The document describes a project by the SPECS Team to perform real-time spectral analysis of large data sets using an FPGA board. The team includes students and faculty from multiple departments who are developing both hardware and software. They are using MATLAB for analysis and algorithm development, Xilinx ISE to design hardware, and an FPGA board for physical implementation. The document provides background on Fourier analysis and how it can decompose signals into frequencies. It also describes the team's work implementing filters and FFT on the FPGA to perform spectral analysis.

1. SITE 2014
SPECS Team
Specialist in Programmable Electronics Concentrating on
Spectral Analysis

2. SPECS Team Members
•SPECS Students
Department of Geological Sciences:
Jonathon Mcgehee
Angela Linder
Department 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 Leaders
Department of Electrical and Computer
Engineering:
Dr. Shahnam Mirzaei
Hossein Salemi
Department of Mathematics:
Dr. Ramin Vakilian
Brianna Amador

3. Introduction, Objective, &
Motivation
• 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.

4. Software and Hardware Packages
MATLab
Used in Project
• Analyze and Visualize Data
• Develop Algorithms and Applications
• Perform Numeric Computations
• Publish Results and Deploy Applications
Xilinx ISE
• Create hardware design
• Simulate design behavior
• Mapping hardware to FPGA chip
Xilinx ATLYS FPGA board
• Hardware to realize physical implementation

5. The Origins of the Fourier Series:
Solving the Heat Equation
• 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.

6. Fourier’s Solution to the Heat Problem and
the Definition of a Fourier Series
• 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.
Definition Formulas of Fourier Series
Fourier’s Solution to the Heat
Diffusion Problem

7. What does the Fourier Series do?
• His theory showed that any periodic signal can be view as a composition of
sine or cosine waves.
• The function typically used
in electrical engineering
today called the
“Gate Function” is represented
here through the convergence
of a Fourier Series.
• Each graph shows the
increasing amount of terms added to the series.

8. The Exponential Fourier Series
• 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.

9. Damped vibrating membrane
Harmonics of a vibrating
membrane

10. Reconfigurable Hardware
Technology
● FPGA structure
○ Logic block
○ Memory block
○ Signal processing block
○ Input/Output block
● Counter example

11. Real-time Chipscope Analyzer
• 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.

12. 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.
Time Domain
Frequency Domain

13. Accuracy of FFT’s

14. FFT Application in Spectral Analysis of
Atlantic Ocean Blue-Whale
• 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
Atlantic Ocean Whale Analysis

15. FFT Application in Communications
• 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)
Amplitude and frequency modulation techniques

16. • What is a Filter?
• Extract desired frequency range
• Eliminate noise
• Types of Filters
• Low Pass
• Band Pass
• High Pass
• Notch Filter
Filtering

17. Filter Implementation
MATLab Filter Design Tool MATLab Filter Simulation

18. Data on Reconfigurable Hardware
Memory: Can be Virtual or Physical. Allocated space used to
store information to use in later referencing.
Using both Matlab and ISE programs we displayed a simulation
of a sound wave going through Fourier transformation without
the FPGA board by storing information on the programs virtual
memory.
Using the FPGA board we loaded the ISE code onto the boards
physical memory, using both software and hardware we were
able to perform the spectral imaging using Fourier transform.

19. Complete System
Implementation Input
Filter
Output
FFT -
Output

20. Acknowledgements
•Dr. Vicki Pedone - Department of Geological Sciences
•Dr. Cristina Cadavid - Department of Physics and
Astronomy
•Dr. Werner Horn - Department of Mathematics

21. SITE 2014
Thank you!