Fixed-point Analysis of Digital Filters

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Fixed-point Analysis of Digital Filters

• for
• VLSI Signal Processing Course

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Quantization in implementing system
A. Ideal system
A/D quantization error
D/A quantization error
B. Nonlinear model
Rounding error
Coefficient quantization error
C. Linear model
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Effect of coefficient quantization in IIR system
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Effect of coefficient quantization in FIR system
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Sensitivity
New pole of are
, i 1,2N
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Example 2nd-order IIR Filter (I)
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Example 2nd-order IIR Filter (II)
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Scaling method

• Three scaling methods

Si Scaling factor Maximum value
of input signal
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Rounding error model

• Range
• Variance

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Direct form I

• Variance of output signal
• Variance of rounding output error

A(z) denominator part of H(z)
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Direct form II

• Variance of output signal
• Variance of rounding output error

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Calculation of SQNR

• SQNR Signal-to-Quantization-Noise Ratio

• SQNR

• In general,SQNR?40dB for practical implementation

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Conclusions

• Fixed-point analysis is required in converting
  floating-point based algorithm into fixed-point
  based implementation (e.g. VLSI circuits
  fixed-point Programmable DSP processors)
• Usually it is done by doing extensive simulations
• Closed-form analytical results help to see the
  effectiveness of each design parameters (W, S,
  etc.)
• Each algorithm has its own numerical property in
  fixed-point implementation