# 6.3 Joint time-frequency analysis

 Page 1 / 1

#### Short time fourier transform

After our system has isolated the whistle sound, it is input to a continuously running analysis algorithm based on the result of a Short-Time Fourier Transform. While the traditional Fourier transforms do not maintain a sense of time, the STFT allows for joint time-frequency analysis. The formula for the STFT is:

$\text{STFT}\left\{x\left[n\right]\right\}=X\left(m,w\right)=\sum _{n\text{=-∞}}^{\infty }x\left[n\right]w\left[n-m\right]{e}^{-\mathrm{jwn}}$

Individual sections of the signal are windowed and their FFT is taken. The result of this operation is a two dimensional function in terms of the offset from zero (“time”) and the frequency content of the signal. According to the Heisenberg Uncertainty Principle, however, we cannot have an arbitrary amount of resolution in both the time and frequency domains. For our application, we are only interested in detecting trends in the frequency with highest power, so time resolution is less important.

#### Spectrogram

Squaring the magnitude of the STFT results in a 3-D function is known as a spectrogram. The spectrogram of a whistle whose pitch goes from low to high looks like this.

Notice that there is a dominant power (dark red) that shows a very clear upward trend over time. Each slice of the frequency axis at a particular time corresponds to a single chunk of the signals’FFTs. The dark red corresponds to the maximum of one of these FFTs, and as time passes (in the positive vertical direction), we see the frequency of highest power increases. Below is a graph of three of these component FFTs, illustrating how the peak frequency increases across time. Since pitch and frequency are essentially synonymous, we can determine what kind of whistle is input by looking at trends in the frequency with the dominant power.

With the dominant frequency for any given windowed input now known, our system then takes the discrete-time derivative of that frequency over the window. Calculus tells us that the derivative of a function at a point is positive for increasing functions and negative for decreasing functions. By continuously taking derivatives of these windows our system can track the basic shape of the spectrogram.

#### Analysis using the stft

Our analysis algorithm keeps a running buffer of the signs of these discrete-time derivatives. It then takes the magnitude signs inside the buffer. If the buffer encounters a number of continuous signs above or below a certain threshold, either positive or negative, it concludes that the input is a whistle with increasing or decreasing pitch, respectively. Finding the optimal threshold value is mostly trial and error; we looked at recordings of sine waves with constant frequencies and white noise in order to determine a reasonable upper bound for the area under the derivative curve.

There is a tradeoff between the size of the buffer and the quality of the analysis. Given that a whistle may last up to three seconds, it’s clear that the buffer need not contain that many samples in order to find and characterize the whistle. But on the same token, too few samples will result in an unusual number of false positives and change the song without any user interaction. And while this is not necessarily complex math, doing it quickly and continuously requires the window be as small as possible.

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
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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 ?
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
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!