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Explain what a Fourrier Transform is and how it is used.?

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  • wd5gnr
    Lv 4
    2 decades ago
    Favorite Answer

    A Fourier Transform is a mathmatical way to convert a time domain signal to a frequency domain signal and vice versa. What does that mean?

    Suppose you want to detect a certain tone. An FT (Fourier Transform) could take the input from a microphone. Imagine that the input is a sine wave at one frequency (say 1kHz). Then the output will be a "spike" at 1kHz since the x axis of the FT is frequency. Feed the spike to the inverse transform and you'd get the sine wave back out.

    So frequency detection is one application. If you put a square wave in, you'd find that the square wave has a spike at the fundamental frequency and spikes at the odd harmonics. If you don't belive that, try sketching some sine waves at f, 3*f, 5*f, 7*f, and add them together (easy with Excel or Matlab) and watch how quick it "squares" up.

    Another application is filtering. Manipulating data in the frequency domain allows you to build very sharp filters... then passing it through the inverse transform produces the signal after filtering.

    There are other applications such as correlation, tomography, etc.

    In the real world, you probably use a Discrete FT (DFT) and probably an FFT (Fast FT) which is a specific computer algorithm for a DFT. DFT means that the input is sampled as it would be for a computer. Computers don't read sine waves, they read little points on sine waves every X microseconds. The frequency they read the signal must be at least twice the frequency of interest, or you won't get proper results.

  • 2 decades ago

    The Fourier Transform of a function gives the distribution of its frequency components. Depending on the periodicity of the function which will be Fourier-transformed the result could be a continuous or discrete distribution (periodic functions produce discrete distributions), and depending if the original function is continuous or discrete the resulting distribution will be aperiodic or periodic (some king of duality here). As we're talking about frequency components, the result of a Fourier transform is (obviously) a function of the frequency, most appropriately, the cyclic frequency omega (in rad/s). Nowadays it is used almost everywhere: digital signal processing (audio, video and still images), medical applications, telecommunications, etc.

  • 2 decades ago

    mathematical approximation: approximateis transcendentic function using the terms of a Fourier series as an approximation

    The Fourier transform, named after Joseph Fourier, is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i.e. as a sum or integral of sinusoidal functions multiplied by some coefficients ("amplitudes"). There are many closely related variations of this transform, summarized below, depending upon the type of function being transformed. See also: List of Fourier-related transforms.

  • bobweb
    Lv 7
    2 decades ago

    In electrical engineering, it's used to find the frequency components that are contained in different time domain waveforms. A pure sinusoidal time domain waveform, for example, has just one line in it's frequency spectrum found by applying the Fourier Transform to the time waveform. The household AC voltage that powers everything plugged into your AC wall sockets is a periodic sinusoidal waveform that repeats 60 times (cycles) per second. One cycle per second is designated as one Hertz. So the Fourier transform of a 60 Hertz sinewave oscillating along a time axis is a single line located at a frequency of 60 Hertz along the frequency domain axis calibrated in frequency increments measured in Hertz. Of course the Fourier Transform is more basic to Mathematics which is included in all engineering curriculums. Since music or voice are complex time domain waveforms containing large numbers of sinewaves, each oscillating at a different sinusoidal periodicity along the time axis, the Fourier Transform is nearly a continuous distribution of spectral lines along the frequency axis extending sometimes up to 20,000 Hertz or more.

  • 2 decades ago

    cheese

    Source(s): ham
  • 2 decades ago

    you dont want to know

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