4.4 Mp3 and aac: mdct processing

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In MP3 and AAC coders, the frequency resolution of the polyphase quadrature filterbank is increased using a cascaded MDCT stage. We describe that here, and give the details of the MDCT stage.

Mdct filterbanks

• Hybrid Filter Banks: In more advanced audio coders such as MPEG “Layer-3” or MPEG“Advanced Audio Coding” (the details of which will be discussed later), the 32-band polyphase quadrature filterbank (PQF) is thought to not giveadequate frequency resolution, and so an additional stage of frequency division is cascaded onto the output of the PQF.This additional frequency division is accomplished using the so-called “Modified DCT” (MDCT) filterbank.(See [link] .)
• Lapped Transforms: The MDCT is a so-called “lapped transform.”At the encoder, blocks of length $2Q$ which overlap by Q samples are windowed and transformed, generating Q subband samples each. At the decoder, the Q subband samples are inverse-transformed and windowed.The windowed output samples are overlapped with and added to the previous Q windowed outputs to form the output stream. [link] gives an intuitive view of the coding/decoding operation, while [link] and [link] specify the specific coder/decoder implementations used in the MPEG schemes.
• Perfect Reconstruction: Based on the cancellation of time-domain aliasing components, Princen, Johnson,&Bradley show (in ICASSP 87 and TASSP 86 papers) that the MDCT acheives perfect-reconstruction when window $\left\{{w}_{n}\right\}$ is chosen so that overlapped squared copies sum to one, i.e.,
$1\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{w}_{n+Q}^{2}+{w}_{n}^{2}\phantom{\rule{1.em}{0ex}}\text{for}\phantom{\rule{1.em}{0ex}}0\le n\le Q-1.$
The “sine” window
${w}_{n}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}sin\left(\frac{\pi }{2Q},n\right)\phantom{\rule{1.em}{0ex}}\text{for}\phantom{\rule{1.em}{0ex}}0\le n\le 2Q-1$
is one example of a window satisfying this requirement, and it turns out to be the one used in MPEG Layer-3.
• Frequency Resolution: With a window length that is only twice the number of transformoutputs, we cannot expect very good frequency selectivity. But, it turns out that this is not a problem.In MPEG Layer-3, sine-window MDCTs appear at the outputs of a 32-band PQF where frequency selectivity is not a critical issue due to thelimited frequency resolution of the human ear. In MPEG AAC, a 4-band PQF in conjunction with an optimized MDCT windowfunction gives frequency selectivity just above that which current psychoacoustic models deem necessary (see M. Bosi et al., "ISO/IEC MPEG-2 Advanced Audio Coding" in JAES Oct 1997).
• Window Switching: Larger values of Q lead to increased frequency resolution but decreased time resolution.Time resolution is linked to the following: error due to the quantization of one MDCT output is spread out over $\approx 2QN$ time-domain output samples. For signals of a transient nature, choosing $QN$ too high leads to audible “pre-echoes.”For less transient signals, on the other hand, the same value of $QN$ might not be perceptible (and the increased frequency resolution might be very beneficial).Hence, most advanced coding schemes have a provision to switch between different time/frequency resolutions depending on localsignal behavior. In MPEG Layer-3, for example, Q switches between 6 and 18. This is accomplished using a sine window of length 36, a sinewindow of length 12, and intermediate windows which are used to switch between the long and short windows while retaining theperfect reconstruction property. [link] shows an example window sequence.

where we get a research paper on Nano chemistry....?
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
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
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
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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