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EE DIGITAL SIGNAL PROCESSING

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					                           EE 556 DIGITAL SIGNAL PROCESSING
                                FALL 1998 IN-CLASS FINAL
1.   A communication signal with the following spectrum is sampled at 152 kHz and is to processed by the
     following DSP system




                                                                                                              f (kHz)
     -63             -38                 -23 -15       0     15        23               38              63
                                            -19                   19



                               Lo-Pass


                                Band
                                                                              Lo-Pass
                                 Pass


                                 Pilot
                                Band             Doubler
                                 Pass

                              Input                                             Output
                                                              FFT
                              Buffer                                            Buffer


                              Window




A. A digital low-pass filter is to be designed to extract the base-band signal. Its performance requirements
   are: passband 0-15 kHz, stopband 19-76 kHz, Out of band attenuation, 60 dB, and in-band ripple 0.1
   dB. The filter will be designed with the Remez algorithm. Estimate the length of the filter. Estimate the
   number of bits required for the filter coefficients for the filter to meet its dynamic range.

B. A digital broadband band-pass filter is to be designed to extract the band-pass signal. Its performance
   requirements are: stopband 0-19 kHz, passband 23-63 kHz, stopband 67-76 kHz, Out of band attenua-
   tion, 60 dB, and in-band ripple 0.1 dB. The filter will be designed with the Remez algorithm. Estimate
   the length of the filter. Estimate the number of bits required for the filter coefficients for the filter to
   meet its dynamic range.

C. A digital narrow-band filter is to be designed to extract the pilot carrier at 19 kHz. Its performance
   requirements are: stopband 0-15 kHz, passband 18.9-19.1 kHz, stopband 23-76 kHz, Out of band at-
   tenuation, 60 dB, and in-band ripple 0.1 dB. The filter will be designed with the Remez algorithm. Es-
   timate the number of bits required for the filter coefficients for the filter to meet its dynamic range.
D. The sampled data is to be processed by a Fast Fourier Transform. The Input sample rate is 152 kHz.
   The desired spectral resolution of the transform is 4 kHz. Estimate the length of the transform.

E. The sampled data is to be processed by a different Fast Fourier Transform. The Input sample rate is
   152 kHz. The desired spectral resolution of the transform is 100 Hz. Estimate the length of the trans-
   form to obtain this resolution.

F.   Someone suggested we build a narrow-band filter that along with a linearly sweeping sinusoid would
     perform the spectral decomposition of the FFT. The specification of the filter is as follows. The input
     sample rate is 152 kHz, the two-sided bandwidth is 50 Hz, the transition bandwidth is 50 Hz, and the
     out-of-band attenuation is 20 dB. Estimate the length of this filter.

G. The sweeping sinusoid required for the above (problem F) is to sweep from zero to 20 kHz in 0.5
   seconds, return to zero frequency for 5 milliseconds, and then start the next sweep.
       i.        Sketch the time profile of the frequency sweep.
       ii.       Sketch the time profile of the frequency sweep in sampled data space
                          (Time axis replaced with sample number, frequency axis replaced with
                          digital frequency of rad/sampl.)
       iii.      Write the MATLAB code to generate this sweep.

H. Someone else suggested we use a rectangle filter of length N, (1 1 1 1 1 1 ….1) as a narrow-band filter.
      i.       Sketch the time response of this filter.
      ii.      Write the z-transform of this filter as a polynomial
      iii.     Write the z-transform of this filter as a ratio of polynomials
      iv.      Sketch the frequency response of this filter. Indicate amplitudes and bandwidths,
      v.       Determine the length of the filter (N) to satisfy the specification listed in F.
      vi.      Determine and sketch the impulse response of the cascade of two filters of length N.
      vii.     Sketch the frequency response of this cascade filter. Indicate amplitudes and bandwidths