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Optimal design of finite precision and infinite precision non-uniform cosine modulated filter bank

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  • This paper investigates the design of non-uniform cosine modulated filter bank (CMFB) with both finite precision coefficients and infinite precision coefficients. The finite precision filter bank has been designed to reduce the computational complexity related to the multiplication operations in the filter bank. Here, non-uniform filter bank (NUFB) is obtained by merging the appropriate filters of an uniform filter bank. An efficient optimization approach is developed for the design of non-uniform CMFB with infinite precision coefficients. A new procedure based on the discrete filled function is then developed to design the filter bank prototype filter with finite precision coefficients. Design examples demonstrate that the designed filter banks with both infinite precision coefficients and finite precision coefficients have low distortion and better performance when compared with other existing methods.

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  • Figure 1.  Uniform CMFB with $M$ subbands

    Figure 2.  Non-uniform CMFB with $\bar{M}$ subbands

    Figure 3.  Magnitude response for the 5-channel non-uniform CMFB with decimation factor (4, 4, 8, 8, 4) and infinite precision coefficients

    Figure 4.  Amplitude distortion for the 5-channel non-uniform CMFB with decimation factor (4, 4, 8, 8, 4) and infinite precision coefficients

    Figure 5.  Magnitude response for the 4-channel non-uniform CMFB with decimation factor (8, 8, 4, 2) and infinite precision coefficients for -85 dB restriction in the prototype filter stopband

    Figure 6.  Amplitude distortion for the 4-channel non-uniform CMFB with decimation factor (8, 8, 4, 2) and infinite precision coefficients for -85 dB restriction in the prototype filter stopband

    Figure 7.  Magnitude response for the 4-channel non-uniform CMFB with decimation factor (8, 8, 4, 2) and infinite precision coefficients for -90 dB restriction in the prototype filter stopband

    Figure 8.  Amplitude distortion for the 4-channel non-uniform CMFB with decimation factor (8, 8, 4, 2) and infinite precision coefficients for -90 dB restriction in the prototype filter stopband

    Figure 9.  Magnitude response for the 4-channel non-uniform CMFB with decimation factor (8, 8, 4, 2) and finite precision coefficients

    Figure 10.  Amplitude distortion for the 4-channel non-uniform CMFB with decimation factor (8, 8, 4, 2) and finite precision coefficients

    Table 1.  Non-uniform (4, 4, 8, 8, 4) CMFB with infinite precision coefficients and N = 154

    MethodsAmplitude
    distortion
    Stopband
    attenuation
    Weighted Chebyshev in [12]0.0042-60.65 dB
    WCLS approach in [12]0.0029-61.49 dB
    Window method [13] with As=650.0067-69.85 dB
    Window method [13] with As=65 as the initial to (12) with a constraint of -65 dB for prototype filter stopband0.0014-65.00 dB
    Proposed method with As=65 and a constraint of -65 dB for prototype filter stopband0.00048-78.23 dB
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    Table 2.  Non-uniform (8, 8, 4, 2) CMFB with infinite precision coefficients

    NMethodsAmplitude dist.Stopband att.
    154Weighted Chebyshev [12]0.0039-60.65 dB
    WCLS [12]0.0028-61.49 dB
    Optimal solution with As=650.00061-71.44 dB
    198 Method in [13] as quoted in [12]0.0025-79.65 dB
    Method in [13] with As=800.0021-89.95 dB
    Proposed method with restriction of -85 dB for prototype filter stopband0.0011-85.00 dB
    Proposed method with restriction of -90 dB for prototype filter stopband0.0012-90.01 dB
     | Show Table
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    Table 3.  Non-uniform (8, 8, 4, 2) CMFB with finite precision coefficients and N = 154

    SPTMethodsAmplitude dist.Stopband att.Total adders
    Inf. precision sol. As=900.0017-90.00 dB-
    Q=250Quantized solution0.0018-81.57 dB250
    $ \epsilon_{d}$=-58 dBLocal optimal0.000696-72.63 dB250
    Optimal solution0.000318-66.52 dB250
    Q=260Quantized solution0.0019-81.63 dB256
    $\epsilon_{d} $=-58 dBLocal optimal0.000684-71.56 dB263
    Optimal solution0.000312-67.84 dB268
    Method in [12] using GA0.0058-56.25 dB266
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    Table 4.  Non-uniform (8, 8, 4, 2) CMFB with finite precision coefficients and N = 198

    SPTMethodsAmplitude dist.Stopband att.Total adders
    Inf. precision sol. $A_s $=900.0012-90.00 dB-
    Q=290Quantized solution0.0013-77.28 dB290
    $\epsilon_{d} $=-75 dBLocal optimal0.000715-75.12 dB289
    Optimal solution0.000498-75.30 dB290
    Q=300Quantized solution0.0014-77.14 dB300
    $\epsilon_{d} $=-75 dBLocal optimal0.00078-76.16 dB300
    Optimal solution0.000505-75.10 dB300
    Method in [12] using GA0.003-62.30 dB315
     | Show Table
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