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The round-off error introduced by quantization is referred to as quantization error. In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation. The error signal is sometimes modeled as an additional random signal called quantization noise because of its stochastic behaviour. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. Because quantization is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible in general to recover the exact input value when given only the output value). The set of possible input values may be infinitely large, and may possibly be continuous and therefore uncountable (such as the set of all real numbers, or all real numbers within some limited range). The set of possible output values may be finite or countably infinite. The input and output sets involved in quantization can be defined in a rather general way. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input data. There are two substantially different classes of applications where quantization is used: The first type, which may simply be called rounding quantization, is the one employed for many applications, to enable the use of a simple approximate representation for some quantity that is to be measured and used in other calculations. This category includes the simple rounding approximations used in everyday arithmetic. This


category also includes analog-to-digital conversion of a signal for a digital signal processing system (e.g., using a sound card of a personal computer to capture an audio signal) and the calculations performed within most digital filtering processes. Here the purpose is primarily to retain as much signal fidelity as possible while eliminating unnecessary precision and keeping the dynamic range of the signal within practical limits (to avoid signal clipping or arithmetic overflow). In such uses, substantial loss of signal fidelity is often unacceptable, and the design often centers around managing the approximation error to ensure that very little distortion is introduced. The second type, which can be called rate – distortion distortion optimized quantization, is encountered in source coding for "lossy" data compression algorithms, where the purpose is to manage distortion within the limits of the bit rate supported by a communication channel or storage medium. In this second setting, the amount of introduced distortion may be managed carefully by sophisticated techniques, and introducing some significant amount of distortion may be unavoidable. A quantizer designed for this purpose may be quite different and more elaborate in design than an ordinary rounding operation. It is in this domain that substantial rate – distortion distortion theory analysis is likely to be applied. However, the same concepts actually apply in both use cases.


1) Quantization The GNUradio Companion with basic blocks (Options block and Variable block)

Options block defines defines the ID, Title and Description of the experiment.


defines to declare variables globally. This block maps a value to a unique u nique Variable Block defines variable. This variable block has no graphical representation. The variable can be referenced (by ID) from other blocks in the flowgraph. o ID = samp_rate Value = 32KHz o

Signal source is a wave form genrator. Very first block genrates the sine wave, second block genrates the square wave, third block genrates triangler wave and finaly fourth block genrates the sawtooth waveform.

o

ID:analog_sig_source_x_0


Output type: float Freq: 1KHz o o Amplitude: 1V Quantizer : Quantization is the procedure of constraining something from a continuous set of values (such as the real numbers) to a relatively small discrete set (such as the integers). ID: channels_quantizer_0 o o Bits: 3 o

WX GUI scope sink: The WX GUI Scope sink is the destination block of the flow chart. This block is used to view the time domain representation of the output. The simulation output of the received signal is seen with this block. ID: wxgui_scopesink2_0 o o Type: float


The Complete block representation

Genrated output


Quantization in GNU Radio

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