# Introduction and motivation

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In this module, we give a brief introduction to sub-band coding, its relation to transform coding, and its use in MPEG-style audio coding.
• Sub-band coding is a popular compression tool used in, for example, MPEG-style audio coding schemes (see [link] ).
• [link] illustrates a generic subband coder. In short, the input signal is passed through a parallel bank ofanalysis filters $\left\{{H}_{i}\left(z\right)\right\}$ and the outputs are “downsampled” by a factor of N . Downsampling-by- N is a process which passes every ${N}^{th}$ sample and ignores the rest, effectively decreasing the data rate by factor N . The downsampled outputs are quantized (using a potentially differentnumber of bits per branch—as in transform coding) for storage or transmission.Downsampling ensures that the number of data samples to store is not any larger than the number of data samples entering the coder;in [link] , N sub-band outputs are generated for every N system inputs.
• Relationship to Transform Coding:   Conceptually, sub-band coding (SC) is very similar to transform coding (TC).Like TC, SC analyzes a block of input data and produces a set of linearly transformed outputs, now called “subband outputs.”Like TC, these transformed outputs are independently quantized in a way that yields coding gain over straightforward PCM.And like TC, it is possible to derive an optimal bit allocation which minimizes reconstruction error variance for a specified average bit rate.In fact, an N -band SC system with length- N filters is equivalent to a TC system with $N×N$ transformation matrix T : the decimated convolution operation which defines the ${i}^{th}$ analysis branch of [link] is identical to an inner product between an N -length input block and ${\mathbsf{t}}_{i}^{t}$ , the ${i}^{th}$ row of T . (See [link] .) So what kind of frequency responses characterize the most-commonly used transformation matrices?Lets look at the DFT first. For the ${i}^{th}$ row, we have
$|{H}_{i}\left(\omega \right)|\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\left|\sum _{n=0}^{N-1},{e}^{-j\frac{2\pi }{N}in},{e}^{-j\omega n}\right|\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\left|\sum _{n=0}^{N-1},{e}^{-j\left(\omega +\frac{2\pi }{N}i\right)n}\right|\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\left|\frac{sin\left(\frac{N}{2}\left(\omega +\frac{2\pi i}{N}\right)\right)}{sin\left(\frac{1}{2}\left(\omega +\frac{2\pi i}{N}\right)\right)}\right|.$
[link] plots these magnitude responses. Note that the ${i}^{th}$ DFT row acts as a bandpass filter with center frequency $2\pi i/N$ and stopband attenuation of $\approx 6$ dB. [link] plots the magnitude responses of DCT filters, where we see that they have even less stopband attenuation.
• Psycho-acoustic Motivations:   We have seen that N -band SC with length- N filters is equivalent to $N×N$ transform coding. But is transform coding the best technique to use in high qualityaudio coders? It turns out that the key to preserving sonic quality under high levels of compression is to shape the reconstruction error so that theear will not hear it . When we talk about psychoacoustics later in the course, we'll see thatthe properties of noise tolerated by the ear/brain are most easily described in the frequency domain.Hence, bitrate allocation based on psychoacoustic models is most conveniently performed when SC outputs represent signal componentsin isolated frequency bands . In other words, instead of allocating fewer bits to sub-band outputshaving a smaller effect on reconstruction error variance, we will allocate fewer bits to sub-band outputs having a smaller contributionto perceived reconstruction error. We have seen that length- N DFT and DCT filters give a $2\pi /N$ bandwidth with no better than 6 dB of stopband attenuation. The SC filters required for high-quality audio coding require muchbetter stopband performance, say $>90$ dB. It turns out that filters with passband width $2\pi /N$ , narrow transition bands, and descent stopband attenuation require impulse responselengths $\gg N$ . In N -band SC there is no constraint on filter length, unlike N -band TC. This is the advantage of SC over TC when it comes to audiocoding A similar conclusion resulted from our comparison of DPCM and TC of equal dimension N ; it was reasoned that the longer “effective” input length of DPCM with N -length prediction filtering gave performance improvement relative to TC. .
• To summarize, the key differences between transform and sub-band coding are the following.
1. SC outputs measure relative signal strength in different frequency bands, while TC outputs might not have a strictbandpass correspondence.
2. The TC input window length is equal to the number of TC outputs, while the SC input window lengthis usually much greater than number of SC outputs (16 $×$ greater in MPEG).
• At first glance SC implementation complexity is a valid concern. Recall that in TC, fast $N×N$ transforms such as the DCT and DFT could be performed using $\sim N{log}_{2}N$ multiply/adds! Must we give up this computational efficiency for better frequency resolution?Fortunately the answer is no ; clever SC implementations are built around fast DFT or DCT transforms and are very efficient as a result.Fast sub-band coding, in fact, lies at the heart of MPEG audio compression (see ISO/IEC 13818-3).

#### Questions & Answers

Eath is Blue marzble
Sreedhar Reply
what is the triad of Venus
Sky Reply
Will you able to discuss what is in the astronomy as a whole?
Joecy Reply
from the beginning of astronomy 'til the present.
Joecy
till the fate of the universe
Kevin
till the universe expanding
Mr
please discuss it to me because it's hard for me to get reliable discussion of it
Joecy
hello joecy well Astronomy is not small to discuss? what do you want To discuss?
Mr
btw we humans first ever recorded counting system and math was based on only 4fingers on the left hand using the left thumb to count the knuckles on 9 digits dating back to Sumerian times
KATASHA
what about a pre-main sequence star. I thought those stars were different from protostar - a type of T Taurie?
Jeffrey
How can we differentiate between space itself expanding and the stuff within space expanding?
Jake Reply
Hello JAKE Astronomers predict that Dark energy is the reason of expansion.Think of the universe as a giant balloon. If you mark multiple points on the balloon, then blow it up, you would note that each point is moving away from all of the others. Universe is expanding from everywhere
Mr
Lol is this a trick question? you can see the obviously basic of things when it's the "stuff within space" is expanding the "stuff" expands individually and completely separate to space itself which is the 'container' for lack of a better word for all "space stuff" Easily discernable either way
KATASHA
The fact that space itself has a finite volume and is expanding is counter intuitive and therefore in principle beyond our imagination. that objects within this finite space are expanding, for example whe xou blow up a balloon is immediately intelligible.
Drafi
It can easily be seen and measured.
Drafi
When we speak of the expanding space, we automatically imagine some kind of voluminous object like a balloon. The term "expansion" itself implies that there is some space, into which the expanding object expands.
Drafi
However, this is not so in the case of the expanding universe. It does not "expand" into some existing space, because it IS space itself. Therefore, the term "expansion" used in connection with the universe is misleading.
Drafi
Ultimately, we have to come to terms with the fact that we live in a world, which is not intelligible on the basis of our personal experience and imagination, but can only be described mathematically. The wonderful and mysterious thing is, however, that these counter intuitive mathematical theories
Drafi
have consequences that can readily be seen and felt and understood.
Drafi
A kind of paradoxical situation, isn't it?
Drafi
The answer to your question, Jake, is therefore something like: The expansion of stuff within space can be seen directly, measured and understood. That is, we can access it intuitively. The expansion of space itself can also be measured as well as explained by mathematical-physsical theories.
Drafi
It can even be seen, albeit only by observing the movement of the galaxies, because in an expanding space their mutual distance increases. Only grasp the whole picture with our imagination we cannot.
Drafi
I dont have a lot of knowledge but let me ask a question None of any satellite has left The milky way galaxy so how did they created the model of the galaxy as they can't see it ? we can understand that we can see other galaxies by telescope but how we were able to see the Milky way galaxy ?
Priyanshu
priyanshu Yep you are right but there are many other galaxies outside our Milky way . Astronomers have observed their positions and behaviors and In the Milky way Astronomers had created the Milky way model by tracking the positions of other stars and their distance and behaviors
Mr
and what is the relation between the universe's expansion and dark matter
Gúñjañ
Gja Rm well Astronomers didn't know that What is actualy Dark Matter but Theory says that our universe is made up of 80%of Dark Matter and about a quarter of its total energy density
Mr
why does the universe expands because the law of conservation of energy says that energy can't be created so by expanding the space is expanding as translational energy and from where this new matter of space is coming for expansion of universe.
Priyanshu
ok what I am trying to say is :where the universe expand ?
Gúñjañ
GÃºÃ±jaÃ±. Think of the universe as a giant balloon. If you mark multiple points on the balloon, then blow it up, you would note that each point is moving away from all of the others. Universe is expanding from everywhere
Mr
priyanshu Let me tell you if the critical density would be more than the actual density of the universe the universe will be expanding forever but if the critical density is less than the actual density then the universe will collapse
Mr
Mr astronomer yah but the ballon expand in its air .do you think that the universe has some things whitch it expand?
Gúñjañ
yep Gja Rm Scientist did measured a crital density of the universe if the critical density would be more than the actual density then the universe will be expanding forever but if the critical density would be less than the actual density then the universe will collide better known as big cruch
Mr
Why does a Neutron star know as the strongest magnet in the universe instead of a Black hole?
Mr Reply
that would be a magnetar- a type of neutron star just like pulsars but with very high B fields.
Kevin
Kevin What is b field? PLEASE could you explain
Mr
what is the cause of blackhole
DazedHotdog Reply
a collapsed massive star
donot
A dead star with intense gravity
Saaketh
star collapse remnant greater than 1.4 solar masses
Kevin
The Chandrasekhar Limit = 1.4 Solar Masses.....
Adam
when a massive star collides Under it's own weight
Mr
when a massive star is run out of fuel to do its activities and the gravity force blow it up
dinda
what about the warmhole?
Gúñjañ
a wormhole or whitehole is predicted to occur naturally or artificially, when two distant entangled black holes are pulled apart, they will form a shortcut that has two ends. help us to travel through universe and time.
dinda
but its is not yet proven, it is just mathematically possible
dinda
what is the difference between An Astronomer and a Cosmologist?
Mr Reply
cosmologist only learn cosmology right. an astronomer is learn all about astronomy, including cosmology
donot
Cosmology Is The Study Of The Universe As A Whole, Origin And Development Of The Universe.....
Adam
astronomy include cosmology, astrophysics, astrodynamic and astrometry
donot
what is astronomy
Joecy Reply
A Branch Of Science That Deals With Celestial Objects And Space.....
Adam
Is the space you had mention is about the outer space?
Joecy
Yes Outer Space.....
Adam
astronomy is the study of the universe beyond the borders of the planet.
rizza
what object can protect my pyramid being affected through doorways and interaction with others?
Christian Reply
what is big bang
Nitesh Reply
This is the blast of extremely huge sphere contains some unique particles from which our lovely universe begins
Aditya
The post-Big Bang universe was composed predominantly of hydrogen, with a little bit of helium thrown in for good measure. Gravity caused the hydrogen to collapse inward, forming structures. However, astronomers are uncertain whether the first massive blobs formed individual stars that later fell to
Mr
The Theory Of The Origin Of Our Universe.....
Adam
Adam ?
Mr
Yes Sir?
Adam
hey Adam You are right
Mr
I Hope So, Lol.....
Adam
Adam ooo well where you from?
Mr
New York City.....
Adam
And Yourself?
Adam
I am from india.I am 15 years old. you?
Mr
I Am 43 Years Old..... From New York City.....
Adam
Can you suggest me some tips to become an Astronomer ? Please
Mr
Start Learning A Lot Of Math Algebra, Calculus Trigonometry, Geometry And Scientific Notation, Get Really Good At It, Once You Can Do All That Math Proficiently, Becoming An Astronmer A Lot Easier..... And When You Win The Nobel In Astronomy, I Can Say I Know You, Lol.....
Adam
you inspired me a lot god bless you! 😄 what is your profession?
Mr
I am Vanessa Harp Future universal traveler 🌌🌌🌌
Vanessa
Iam A Doorman By Trade, I Also Have A Degree In Philosophy.....
Adam
well that's awesome dude
Mr
vanessa i am a mere amateur astronomer but if you do start traveling the universe can i tag along?
josh
I Also Am An Amateur Astronomer.....
Adam
Can we say that there is constant gravitational force in outer space instance of 0 gravity
Aditya Reply
i think garvity is not constat in every place in space,depends on the cosmic that u r near for...
Israel
I think I am right if we imagine a universe in a completely circular sphere or as an atom of some unknown element ... ....
Aditya
if you think this then think about them who use material made up of that
Ashish
element
Ashish
This is not so interesting
Aditya
I also think our universe as complex as our brain and as a computer program
Aditya
yes bro we have not that powers or that is a different dimension which a human brain does not think yet but may be possible after some time
Ashish
a group of seven stars is called
raju Reply
saptarishi
Suresh
The Pleiades.....
Adam
adam is correct
Kayleigh
Both are correct
Pavan
which is the biggest star?
Prabha
I think supper massevic black holes are biggest star
Patel
some stars are small in the size but they powerful then other
Patel
UY Scooty
Pavan
what?
Patel
UY SCUTI biggest star
Siddhansh
Why a neutron star forms ?
Priyanshu
When the star of average size complete their life time.. Then it turns to neutron star,,, our sun is a small star.. So at end he turns into an white dwarf,,, and any other stars which are very big.. The will turn into an black hole..
Pavan
how does a black hole destroys ?
Priyanshu
Well exactly don't know but after engulfs all nearby matter
Pavan
Why our earth or other celestial bodies is approx or completely spherically bounded why this is not square ,rectangle..... .I want to know that universal force which bound them
Aditya Reply
The most stable 3 dimensional shape which keeps the spinning material of that celestial body together in an equilibrium is a sphere. So the shapes are spheres and not squares or something different.
Ujwala
gravity. this force favors spheres and spheroids because spheres allow gravity to act equally in all directions whereas a rectangle or square wouldn't.
Mark
what do you mean by flint glass?
Suresh
which glass is called flint glass?
Suresh
who said Flint glass?
Mark
Stars, planets and moons can be made of gas, ice or rock. Get enough mass in one area, and it’s going to pull all that stuff into a roughly spherical shape. Less massive objects, such as asteroids, comets, and smaller moons have less gravity, so they may not pull into perfect spheres.
Kevin
the mass needed goes by a funny name: the potato radius
Mark
where you heared
Ashish Reply
what?
Grisha
i mean when u enter to a black hole it will take u a billions of light-years away...
Israel
yes because time slows down in more gravity
Ashish
and they said they are not always black
Israel
i don't understand this
Ashish
what do wanna say
Ashish
are black holes always black? what if there is a black hole with a blue color...
Israel
I guess black hole is called black hole because it was sucking matters that around them, including dark matter.
donot
what do u mean by "dark matter"
Israel
How man.. We don't even know what's inside the Black hole.. Just know that even light can't overcome against the gravity of BH.. So BH don't reflect any type of light..
Pavan
in universe black is not colour like other colours you can't change colour of universe because it is its nature given colour if light reflects and then come to our eyes then we saw the colour but a black hole absorbs light and never reflects it back
Ashish
are you never heard of it? well, when you look at space it never illuminated by star's lights right. space itself always look black or you can say dark although there more than zillion stars around
donot
ok then what happens to the materials which are trapped in BH when it dies
Israel
that is why scientist named them by dark matter
donot
Just quit knows about the event horizon,,,.. We don't know that what's beyond the Singularity of BH.. If any others BH singularity joins other singularity then possible well.. Don't know
Pavan
oky thanks guys...
Israel
what begin the black hole? or what is the original form of black hole? its a exploded star and black hole is just making a new star by collecting matters around them If they die, well they just became a material
donot
in our universe real and natural colour is black and light is a form of energy which emit photons colour is of that objects which are in 3 dimensions and when light reflects from these objects it comes back to our eyes space is not 3d so it is not our dimension
Ashish
Its just my thought, okay. if you wanted to know more ask some professor or search it or read a book about BH
donot
i cant know more about it becaus i had just passed my 12th class
Ashish
Well even scientists are still researching about universe we cannot sure yet, if we don't prove it
donot
its my own thinking i can't prove this now but may be in future
Ashish
really, you want to prove it too
donot
yes i wamt but at present i am a student and i have no contact to reserchers if you are then plz help me
Ashish
am also a student in 11th grade...do u some advice for me...
Israel
from which country you are
Ashish
How much u got in 12?
Pavan
from Ethiopia
Israel
i got 80 percent
Ashish
i am from india so i cant know about your country
Ashish
astronomy is world wide..ok which subjects should i pay more attention?
Israel
physics >maths >chemistry
Ashish
ok then thanks again.. stay safe..
Israel
which acid is also called chamber acid?
Suresh
sulfuric because a lead chamber was used to manufacture and process it.
Mark
thank u very much.
Suresh
i heard that black holes are not always black and they can take u to another coordinate...is this true?
Israel Reply
They have no color, and no
Cyclone
black holes have no hair.
hair?... what do you mean by that..
Israel
***en.wikipedia.org/wiki/No-hair_theorem
Black holes size gets increase by Eating massive stars and black hole are made from high massive stars who were exploded in supernova.when a black hole ears a star A quasar is formed thus a black hole is not always black
Mr
Black holes can change its shape by attracting all planets and even light
Saaketh
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
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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, An introduction to source-coding: quantization, dpcm, transform coding, and sub-band coding. OpenStax CNX. Sep 25, 2009 Download for free at http://cnx.org/content/col11121/1.2
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