interpolation in gnu radio

8/9/2019 Interpolation in GNU Radio

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2015

Author: Rakesh

Email id: [email protected]

Interpolation using FIR Filter


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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 readily-

available 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 ofthe 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 ways 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.



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What do you mean by interpolation?

In the mathematical field of numerical analysis, interpolation is a method of constructing new

data points within the range of a discrete set of known data points.

In engineering and science, one often has a number of data points, obtained

by sampling or experimentation, which represent the values of a function for a limited

number of values of the independent variable. It is often required to interpolate (i.e.

estimate) the value of that function for an intermediate value of the independent variable.

This may be achieved by curve fitting or regression analysis.

A different problem which is closely related to interpolation is the approximation of a

complicated function by a simple function. Suppose the formula for some given function

is known, but too complex to evaluate efficiently. A few known data points from the

original function can be used to create an interpolation based on a simpler function. Of

course, when a simple function is used to estimate data points from the original,

interpolation errors are usually present; however, depending on the problem domain and

the interpolation method used, the gain in simplicity may be of greater value than the

resultant loss in accuracy.

There is also another very different kind of interpolation in mathematics, namely the

"interpolation of operators". The classical results about interpolation of operators are

the Riesz – Thorin theorem and the Marcinkiewicz theorem. There are also many other

subsequent results.

In the domain of digital signal processing, the term interpolation refers to the process of

converting a sampled digital signal (such as a sampled audio signal) to a higher

sampling rate (Upsampling) using various digital filtering techniques (e.g., convolution

with a frequency-limited impulse signal). In this application there is a specific

requirement that the harmonic content of the original signal be preserved without

creating aliased harmonic content of the original signal above the original Nyquist limit

of the signal (i.e., above fs/2 of the original signal sample rate). An early and fairly

elementary discussion on this subject can be found in Rabiner and Crochiere's

book Multirate Digital Signal Processing

http://www.tenettech.com/http://www.tenettech.com/http://www.tenettech.com/mailto:[email protected]://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Numerical_analysishttp://en.wikipedia.org/wiki/Discrete_sethttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Sampling_(statistics)http://en.wikipedia.org/wiki/Experimentationhttp://en.wikipedia.org/wiki/Curve_fittinghttp://en.wikipedia.org/wiki/Regression_analysishttp://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin_theoremhttp://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin_theoremhttp://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin_theoremhttp://en.wikipedia.org/wiki/Marcinkiewicz_theoremhttp://en.wikipedia.org/wiki/Upsamplinghttp://en.wikipedia.org/wiki/Upsamplinghttp://en.wikipedia.org/wiki/Marcinkiewicz_theoremhttp://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin_theoremhttp://en.wikipedia.org/wiki/Regression_analysishttp://en.wikipedia.org/wiki/Curve_fittinghttp://en.wikipedia.org/wiki/Experimentationhttp://en.wikipedia.org/wiki/Sampling_(statistics)http://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Discrete_sethttp://en.wikipedia.org/wiki/Numerical_analysishttp://en.wikipedia.org/wiki/Mathematicsmailto:[email protected]://www.tenettech.com/


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1) Interpolation

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

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



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Variable Block defines to declare variables globally. This block maps a value to a unique

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

o Value = 32000Hz

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 thesawtooth waveform.

o ID:analog_sig_source_x_0

o Output type: float

o Freq: 100Hz

o Amplitude: 1V



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Interpolating FIR filter: This filter increases the sampling rate of signal by a interpolation

factor.

ID: fir_filter_xxx_0

Type: float

Interpolation: 10

Taps:1

Throttel block : Throttel is a device that control the flow of samples such that average rate does

not exceeds samples/sec. Throttle is used because no hardware interface has done.

o ID: blocks_throttel

o Type: float

o Vec length: 1



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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.

o ID: wxgui_scopesink2_0

o Type: float



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The Complete block representation

interpolation in gnu radio

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