<< Chapter < Page Chapter >> Page >
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 11025 13230 . The datarate is 11025 16 176.4 kbps. The storage required would be 26460 bytes.

Got questions? Get instant answers now!

Speech spectrogram

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] ).

Spectrogram hanning vs. rectangular

The top waveform is a segment 1024 samples long taken from the beginning of the "Rice University" phrase. Computing [link] involved creating frames, here demarked by the vertical lines, that were 256 sampleslong and finding the spectrum of each. If a rectangular window is applied (corresponding to extracting a frame fromthe signal), oscillations appear in the spectrum (middle of bottom row). Applying a Hanning window gracefully tapers thesignal toward frame edges, thereby yielding a more accurate computation of the signal's spectrum at that moment of time.
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 n N 1 . A much more graceful window is the Hanning window ; it has the cosine shape w n 1 2 1 2 n N . 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- 2 N discrete Fourier transform of a length- N pulse? The pulse emulates the rectangular window, and certainly has edges.Compare your answer with the length- 2 N transform of alength- N Hanning window.

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

Got questions? Get instant answers now!

Non-overlapping windows

In comparison with the original speech segment shown in the upper plot, the non-overlapped Hanning windowed version shownbelow it is very ragged. Clearly, spectral information extracted from the bottom plot could well miss importantfeatures present in the original.

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.

Overlapping windows for computing spectrograms

The original speech segment and the sequence of overlapping Hanning windows applied to it are shown in the upper portion.Frames were 256 samples long and a Hanning window was applied with a half-frame overlap. A length-512 FFT of each frame wascomputed, with the magnitude of the first 257 FFT values displayed vertically, with spectral amplitude valuescolor-coded.

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.

Got questions? Get instant answers now!

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Fundamentals of signal processing. OpenStax CNX. Nov 26, 2012 Download for free at http://cnx.org/content/col10360/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of signal processing' conversation and receive update notifications?