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Information about Acoustic Spectroscopy

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A spectrogram of violin playing with linear frequency on the vertical axis and time on the horizontal axis. The bright lines show how the spectral components change over time. The intensity coloring is logarithmic (black is −120 dBFS).


The spectrogram is the result of calculating the frequency spectrum of windowed frames of a compound signal. It is a three-dimensional plot of the energy of the frequency content of a signal as it changes over time.

Spectrograms are used to identify phonetic sounds, to analyse the cries of animals, and in the fields of music, sonar/radar, speech processing, etc. A spectrogram can also be called a spectral waterfall, sonogram, voiceprint, or voicegram. The instrument that generates a spectrogram is called a sonograph.

Format

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A spectrogram of an FM signal.


In the most usual format, the horizontal axis represents time, the vertical axis is frequency, and the intensity of each point in the image represents amplitude of a particular frequency at a particular time. Often the diagram is reduced to two dimensions by indicating the intensity with thicker lines, more intense colors or grey values.

There are many variations of format. Sometimes the vertical and horizontal axes are switched, so time runs up and down. Sometimes the amplitude is represented as the height of a 3D surface instead of color or intensity. The frequency and amplitude axes can be either linear or logarithmic, depending on what the graph is being used for. For instance, audio would usually be represented with a logarithmic amplitude axis (probably in dB), and frequency would be linear to emphasize harmonic relationships, or logarithmic to emphasize musical, tonal relationships.

Generation

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Spectrogram of a male voice saying "tatata"
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Spectrogram of a Japanese woman saying "minato"


Spectrograms are usually created in one of two ways; either with a series of bandpass filters, or calculated from the time signal using the short-time Fourier transform (STFT).

The filter method is usually used in the analog, continuous version of measurement. The frequency range of the signal (an audio signal, for instance, would have frequencies in the range of 20 Hz - 20 kHz) is divided into equal sections, either linearly (0-100, 100-200, 200-300, ...), or logarithmically (10-100, 100-1000, 1000-10000, ...). The signal is input to a corresponding filter, which removes most of the signal that does not fall within its frequency band (imperfect window functions and limited frequency resolution will cause some "bleeding" between adjacent frequency bands). The magnitudes of each filter's output are recorded as functions of time. Each recording then corresponds to a horizontal line in the image; a measurement of magnitude versus time for a specific frequency band.

To calculate the spectrogram using the magnitude of the STFT is usually a digital process. Digitally sampled data, in the time domain, is broken up into chunks, which usually overlap, and Fourier transformed to calculate the magnitude of the frequency spectrum for each chunk. Each chunk then corresponds to a vertical line in the image; a measurement of magnitude versus frequency for a specific moment in time.

The spectrums or time plots are then "laid side by side" to form the image or a three-dimensional surface.

The spectrogram is given by the magnitude of the STFT of the function:

Creating sound from a spectrogram

The above process can be reversed; some programs are available that turn a digital image into sound:
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A spectrograph of the white noise at the end of the leaked version of "My Violent Heart," from Nine Inch Nails' Year Zero
This technique allows electronic music artists to "hide" images in their music. Examples include:
  • Aphex Twin hid an image of himself in a spectrogram. The image can be found on Track 2 of the Windowlicker EP as a nine-second sweeping section right at the end. (It is recognizable in an MP3, but the compression changes the spectrogram and it is not as clear as from the CD.) Aphex Twin also hid the image of a spiral shape in his first track from the "Windowlicker" EP. http://www.bastwood.com/aphex.php
  • The song "Look" from Venetian Snares' album Songs About My Cats, contains several images of his cats.
  • The song "3recurring" from Plaid on their album Rest Proof Clockwork contains the recurring 3s represented as a logo on the cover of the "Not for Threes" album.
  • Nine Inch Nails has employed this technique on a few occasions as part of an ongoing Alternate Reality Game for their latest album Year Zero.
  • The MP3 version of "My Violent Heart" (deliberately leaked before Year Zero was released) contains a few brief moments of static at the end. When analyzed in a spectrogram, it reveals the image of a hand reaching down from the sky. This image echoes a similar theme seen throughout the viral marketing campaign launched for the album. On the official version of the album, the sound appears at the end of the song "The Warning."
  • Another new Nine Inch Nails track from Year Zero was also found on a flash drive in a bathroom stall on their current European tour. This time it was "Me, I'm Not." Along with the song, was an MP3 of "cricket chirping", which when put through a spectrogram revealed the number: 216.333.1810.
  • Using this method again to deliver clues as part of the Year Zero ARG, there were two extra audio files included in the Garageband Multitrack files for the song Capital G. The images in the sounds are of various avatars of user at the Nine Inch Nails oriented forum Echoing the Sound. The user names are used to form the title of a new site that is part of the ARG.
Some modern music is also created using spectrograms as an intermediate medium; changing the intensity of different frequencies over time, or even creating new ones, by drawing them and then inverse transforming.

VLF-reception with the PC

Using spectrograms generated by audio-band FFT-software is a very convenient way to receive frequencies below 24 kHz. This technique allows wide-range reception of the VLF-range.

Further applications

On spectrograms of the records of Mike Oldfield's song "Tubular Bells" signals from the Rugby VLF transmitter are found.

See also

External links

frequency spectrum of the light. When all the visible frequencies are present in equal amounts, the effect is the "color" white, and the spectrum is a flat line. Therefore, flat-line spectrums in general are often referred to as white
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In signal processing, a window function (or apodization function) is a function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window
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signal is any time-varying quantity. Signals are often scalar-valued functions of time (waveforms), but may be vector valued and may be functions of any other relevant independent variable.

The concept is broad, and hard to define precisely.
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Phonetics (from the Greek word φωνή, phone meaning 'sound, voice') is the study of the sounds of human speech. It is concerned with the actual properties of speech sounds (phones), and their production, audition and perception, while phonology, which
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SONAR (SOund NAvigation and R anging) — or sonar — is a technique that uses sound propagation under water (primarily) to navigate, communicate or to detect other vessels. There are two kinds of sonar — active and passive.
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Radar is a system that uses electromagnetic waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain.
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Speech processing is the study of speech signals and the processing methods of these signals.

The signals are usually processed in a digital representation whereby speech processing can be seen as the intersection of digital signal processing and natural language processing.
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time.

One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. A sequel, titled Amplitude was released in 2003.
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Intensity is a widely-used term, which can mean:

In colloquial use:
  • Strength
  • Amplitude
  • Level
  • Magnitude
In physics:
  • Intensity (physics), power per unit area (W/m2)

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logarithm (to base b) of a number x is the exponent y that satisfies x = by. It is written logb(x) or, if the base is implicit, as log(x).
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The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level.
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band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. An example of an analogue electronic band-pass filter is an RLC circuit (a resistor-inductor-capacitor circuit).
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The short-time Fourier transform (STFT), or alternatively short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.
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An analog or analogue signal is any time continuous signal where some time varying feature of the signal is a representation of some other time varying quantity. It differs from a digital signal in that small fluctuations in the signal are meaningful.
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An audio filter is a type of filter used for processing sound signals. Many types of filters exist for applications including graphic equalizers, synthesizers, sound effects, CD players and virtual reality systems.
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In signal processing, a window function (or apodization function) is a function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window
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The term digital signal is used to refer to more than one concept. It can refer to discrete-time signals that are digitized, or to the waveform signals in a digital system.
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In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous-time signal) to a sequence of samples (a discrete-time signal).
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For other senses of this word, see magnitude.


The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which
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Macintosh, commonly known as Mac, is a brand name which covers several lines of personal computers designed, developed, and marketed by Apple Inc. Named after the McIntosh variety of apple, the original Macintosh was released on January 24, 1984.
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FL Studio (formerly Fruity Loops) is a digital audio workstation, developed by Didier Dambrin (also known as 'Gol'), lead programmer of Image-Line Software. Music is created by recording and mixing audio and/or MIDI data together to create a song, which can then be saved to
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Electronic music refers to music that emphasizes the use of electronic musical instruments or electronic music technology as a central aspect of the sound of the music. [1]
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