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PDF The Complex Fourier Transform

Transform Fourier Series) can be carried out with either real numbers or complex numbers This group of data becomes the real part of the time domain signal 

  • What is the input of FFT?

    Because you want to analyze audio data, your input to the discrete Fourier transform (DFT or FFT), is a 1-dimensional sequence of real numbers, which represents the changing voltage of the audio signal over time, and your audio file is a digital representation of that changing voltage over time.

  • For a signal with only cosine waves, fourier transform, aka.
    FFT produces completely real output.
    For a signal composed of only sine waves, it produces completely imaginary output.
    A phase shift in any of the signals will result in a mix of real and complex.24 avr. 2012

  • What is the number of complex additions in FFT?

    The number of complex additions is Nlog2N.
    For illustrative purposes, Figure TC. 3.2 depicts the computation of N = 8 point DFT.
    We observe that the computation is performed in tree stages, beginning with the computations of four two-point DFTs, then two four-point DFTs, and finally, one eight-point DFT.

  • Complex numbers are generated when using FFT because they are needed to represent the magnitude and phase of the frequency components in a signal. The complex numbers are generated when using FFT because they represent both the magnitude and phase information of the frequency components in the input signal.
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