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This module describes how we implemented the inverse filter for the laser microphone

We observed that the system did not transmit sound information perfectly, and transmitted speech signals suffered some distortion. This distortion happens for two reasons: (1) the physical properties of the glass cause it to respond differently to different frequencies, and (2) low-frequency vibrations caused by air-conditioning systems and other building vibrations are constantly present in the window. We attempted to compensate for this observed distortion by building an inverse filter. We accomplished this in three steps:

Step 1: measure the frequency response

In order to accurately model the system, we needed to measure its frequency response. We blasted a 30-second sound clip of pure white noise at the window and recorded the signal measured by the detection unit. Since we knew the input of the system (the white noise) had a completely flat spectrum, the output’s spectrum should represent the frequency response. To compute the spectrum of the output (the recorded signal), we windowed portions of the signal using a Hamming window, computed the FFT’s of each windowed portion, and then averaged the FFT’s. This average FFT represents the frequency response of our system.

The plot shows some strong low-frequency vibrations in the window. We attributed these to the air-conditioning unit in the building and to other random vibrations in the environment. We also noticed that the window responded better to low frequencies than to high frequencies. This could be a result of the physical properties of the glass as well as the physical dimensions of the window.

Step 2: model the system

Once we had a good idea of the system’s frequency response, we attempted to model the system using a linear prediction filter. We used a linear prediction filter because it made the inverse filter simple to implement, and it guaranteed that the inverse filter would be inherently stable and have a linear phase response. A linear prediction filter estimates its next output by the current input and a linear combination of n previous outputs:

The first step to building this filter is to compute the autocorrelation coefficients of the recorded signal. The autocorrelation coefficients are a measure of the correlation between samples of the signal. Since the filter must accurately estimate the output based on previous outputs, it must preserve the correlation between samples. One autocorrelation coefficient r[i] can be expressed as:

The next step to building the filter was to compute the filter coefficients. We used a recursive algorithm called Burden’s Algorithm to do this. We set the first coefficient a[0] = 1 and then compute the other coefficients recursively:

We could perform this recursion as many times as we needed to compute the desired amount of coefficients. We wrote a MATLAB program to perform the algorithm N times on the windowed signal to generate N coefficients. We used these coefficients in the feedback branches of the filter. We found that we could accurately model the system using a linear prediction filter with 50 coefficients. The frequency response of this filter has a similar shape to the measured frequency response of the system:

Step 3: Build the Inverse Filter

Step 3: build the inverse filter

The linear prediction filter is simple to invert. Since it uses only the previous outputs to generate the next output, it is an all-pole filter with only feedback branches. To build the inverse filter, we used all the feedback coefficients that we generated using Burden’s Algorithm as the feed-forward coefficients of the inverse filter. The frequency response of the inverse filter looks like:

We observed that the inverse filter accurately inverted the response of the system. It successfully attenuated the low-frequency window vibrations, and it amplified the higher frequencies that the system attenuated.

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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what is system testing?
AMJAD
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Remote sound detection using a laser. OpenStax CNX. Dec 19, 2007 Download for free at http://cnx.org/content/col10500/1.1
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