# 2.9 Spectrograms

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Spectrograms visually represent the speach signal, and the calculation of the Spectrogram is briefly explained.

We know how to acquire analog signals for digital processing ( pre-filtering , sampling , and A/D conversion ) and to compute spectra of discrete-time signals (using the FFT algorithm ), let's put these various components together to learn how the spectrogram shown in [link] , which is used to analyze speech , is calculated. The speech was sampled at a rate of 11.025 kHzand passed through a 16-bit A/D converter.

Music compact discs (CDs) encode their signals at a sampling rate of 44.1 kHz. We'll learn the rationale for thisnumber later. The 11.025 kHz sampling rate for the speech is 1/4 of the CD sampling rate, and was the lowest availablesampling rate commensurate with speech signal bandwidths available on my computer.

Looking at [link] the signal lasted a little over 1.2 seconds. How long was thesampled signal (in terms of samples)? What was the datarate during the sampling process in bps (bits per second)?Assuming the computer storage is organized in terms of bytes (8-bit quantities), how many bytes of computer memory doesthe speech consume?

Number of samples equals $1.2\times 11025=13230$ . The datarate is $11025\times 16=176.4$ kbps. The storage required would be $26460$ bytes.

The resulting discrete-time signal, shown in the bottom of [link] , clearly changes its character with time. To display these spectral changes, thelong signal was sectioned into frames : comparatively short, contiguous groups of samples.Conceptually, a Fourier transform of each frame is calculated using the FFT. Each frame is not so long that significantsignal variations are retained within a frame, but not so short that we lose the signal's spectral character. Roughly speaking, the speech signal's spectrum is evaluated over successive time segments and stacked side by side so that the $x$ -axis corresponds to time and the $y$ -axis frequency, with color indicating the spectral amplitude.

An important detail emerges when we examine each framed signal ( [link] ).

At the frame's edges, the signal may change very abruptly, a feature not present in theoriginal signal. A transform of such a segment reveals a curious oscillation in the spectrum, an artifact directlyrelated to this sharp amplitude change. A better way to frame signals for spectrograms is to apply a window : Shape the signal values within a frame so that the signal decaysgracefully as it nears the edges. This shaping is accomplished by multiplying the framed signal by the sequence $w(n)$ . In sectioning the signal, we essentially applied a rectangular window: $w(n)=1$ , $0\le n\le N-1$ . A much more graceful window is the Hanning window ; it has the cosine shape $w(n)=\frac{1}{2}(1-\cos \left(\frac{2\pi n}{N}\right))$ . As shown in [link] , this shaping greatly reduces spurious oscillations in each frame'sspectrum. Considering the spectrum of the Hanning windowed frame, we find that the oscillations resulting from applying therectangular window obscured a formant (the one located at a little more than half the Nyquist frequency).

What might be the source of these oscillations? To gain some insight, what is thelength- $2N$ discrete Fourier transform of a length- $N$ pulse? The pulse emulates the rectangular window, and certainly has edges.Compare your answer with the length- $2N$ transform of alength- $N$ Hanning window.

The oscillations are due to the boxcar window's Fourier transform, which equals the sinc function.

If you examine the windowed signal sections in sequence to examine windowing's effect on signal amplitude, we see that wehave managed to amplitude-modulate the signal with the periodically repeated window ( [link] ). To alleviate this problem, frames are overlapped (typically by half a frame duration). This solutionrequires more Fourier transform calculations than needed by rectangular windowing, but the spectra are much better behavedand spectral changes are much better captured.

The speech signal, such as shown in the speech spectrogram , is sectioned into overlapping, equal-length frames, with a Hanning window appliedto each frame. The spectra of each of these is calculated, and displayed in spectrograms with frequency extending vertically,window time location running horizontally, and spectral magnitude color-coded. [link] illustrates these computations.

Why the specific values of 256 for $N$ and 512 for $K$ ? Another issue is how was the length-512 transform of each length-256 windowed framecomputed?

These numbers are powers-of-two, and the FFT algorithm can be exploited with these lengths. To compute a longertransform than the input signal's duration, we simply zero-pad the signal.

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
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.
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
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
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Porter
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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
how did you get the value of 2000N.What calculations are needed to arrive at it
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