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picture1_Fourier Transformation Pdf 179978 | M7   Spectrum Representation Of Discrete Time Signals


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File: Fourier Transformation Pdf 179978 | M7 Spectrum Representation Of Discrete Time Signals
sel4223 digital signal processing spectrum representation of discrete time signals musa mohdmokji fourier transformation family periodic signal aperiodic signal continuous fourier transform ft frequency x x f continuous time signal ...

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   SEL4223 Digital Signal Processing
    Spectrum representation of 
      discrete-time signals
        Musa MohdMokji
              Fourier transformation family
                                           Periodic Signal              Aperiodic Signal
                       Continuous                              Fourier Transform (FT)
                       frequency                  -                       X Ω ,X(F)
     Continuous-
     time signal       Discrete          Fourier Series (FS)
                       frequency                                              -
                                                               Discrete-time Fourier Transform 
                       Continuous                 -            (DTFT)
                       frequency                                          X ω ,X(f)
     Discrete-time 
     signal                             Discrete-time Fourier  Discrete Fourier Transform (DFT)
                       Discrete             Series (DTFS)      Fast Fourier Transform (FFT)
                       frequency                                         X[k]
                               Fourier Series
      •   Fourier series is the foundation to all of the Fourier transformation 
          family
      •   The name Fourier Series is actually refers to a representation of 
          periodic signal in terms of sine and cosine signal where sine and 
          cosine signals are known to be a single frequency signal.
      •   In other words, Fourier Series decomposes periodic signal into a 
          series of single frequency signals.
                       Fourier Series (cont.)
      •   Frequency response of the Fourier Series is called ‘Fourier Series 
          Coefficient’.
             Fourier	series,x t        !    Fourier	Series	Coefficient,a%
              (time−domain) 				               				  (frequency−domain)
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...Sel digital signal processing spectrum representation of discrete time signals musa mohdmokji fourier transformation family periodic aperiodic continuous transform ft frequency x f series fs dtft dft dtfs fast fft is the foundation to all name actually refers a in terms sine and cosine where are known be single other words decomposes into cont response called coefficient t domain...

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