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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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