[PDF] advantages of fourier series

Some advantages of Fourier series
  • A function which is discontinuous can be represented by the Fourier series.
  • The Fourier series of a discontinuous function is not uniformly convergent at all points.
  • Expansion of an oscillating function by Fourier series provides all modes of oscillation.
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  • What are the advantages of Fourier series over Taylor series?

    One of the advantages of a Fourier representation over some other representation, such as Taylor series, is that it may represent a discontinuous function. An example is the sawtooth wave. Another advantage is the representation of periodic functions. easier than dealing with the original driving force.

  • What are the advantages and disadvantages of Fourier Transform?

    The Fourier Transform is limited to analyzing signals that are continuous in time, so it cannot be used to analyze signals that are discrete in time. It is sensitive to noise, so signals with high levels of noise may not be accurately represented by the Fourier Transform.

  • Why is Fourier series important in physics?

    The Fourier series can be defined as a way of representing a periodic function (possibly infinite) as a sum of sine functions and cosine functions. The Fourier series is known to be a very powerful tool in connection with various problems involving partial differential equations.
  • The algorithms for this special case are called fast Fourier transform (FFT). The advantages of the FFT include speed and memory efficiency. The DFT can process sequences of any size efficiently but is slower than the FFT and requires more memory, because it saves intermediate results while processing.
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