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Filter Design

  1. FILTER SPECIFICATION

    The specifications of this filter will be based upon the calculations we have done so far. We have chosen Phase Shift Keying as the Modulation scheme for transmission. The specifications are listed below:

  2. COEFFICIENT CALCULATION

    The method chosen for coefficient calculations was the window method employing the Blackman Window because of its high attenuation factor. A Digital Filter Development software called MultiDSP Digital Filter Design. This software was a student version which enabled only 63 coefficients to be generated at a maximum. The calculated number of coefficients for this filter is 265. The number of bits the coefficients were quantized to were 24 bits. The coefficients are shown below:

     ************************* FILTER SPECIFICATION
    *************************
    
        FILTER TYPE               : BAND PASS
        FILTER SYMMETRY           : SYMMETRIC
        DESIGN APPROACH           : WINDOW METHOD
        WINDOW OPTION             : BLACKMAN WINDOW
        GAIN                      : MAXIMUM GAIN OF 1.0
        QUANTIZATION              :  24 BIT FIXED POINT
        FILTER TAP                :  63 Taps
        SAMPLING FREQUENCY        :            48000 Hz
        PASSBAND CUTOFF FREQ 1    :            15000 Hz
        PASSBAND CUTOFF FREQ 2    :            16000 Hz
        STOPBAND CUTOFF FREQ 1    :            14000 Hz
        STOPBAND CUTOFF FREQ 2    :            17000 Hz
        PASSBAND RIPPLE           :            0.500 dB
        STOPBAND RIPPLE           :           50.000 dB
    
        ************************* BEFORE QUANTIZATION
    **************************
    
        ************** UNQUANTIZED IMPULSE RESPONSE COEFFICIENTS
    ***************
    
         2.714995949E-19    /*  COEFFICIENT   0,  COEFFICIENT  62  */
         6.348643163E-06    /*  COEFFICIENT   1,  COEFFICIENT  61  */
         3.939484940E-05    /*  COEFFICIENT   2,  COEFFICIENT  60  */
        -1.124284746E-04    /*  COEFFICIENT   3,  COEFFICIENT  59  */
         3.280646976E-05    /*  COEFFICIENT   4,  COEFFICIENT  58  */
         1.506520083E-04    /*  COEFFICIENT   5,  COEFFICIENT  57  */
        -1.328757371E-04    /*  COEFFICIENT   6,  COEFFICIENT  56  */
        -4.337752824E-21    /*  COEFFICIENT   7,  COEFFICIENT  55  */
        -2.759598629E-04    /*  COEFFICIENT   8,  COEFFICIENT  54  */
         6.648689100E-04    /*  COEFFICIENT   9,  COEFFICIENT  53  */
         3.244345603E-04    /*  COEFFICIENT  10,  COEFFICIENT  52  */
        -2.763367038E-03    /*  COEFFICIENT  11,  COEFFICIENT  51  */
         2.975420303E-03    /*  COEFFICIENT  12,  COEFFICIENT  50  */
         2.563065753E-03    /*  COEFFICIENT  13,  COEFFICIENT  49  */
        -9.466794531E-03    /*  COEFFICIENT  14,  COEFFICIENT  48  */
         6.469397439E-03    /*  COEFFICIENT  15,  COEFFICIENT  47  */
         9.494757604E-03    /*  COEFFICIENT  16,  COEFFICIENT  46  */
        -2.176452156E-02    /*  COEFFICIENT  17,  COEFFICIENT  45  */
         8.841342829E-03    /*  COEFFICIENT  18,  COEFFICIENT  44  */
         2.382572308E-02    /*  COEFFICIENT  19,  COEFFICIENT  43  */
        -3.828278312E-02    /*  COEFFICIENT  20,  COEFFICIENT  42
    *OEFFICIENT   0 =     1.000000000E+00    = COEFFICIENT  62
        COEFFICIENT   1 =     9.957970570E-01    = COEFFICIENT  61
        COEFFICIENT   2 =     9.832815956E-01    = COEFFICIENT  60
        COEFFICIENT   3 =     9.627307035E-01    = COEFFICIENT  59
        COEFFICIENT   4 =     9.345962593E-01    = COEFFICIENT  58
        COEFFICIENT   5 =     8.994904289E-01    = COEFFICIENT  57
        COEFFICIENT   6 =     8.581661408E-01    = COEFFICIENT  56
        COEFFICIENT   7 =     8.114932836E-01    = COEFFICIENT  55
        COEFFICIENT   8 =     7.604315260E-01    = COEFFICIENT  54
        COEFFICIENT   9 =     7.060007887E-01    = COEFFICIENT  53
        COEFFICIENT  10 =     6.492504730E-01    = COEFFICIENT  52
        COEFFICIENT  11 =     5.912285972E-01    = COEFFIC273516062E-02    =
    COEFFICIENT  38
        COEFFICIENT  25 =     3.740269940E-02    = COEFFICIENT  37
        COEFFICIENT  26 =     2.514381255E-02    = COEFFICIENT  36
        COEFFICIENT  27 =     1.563844754E-02    = COEFFICIENT  35
        COEFFICIENT  28 =     8.591446951E-03    = COEFFICIENT  34
        COEFFICIENT  29 =     3.751654200E-03    = COEFFICIENT  33
        COEFF43E-02    /*  COEFFICIENT  20,  COEFFICIENT  42  */
         6.210189198E-03    /*  COEFFICIENT  21,  COEFFICIENT  41  */
         4.571707337E-02    /*  COEFFICIENT  22,  COEFFICIENT  40  */
        -5.408606188E-02    /*  COEFFICIENT  23,  COEFFICIENT  39  */
        -4.563523902E-03    /*  COEFFICIENT  24,  COEFFICIENT  38  */
         7.088827121E-02    /*  COEFFICIENT  25,  COEFFICIENT  37  */
        -6.246727335E-02    /*  COEFFICIENT  26,  COEFFICIENT  36  */
        -2.293951047E-02    /*  COEFFICIENT  27,  COEFFICIENT  35  */
         9.138002032E-02    /*  COEFFICIENT  28,  COEFFICIENT  34  */
        -5.876849340E-02    /*  COEFFICIENT  29,  COEFFICIENT  33  */
        -4.361423565E-02    /*  COEFFICIENT  30,  COEFFICIENT  32  */
         9.930989521E-02    /*  COEFFICIENT  31  */
    
        ********* HEX MODE OF QUANTIZED IMPULSE RESPONSE COEFFICIENTS
    **********
    
                       0    /*  COEFFICIENT   0,  COEFFICIENT  62  */
                      34    /*  COEFFICIENT   1,  COEFFICIENT  61  */
                     14A    /*  COEFFICIENT   2,  COEFFICIENT  60  */
                  FFFC52    /*  COEFFICIENT   3,  COEFFICIENT  59  */
                     112    /*  COEFFICIENT   4,  COEFFICIENT  58  */
                     4EF    /*  COEFFICIENT   5,  COEFFICIENT  57  */
                  FFFBA6    /*  COEFFICIENT   6,  COEFFICIENT  56  */
                       0    /*  COEFFICIENT   7,  COEFFICIENT  55  */
                  FFF6F6    /*  COEFFICIENT   8,  COEFFICIENT  54  */
                    15C9    /*  COEFFICIENT   9,  COEFFICIENT  53  */
                     AA0    /*  COEFFICIENT  10,  COEFFICIENT  52  */
                  FFA574    /*  COEFFICIENT  11,  COEFFICIENT  51  */
                    617F    /*  COEFFICIENT  12,  COEFFICIENT  50  */
                    53FB    /*  COEFFICIENT  13,  COEFFICIENT  49  */
                  FEC9CC    /*  COEFFICIENT  14,  COEFFICIENT  48  */
                    D3FC    /*  COEFFICIENT  15,  COEFFICIENT  47  */
                   1371F    /*  COEFFICIENT  16,  COEFFICIENT  46  */
                  FD36D3    /*  COEFFICIENT  17,  COEFFICIENT  45  */
                   121B5    /*  COEFFICIENT  18,  COEFFICIENT  44  */
                   30CB8    /*  COEFFICIENT  19,  COEFFICIENT  43  */
                  FB198E    /*  COEFFICIENT  20,  COEFFICIENT  42  */
                    CB7E    /*  COEFFICIENT  21,  COEFFICIENT  41  */
                   5DA0E    /*  COEFFICIENT  22,  COEFFICIENT  40  */
                  F913B6    /*  COEFFICIENT  23,  COEFFICIENT  39  */
                  FF6A77    /*  COEFFICIENT  24,  COEFFICIENT  38  */
                   912DD    /*  COEFFICIENT  25,  COEFFICIENT  37  */
                  F80113    /*  COEFFICIENT  26,  COEFFICIENT  36  */
                  FD1052    /*  COEFFICIENT  27,  COEFFICIENT  35  */
                   BB257    /*  COEFFICIENT  28,  COEFFICIENT  34  */
                  F87A47    /*  COEFFICIENT  29,  COEFFICIENT  33  */
                  FA6ADA    /*  COEFFICIENT  30,  COEFFICIENT  32  */
                   CB62F    /*  COEFFICIENT  31  */
    

  3. REALIZATION

    The structure of the filter is shown below. The transversal structure is shown below as the chosen structure for the filter. This structure is the structure for convolution and provides the simplest and ost effective filter structure form.

    structure

  4. ANALYSIS OF FINITE WORDLENGTH EFFECTS

    The analysis will be shown by the Graphs which are the plot of the quantized coefficients. The graphs will show that the effect of finite wordlength does not hinder in filter performance.

  5. IMPLEMENTATION

    The implementation of the filter will be shown in the assembly code which was written to perform the convolution and sample the input signals. The hardware used was the 56002 Evaluation Module employing the 65002 Digital Signal Processor and the CS4215 Audio Codec.

    Contents

  6. FILTER TYPE:Bandpass Filter
    PASSBAND FREQUENCIES15 - 16 kHz
    TRANSITION WIDTH1 kHz
    STOPBAND ATTENUATION> 50 dB
    SAMPLING FREQUENCY> 48 kHz