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picture1_Processing Pdf 180079 | Chapter 4 B Handout


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File: Processing Pdf 180079 | Chapter 4 B Handout
eele 4310 digital signal processing dsp chapter 4 frequency analysis of signals part two spring 2012 2013 eele 4310 digital signal processing dsp ch 4 dr musbah shaat 1 13 ...

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                  EELE 4310: Digital Signal Processing (DSP)
                         Chapter # 4 : Frequency Analysis of Signals
                                                       (Part Two)
                                                     Spring, 2012/2013
    EELE 4310: Digital Signal Processing (DSP) - Ch.4                         Dr. Musbah Shaat                           1/13
                   Outline
     1    Frequency Analysis of Discrete-Time Signals
    EELE 4310: Digital Signal Processing (DSP) - Ch.4                         Dr. Musbah Shaat                           2/13
                   Frequency Analysis of Discrete-Time Signals
                   The Fourier Series for Discrete-Time Periodic Signals ... 1
             The Fourier series representation of continuous time periodic signal:
                     Can consist of an infinite number of frequency components (possible
                     frequency range −∞ < f < ∞).
                     The frequency spacing between two successive harmonically related
                     frequencies is 1 , where T is the fundamental period.
                                          Tp                p
             The frequency range of discrete-time signals is unique over the
             interval (−π,π) or (0,2π).
             Adiscrete-time signal of fundamental period N can consist of
             frequency components separated by 2π radians or f = 1 cycles.
                                                                         N                             N
      The Fourier series representation of the discrete time periodic signal will
      contain at most N frequency components.
    EELE 4310: Digital Signal Processing (DSP) - Ch.4                         Dr. Musbah Shaat                           3/13
                   Frequency Analysis of Discrete-Time Signals
                   The Fourier Series for Discrete-Time Periodic Signals ... 2
      Discrete-Time Fourier Series (DTFS)
                                                            P
             Synthesis equation : x(t) =                        N−1c ej2πkn/N
                                                          Pk=0 k
             Analysis equation : c = 1                        N−1x(n)e−j2πkn/N
                                               k       N      n=0
             where N is the fundamental period of the signal.
             The Fourier series coefficient {ck} form a periodic sequence when
             extended outside of the range k = 0,1,··· ,N − 1, i.e. c                                            =c
                                                                                                         k+N           k
                               P                                                 P
             c         = 1         N−1x(n)e−j2π(k+N)n/N = 1                          N−1x(n)e−j2πkn/N = c
               k+N         N       n=0                                        N      n=0                                  k
      The spectrum of a signal x(n), which is periodic of period N, is a
      periodic sequence with period N. Consequently, any N consecutive
      samples of the signal or its spectrum provide a complete description of
      the signal in the time and frequency domains.
    EELE 4310: Digital Signal Processing (DSP) - Ch.4                         Dr. Musbah Shaat                           4/13
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...Eele digital signal processing dsp chapter frequency analysis of signals part two spring ch dr musbah shaat outline discrete time the fourier series for periodic representation continuous can consist an innite number components possible range f spacing between successive harmonically related frequencies is where t fundamental period tp p unique over interval or adiscrete n separated by radians cycles will contain at most dtfs synthesis equation x c ej kn pk k e j coecient ck form a sequence when extended outside i spectrum which with consequently any consecutive samples its provide complete description in and domains...

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