# 4.2 Active sonar detection in ambient noise  (Page 2/4)

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$h=\left(x,y\right)\in {H}^{\tau }$ if ${R}_{\text{min}}<\sqrt{\left(x-{x}_{r}{\right)}^{2}+\left(y-{y}_{r}{\right)}^{2}}<{R}_{\text{max}}$

Where we are assuming that the depth of the target is small when compared to its $\left(x,y\right)$ coordinates, the receiver is located at $\left({x}_{r},{y}_{r}\right)$ . ${R}_{\text{min}}$ is the range at which the echo is noise, not reverberation limited, and ${R}_{\text{max}}$ is the farthest range of interest. For this problem, $h$ is an index into the target range from the sonar.

The sonar transmits the waveform $m\left(t\right)$ for each ping. In most sonar transmitters, the transmitted waveform is narrow-band, that is, the waveform bandwidth is much smaller than its center frequency, $f$ . This is true because efficient sonar transmitters use resonant mechanical and electrical components to provide maximum electrical to sound power transfer. An approximation therefore is to model the transmitted waveform as an amplitude modulated carrier:

$m\left(t\right)=\text{sin}\left(2\pi \text{ft}\right)w\left(t\right)$ , $t=\left(0,T\right)$

We will assume that the target is motionless, so that Doppler effects can be ignored. We will assume that the sonar receiver is a single sensor, with no directionality characteristics. For each target location hypothesis $h=\left(x,y\right)$ we know approximately the received echo time series:

$g\left(t\mid h\right)=\text{Bm}\left(t-2R/c\right)$

The amplitude $B$ is related to the propagation loss out to the target hypothesis location, and the reflection characteristics of the target. The time delay $2R/c$ corresponds to the time it takes for the transmission waveform to reach the target and return to the sonar. $R$ is the range to the target and c is the effective speed of sound, when including refraction and boundary reflections.

The received echo is band-limited to approximately the same frequency band as the transmission. The receiver bandwidth may be greater than the transmitted bandwidth due to Doppler frequency shifts, but for the present, we are assuming that the target is not moving. Sonar receivers use heterodyne techniques to reduce the data storage of the ping history. The sonar receiver multiplies the ping history by a carrier signal ${e}^{-\mathrm{j2\pi }\text{ft}}$ to shift the positive frequency part of the received echo closer to DC. The resulting signal is then low pass filtered to eliminate the shifted negative frequency part of the ping history. Since the original ping history was real, the negative frequency part of the signal spectra carries no additional information. The result is a complex signal with a lower bandwidth, but retains all of the echo related information of the original ping history. This heterodyne process can be done in the analog or digital domain.

A target echo passing through the heterodyne part of the sonar receiver becomes:

$r\left(t\mid h\right)={\text{Ae}}^{\mathrm{j\theta }}w\left(t-2R/c\right)$

The phase shift $\theta$ corresponds to the phase shift due to heterodyne operation; the uncertainty in propagation conditions; and the summation of multi-path arrivals with almost the same time delay, etc.

We will assume that the target echo amplitude, ${\text{Ae}}^{\mathrm{j\theta }}$ ,is a complex Gaussian random variable with zero mean and with standard deviation ${\sigma }^{2}\left(h\right)\text{.}$ We are modeling the echo as having the same waveform as the transmission, but with an uncertain phase and amplitude. This is assuming that the target echo amplitude obeys Swerling target type I statistics with unknown phase.

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
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Damian
yes that's correct
Professor
I think
Professor
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nanocopper obvius
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Damian
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LITNING
scanning tunneling microscope
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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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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
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