SPECS TeamSpecialist in Programmable Electronics

Concentrating on Spectral Analysis

SITE 2014

SPECS Team Members•SPECS Students Department of Geological Sciences:

Jonathon Mcgehee Angela LinderDepartment of Mechanical Engineering:Martin Guzman Bruce Balderrama Rajpreet Chehal Minna Gundy

Department of Computer Science:Angel Hernandez Steve Chang

Department of Electrical and Computer Engineering:

Luis Chavez Ismael Banihamed Christian Zamudio Manuel Jaquez

•SPECS Team LeadersDepartment of Electrical and Computer Engineering:

Dr. Shahnam Mirzaei Hossein Salemi

Department of Mathematics:Dr. Ramin Vakilian Brianna Amador

• Project challenge: To perform spectral analysis of large data sets in real-time.

• An interdisciplinary effort that integrates hardware, scientific computing software, and the mathematical theory of Fast Fourier Transform.

• Implementation of a real application on FPGA to perform the signal analysis in real time.

• A reconfigurable hardware platform (FPGA) is chosen to realize the physical implementation of the project.

• An entirely hands-on approach, in which all elements will be developed in our computer laboratories.

Introduction, Objective, & Motivation

MATLab• Analyze and Visualize Data• Develop Algorithms and Applications• Perform Numeric Computations• Publish Results and Deploy ApplicationsXilinx ISE• Create hardware design• Simulate design behavior• Mapping hardware to FPGA chip

Xilinx ATLYS FPGA board • Hardware to realize physical implementation

Software and Hardware Packages Used in Project

• The Institut de France presented a mathematical challenge based off of Fourier’s early work, the problem they gave was solving the heat equation.

• In 1822, born out of Fourier’s answer to the challenge the young mathematician published, “Mathematical Theory of Heat”.

• This paper presented the solution to this perplexing problem, Fourier’s simple mathematical approach held immense significance.

• Fourier’s solution to this partial differential equation is known as the Fourier Series.

The Origins of the Fourier Series:Solving the Heat Equation

• When Fourier proclaimed his solution to the heat equation, the concept of limits for functions or the process of limit of a sequence of partial series was not understood by mathematicians. • It took about 100 years for Mathematicians to finally have an understanding of the series and limits.

Fourier’s Solution to the Heat Problem and the Definition of a

Fourier Series

Definition Formulas of Fourier Series

Fourier’s Solution to the Heat Diffusion Problem

• His theory showed that any periodic signal can be view as a composition of sine or cosine waves.

• The function typically usedin electrical engineering today called the“Gate Function” is representedhere through the convergenceof a Fourier Series.

• Each graph shows the increasing amount of terms added to the series.

What does the Fourier Series do?

• The Fourier Series holds many forms, but through the use of Euler’s formula the preferred form is as follows:

• The graph illustrated to the right shows the amplitude spectrum of the exponential Fourier Series applied to a gate function.

The Exponential Fourier Series

Damped vibrating membrane

Harmonics of a vibrating membrane

Reconfigurable Hardware Technology

● FPGA structure○ Logic block ○ Memory block ○ Signal processing block ○ Input/Output block

● Counter example

• A software tool to monitor the real-time events inside FPGA

•Chipscope software was used throughout the project to analyze transform output and filtered signals.

Real-time Chipscope Analyzer

Fast Fourier Transform (FFT)

•FFT – A rapid computational algorithm that converts time domain signal to frequency domain signal.

•Time domain data: A mixture of information signal and noise that is not obvious to user.

•Frequency domain data: Extracted dominant frequencies available in the information signal through application of FFT and suppressing surrounding noise.

Frequency Domain

Time Domain

Accuracy of FFT’s

• The Atlantic Ocean Blue Whale makes sounds at 17 Hz which can’t be heard by humans

• Time domain sound analysis does not give an indication of a whale’s presence while frequency domain spectrum using Fast Fourier Transform does

• Sound recording and analysis techniques allows scientists to monitor the vocal behavior and movements of many animal species, providing new insight into complex migration and communication patterns

FFT Application in Spectral Analysis

of Atlantic Ocean Blue-Whale

Atlantic Ocean Whale Analysis

• Modulation: a technique to transport a message over a medium, such as air • Modulation uses high frequency carrier and signal information• High frequency carrier immunizes information signal to noise • Common modulation techniques:

•Amplitude modulation (AM) •Frequency modulation (FM)

FFT Application in Communications

Amplitude and frequency modulation techniques

• What is a Filter?• Extract desired frequency range• Eliminate noise

• Types of Filters• Low Pass • Band Pass• High Pass• Notch Filter

Filtering

Filter Implementation

MATLab Filter Design Tool MATLab Filter Simulation

Memory: Can be Virtual or Physical. Allocated space used tostore information to use in later referencing.

Using both Matlab and ISE programs we displayed a simulationof a sound wave going through Fourier transformation withoutthe FPGA board by storing information on the programs virtualmemory.

Using the FPGA board we loaded the ISE code onto the boardsphysical memory, using both software and hardware we wereable to perform the spectral imaging using Fourier transform.

Data on Reconfigurable Hardware

Complete System ImplementationInput

FFT - Output

Filter Outpu

t

•Dr. Vicki Pedone - Department of Geological Sciences

•Dr. Cristina Cadavid - Department of Physics and Astronomy

•Dr. Werner Horn - Department of Mathematics

Acknowledgements

Thank you!SITE 2014