1. Home
  2. Fundamentals of electrical
  3. Digital signal processing
  4. Spectrograms

5.9 Spectrograms

<< Chapter < Page
  Fundamentals of electrical   Page 1 / 1
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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of electrical engineering i' conversation and receive update notifications?

Ask