1. Fixed-point Analysis of Digital Filters
for
VLSI Signal Processing Course

2. 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

3. Effect of coefficient quantization in IIR system

4. Effect of coefficient quantization in FIR system

5. Sensitivity
New pole of are
, i = 1,2…N

6. Example:
2nd-order IIR Filter (I)

7. Example:
2nd-order IIR Filter (II)

8. Scaling method Three scaling methods Si : Scaling factor
: Maximum value
of input signal

9. Rounding error model
Range :
Variance :

10. Direct form I Variance of output signal
Variance of rounding output error
A(z) : denominator part of H(z)

11. Direct form II Variance of output signal
Variance of rounding output error

12. Calculation of SQNR SQNR: Signal-to-Quantization-Noise Ratio SQNR
In general,SQNR40dB for practical implementation

13. 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