# 4.1 Explanation of wiener deconvolution

 Page 1 / 1

## How to use the connexions document template

Our system can be described in block diagram form as:

Where:

• f[n] = our original signal
• h[n] = the room response
• y[n] = measured recording in the room

Assuming the room is an LTI system, y[n] isrelated to f[n] and h[n]by discrete time convolution:

f[n]*h[n]=y[n]

Convolution is commutative so the following also holds:

h[n] * f[n]= y[n]

Taking the Discrete Time Fourier Transform of f[n], h[n], and y[n]shows that in the frequency domain, the convolution of f[n]and h[n] is equivalent to multiplication oftheir Fourier counterparts:

F(jw) H(jw) = Y(jw)

Given a known original signal and a known measured recording, the room’s frequency response can be determinedby division in the frequency domain:

H(jw) = Y(jw) /F(jw)

Similarly, given a known room response and known measured recording, the original signal can be determined by division in the frequency domain.

F(jw) = Y(jw) /H(jw)

The inverse DTFT can then be used to determine the impulse response h[n]or the recovered signal f[n].

## Room noise

The room also contains additive noise (which can be recorded). A more accurate block diagram drawing of oursystem is:

The measured recording, y[n] can be related tothe original signal, room response, and noise in frequency as:

F(jw) H(jw) + N(jw)= Y(jw)

In order to compute the room’s frequency response or the DTFT of the recovered signal, division in thefrequency domain is again performed:

H(jw) = (Y(jw) / F(jw)) – (N(jw)/ F(jw))

F(jw) = (Y(jw) / H(jw)) – (N(jw)/ H(jw))

Many of the fourier coefficients of the room response are small (especially at high frequencies), sodeconvolution has the undesirable effect of greatly amplifying the noise.

## Noise reduction

An improvement upon normal deconvolution is to apply a Wiener filter before deconvolution to reduce the additive noise. The Wiener filter utilizes knowledge of thecharacteristics of the additive noise and the signal being recovered to reduce the impact of noise on deconvolution. Thisprocess is known as Wiener deconvolution . The Wiener filter’s mathematical effect on the room’s frequency response can be seenbelow:

Where “x” is the frequency variable, H(x) is the room’s frequency response, G(x) is the wiener-filtered versionof the inverse of the room response and, S(x) is the expected signal strength of the original signal f[n], and N(x) is the expected signal strength of the additive noise.

F(x) =G(x) Y(x)

Where F(x) is the DTFT of the recovered signal and Y(x) is the DTFT of the measured recording.

The following example from image processing shows effectiveness of Wiener deconvolution at reversing a blurringfilter while accounting for noise.

Because of the added S(x) and N(x) terms, Wiener deconvolution cannot be used without knowledge of theoriginal signal and noise. Voice characteristics are fairly predictable, whereas the characteristics of the room are difficultto estimate. Therefore, Wiener deconvolution can only be used when recovering the audio signal (not to determine the roomresponse).

More information on Wiener Deconvolution can be found here .

#### Questions & Answers

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
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
it is a goid question and i want to know the answer as well
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

### Read also:

#### Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Elec 301 projects fall 2006. OpenStax CNX. Sep 27, 2007 Download for free at http://cnx.org/content/col10462/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elec 301 projects fall 2006' conversation and receive update notifications?

 By Mistry Bhavesh By Rhodes By By