Title: Using Fourier Domain Techniques to Characterize String Instruments, Nano-Scale Quantum Devices, and Human Brain Waves
1Using Fourier Domain Techniques to Characterize
String Instruments, Nano-Scale Quantum Devices,
and Human Brain Waves
2Problems Addressed in Our Researches
- How can we characterize the quality of a string
instrument independent of human subjectivity? - How can we evaluate the quality of a quantum
cascade laser wafer prior to the fabrication and
testing processes? - How can we typify the mental health of
psychiatric patients by looking at brain waves? - How can Fourier Analysis simplify the evaluation
process and help to extract key features from all
the above signals? - How can these seemingly unconnected subject areas
be correlated through Fourier Analysis?
3Fourier Transform (Time ? Frequency or Spatial
? K )
x(t)
X(f)
4Fourier Transform
FREQUENCY DOMAIN
TIME DOMAIN
Amplitude
Amplitude
Amplitude
Amplitude
Amplitude
Amplitude
5Fourier Analysis
Inverse Fourier transform is converting frequency
domain signals into time domain signals a time
domain signal can be synthesized by adding
together different frequency components. Individua
l harmonics in the frequency domain can be
selectively added together to synthesize a time
domain signal.
X(f)
x(t)
6Applications to String Instruments
- Using Fourier Analysis to evaluate the quality of
string instruments - Time domain signals -gt Frequency domain spectra
- Analyze both static and dynamic spectra (vibrato
efficiency) - Ref Real time spectrum analyzer analysis and
evaluation of string instruments, Acoustic
Research Institute, The 16th International
Congress on Sound and Vibration, Kraków, Poland,
5-9 July 2009.
7Introduction- Modes
- Fundamental Frequency longest wave in a family
of standing waves determined by the string length
and resonates with the cavity the original
pitch. - Higher (Nth) Harmonic has a frequency that is an
integer multiple (N) of the fundamental pitch
(and with a wavelength N times shorter than the ?
of the fundamental)
The degree to which the harmonics are expressed
depends on the instrument material and pattern
(Chladni patterns for violins).
8Static Spectra Comparison of Different Violins
G-string X-axis in unit of (Hertz), Y-axis in
unit of (dB)
- What to look for
- Presence of harmonics no missing harmonics
- Number of harmonics the more the better
- Narrow peaks no extra noise
- Spectrum of one note at one instance a whole
family of harmonics is shown
Higher Price gt18,000
Lower Price lt2,000
9Extracting Statistic Data From Dynamic Spectra
10Frame 0
Frame 1
In Frame -1 All harmonic peaks Shifted to higher
frequency compared with frame 0
Total gt50 frames here
9 frames here
First 3 of the 9 frames
Frame -2
Frame -1
Frame 0
11Statistical Data of Frequency Modulated Harmonic
Peaks (Oscillating up and down in Unit of Hz)
(a)
(b)
Single tone data generated from (a) a less
expensive violin and (b) a higher price violin.
Bottom red numbers are the Standard Deviations of
their data above The higher price violin
apparently has a higher FM efficiency
12Applications to Nano-Scale Quantum Devices
(Quantum Cascade Lasers)
- Use Fourier Analysis to evaluate quality of grown
laser materials (very useful to manufacturers) - Spatial Domain Structure -gt k(angle) -domain
x-ray spectra - Correlate x-ray diffraction patterns to various
growth problems understand what has happened
during growths, decide whether to proceed on to
fabrication - Ref
- 1. Evaluation of nano-scale quantum devices
using x-ray diffraction and Fourier analysis,
Material Research Society Spring Meeting, Paper
HH8.3, San Francisco, CA, April 13 17, 2009. - 2. X-ray diffraction analysis of quantum
cascade lasers, IEEE, LEOS, The 21st
International Conference on Indium Phosphide and
Related Materials, paper WP2, Newport Beach, CA,
May 10 14, 2009.
13Quantum Cascade Laser Applications
Gas sensing and chemical detection for chemical
industry, health, environmental
Infrared counter measure
See-through Imaging for homeland security and
health
Breath Analysis Portable (equivalent) blood
testing, Drug dynamics study
14QCL Processing and Characterization
Testing
Compare X-ray, PL, data with final laser L-I, I-V
results Identify design and growth problems
15Quantum Cascade Lasers X-Ray Analysis and Bragg
Diffraction
Madmax
- Can be used to monitor the growth results of
Quantum Cascade Lasers (QCLs) - The gradual change in the superlattice period can
be seen in the Fourier domain as a reduction of
the convolution length. - The degradation of the superlattice periodicity
will affect the line-shape, width, and height of
satellite peaks in a x-ray scan diffraction
pattern.
Bragg diffraction is a Fourier Transformation
from the spatial domain to the k domain
(represented by angles)
16Straining and Hetero-Interface Defects
Compressive Straining Indium Rich In atoms
are larger than Ga or Al ones grown material
has larger lattice constant than that of the
wafer material lattice mismatch between the
wafer and substrate peaks shift left Tensile
Straining the opposite of compressive
straining grown material has a smaller lattice
constant than that of wafer material peaks shift
right Blue Arrow
hetero-interface defects
17Change in Growth Rate
Double Peaks wafer growth rate changes suddenly,
resulting in two different lattice constants
Double Peak simulation using Bede By suddenly
changing to a 2nd growth rate
18Chirping
X-ray spectra of a high-power room temperature CW
QCLs (blue) and X-ray scans from the same layer
structure but with dramatically worse device
performance (red).
Chirping gradually changing chemical
composition asymmetric satellite peaks
19Relaxation in Strain Balanced Superlattices
- Strain Balanced Superlattice layers alternately
compressed and tensile strained. Overall strain
is balanced - the average lattice constant close
to the substrate lattice constant. - Relaxation Occurs in the thicker layers - layers
are strained too much, chemical bonds between
atoms begin to break, degrading the periodicity.
Fig. 1 (a) Simulated layer relaxation with around
0.3 relaxation in some of the thicker InGaAs
layers note how peaks tilt upwards from left to
right (b) 0.3 relaxation in some of the thicker
InAlAs layers note how peaks tilt downwards
from left to right. (c) experimental results of a
seriously relaxed superlattice material. (d)
Simulation - .2 relaxation in some of the
thicker InAlAs layers
19
19
20Table of QCL Performance Degradations
No chirping
Parameters for evaluating QCL performance Thresho
ld the lower the better Temperature Range the
larger the better P max the greater the
better, best is to achieve continuous wave (CW)
21Applications to Human Brain Waves
- Use Fourier Transform to evaluate the health of
human brain waves - Signals are less periodic (compared with music
signals and superlattice structures) and more
noisy (needs averaging and filtering). - Comparison of brainwaves of psychiatric patients
to typical brainwaves - Is the gating effect observed?
- Publication for new results (new gating effect at
Fourier domain) is in preparation.
22Human Brain Waves Setup
- EEG patterns measured for both normal people and
psychological patients - Comparison of excitement from first stimulus with
excitement from second stimulus for various brain
wave rhythms. - Observation of the brains gating effect is
there suppression of response to repeated audio
stimuli? - Time domain EEG waves must be Fourier transformed
into the frequency domain in order to compare
power graphs for normal vs. abnormal brain
functioning.
Rhythm Freq (Hz) Amp(µV)
alpha 8-13 20-200
beta 13-30 5-10
delta 1-5 20-200
theta 4-8 10
23Human Brain Wave Fourier Domain Comparison Graphs
Blue-1, Red-2
Control
Patient
24Discussion and Conclusions
Highly Periodic Signals String Instruments Quantum Cascade Lasers
Symmetry of Satellite Peaks - The more symmetric the better string density and diameter is uniform and constant - The more symmetric the better satellite peaks become asymmetric when chemical composition is not constant
Number of Peaks -The more harmonics - the more colorful and vibrant the sound The more peaks- the better the growth and the more angles there are for good constructive interference the better the growth periodicity and laser gain
Width of Peaks The narrower the better the sound is clear and pure no extra noise -The narrower the linewidth the better- the less defects and the less relaxation damages in strain balanced superlatticess
For less periodic and noisy signals like brain
waves, Fourier analysis is still helpful to
identify patients from normal people. Our new
study results (publishable) clearly show that the
patients frequency peaks of the two auditory
responses are shift instead of aligned (normal).
25Acknowledgements
- Professor Jacob Khurgin, the Johns Hopkins
University, Department of Electrical and Computer
Engineering - QCL Crystal Growers
- Dr. Jiaxing. Chen - Princeton University,
- Mr. Liwei Cheng - UMBC,
- Dr. Xiaojun Wang Adtech Optics Inc.
- Dr. Elliot Hong, Maryland Psychiatric Research
Center, UMAB
26Questions?
27(No Transcript)
28Laser Growth Problems Interpreted with Madmax
and Bede Ray Simulations
Indium Rich In atoms are larger than Ga or Al
ones, so lattice constant increases, resulting in
lattice mismatch between the wafer and
superlattice compressive straining shown in red
Blue Arrow
hetero-interface defects
Double Peaks wafer growth rate changes suddenly
resulting in two different lattice constants
Double Peak simulation using Bede Rays
Chirping gradually changing chemical
composition asymmetric satellite peaks
X-ray spectra of a high-power room temperature CW
QCLs (blue) and X-ray scans from the same layer
structure but with dramatically worse device
performance (red).