# 0.3 Reconstructing a dft with a pitch shift

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This is an overview of the technique used to recompse an audio signal from one half of the DFT as well as shifting the harmonics in the signal.

## Reconstructing the first half of the dft

With the first harmonic in hand (if, of course, it exists) the program is ready to manipulate the signal chunk by building a new DFT from scratch but based upon the original. The pitch you hear is the position of the fundamental frequency – the first harmonic. So the new DFT must take the frequencies at and around the original first harmonic and copy them, without alteration, to a spot further down the spectrum. Further, in fact, by exactly the desired pitch shift. The frequency of the second harmonic needs to be twice as large as the first so that the new voice sounds like it came from a real person, so the second harmonic and its neighboring frequencies are shifted twice as far down the spectrum as the first group. This is repeated with every harmonic in a similar way until half of the new DFT is full.

## Reconstructing the second half of the dft

To reduce computational complexity, there is no need to perform this same task starting at the end of the original DFT working our way towards the middle. We know that the resulting time-domain signal we produce must be comprised of real numbers since people are going to actually listen to it, so we can exploit the symmetry properties of the DFT. That is, the DFT of a real-valued signal follows rule that the real part of the samples in the first half is a mirror image of the real part of the samples in the second half. Similarly, the imaginary part of the samples in the second half is a flipped (negative) mirror image of the imaginary part of the samples in the second half. This line simple for loop constructs the entire second half of the new DFT without any further analysis or computation. Here is an example of the magnitude of the spectrum for a chunk of signal before and after pitch manipulation. Notice how the harmonics are not merely shifted over, but spread out as well.

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
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
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
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?
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Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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