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This module discusses the conclusions we have drawn as a result of our project exploring the implementation of a delay and sum beamformer with a two-dimensional array.

Summary of results of data

As can be seen in the screenshots given in the results section, the setup and program work at least some of the time. As was noted in the introduction , there is a small degree of ambiguity resulting from the two-dimensional natureof the array in that the array and algorithm will not be able to distinguish at all, theoretically, between a source above the array and an identical source ata location that is the original source reflected across the plane of the array. Practically, this should not matter at all if the array is mounted on a wallor on the ground, but should the need arise, the problem can be eliminated completely by taking the array to three dimensions.

As the arccosine function was used in the computation of one of the angles, accuracy is much worseas the angle approaches ±pi/ 2 due to the slope of the arccosine function going toinfinity in that region. The shortcuts we took were probably detrimental to the accuracy of the project, but once again, they were necessary to have it runat all on what we had to work with. Scanning with only three microphones instead of with all eight does not fully utilize the noise-reducing capability ofthe delay and sum technique, but it does conserve a great deal of computing power. The simplification made by assuming that the three microphones usedto scan could be broken up into pairs will sometimes yield ”Not a Number” as one of the angles because the resulting delays are not physically realizable.

When it works, the simplification cuts computation for that portion of the program from complexity O(n^2) to O(n). The reason for this is that the”safe” way to scan using the three microphones would be to check each valid pair of delays, where valid would mean that the delays between themicrophones was physically realizable, and then take the pair corresponding to the maximum power whilst the ”quick” way to do so that we ended up usingwas to compute the delay for one pair, compute the delay for the other pair, and then assume that the two delays as a pair were physically realizable. Thisworks if the maximum power is located at one of the valid pairs of delays (as, in most cases where there is a well defined signal, it will be) and fails if it is not, but is in return far faster, much as the reduction in computationalcomplexity would suggest.

Limitations of hardware and computing power

Any increases in computing power and hardware would always be welcome in a computationally intensive project such as this; however, the computersand hardware that were used were far from top of the line, even for five years ago. The DAQ card that was available for use is far enough out of date that it is no longer supported byNational Instruments; in fact, the current version of Labview does not even recognize it.

As a result, in order to be able to interface with the DAQ card that was available, the version of Labview this project was implemented on was also greatly out of date -- to the point where the NI website no longer provided support. A good indicator of the age of the hardware is the fact that the computer used possessed a turbo button. In fact, it seemsthat the computers were probably very good when they were first purchased as the RAM size is actually 32 megabytes. However, that was enough years ago to where they no longer are adequate for the level of processing we wished to do.

With more computing power and better hardware, it would be possible to increase the amount of sampling (restricted by a 64kbyte buffer) and upsampling to increase accuracy and precision, take fewer shortcuts, also to the same effect, or perhaps run in real time (a feat possible only if the processing time is of equivalent length to or less than the time it takes to input a "chunk" of the signal).

Possible extensions

One obvious extension to this project would be to go to a 3-dimensional array, eliminating the ambiguity arising from reflection of signals across the planeof the array. Another possible improvement would be to increase the processing speed to the point where processing in real time could be a possibility. This project only dealt with calculations in far field, which seem to be less computationallytaxing than calculations in near field. Thus, another possible extension would be to implement something that could accurately locate signals in near field. Another possible region of interest might be to investigate beamforming when dealing with multiple signal sources.

Simple delay and sum is optimal (in ability to distinguish, if not in computational complexity) for a single source and white noise, but we are unsure if it is optimal if some structure to the noise is known. In thecase of multiple signals, the other signals would be considered noise when focusing in on one signal. Itmay be possible to focus on each of the signals and separate them. If there is not a closed form for doing so, theseparation could probably be done iteratively by some sort of subtraction. A further extension of this would be to apply blind signal separation techniquesto distinguish signal sources that seem to overlap.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
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Sherica
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Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Investigation of delay and sum beamforming using a two-dimensional array. OpenStax CNX. Feb 04, 2006 Download for free at http://cnx.org/content/col10315/1.3
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