Quick Answer
Calculate FPGA IIR Filter Minimum Pole-to-Unit-Circle Distance under Coefficient Quantization
Calculator
Result Interpretation
FPGA IIR Filter Minimum Pole-to-Unit-Circle Distance under Coefficient Quantization Calculator computes Minimum pole-to-unit-circle distance in dimensionless using the defined engineering formula and the input values provided.
Worked Example
Verified calculation
Given:
- Coefficient quantization step size = 0.00390625
- Imaginary part of dominant pole (quantized) = 0.05
- Real part of dominant pole (quantized) = 0.98
Expected Result:
- Minimum pole-to-unit-circle distance = 0.018725318781739
Engineering Interpretation:
Under the given input conditions, the calculated result is: Minimum pole-to-unit-circle distance = 0.018725318781739 dimensionless.
The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from automatically validated test cases.
Formula / Method
minimum pole-to-unit-circle distance = abs(1.0 - sqrt(pow(quantized, 2) + pow(quantized, 2)))Formula family: formula_dsp_fpga_based_real_time_iir_filter_stability_margin_vs_coefficient_quantization_step_calculator
Variables
| Symbol | Label | Role | Description |
|---|---|---|---|
| real_part_of_dominant_pole | Real part of dominant pole (quantized) | INPUT | Real part of dominant pole (quantized) |
| imag_part_of_dominant_pole | Imaginary part of dominant pole (quantized) | INPUT | Imaginary part of dominant pole (quantized) |
| quantization_step | Coefficient quantization step size | INPUT | Coefficient quantization step size |
| minimum_pole_to_unit_circle_distance | Minimum pole-to-unit-circle distance | OUTPUT | Minimum pole-to-unit-circle distance |
Calculation Steps
- Enter the real part of dominant pole (quantized) in dimensionless.
- Enter the imaginary part of dominant pole (quantized) in dimensionless.
- Enter the coefficient quantization step size in dimensionless.
- Step 1: Compute minimum pole-to-unit-circle distance.
- Read the minimum pole-to-unit-circle distance (dimensionless) from the results.
Engineering Summary
Calculate FPGA IIR Filter Minimum Pole-to-Unit-Circle Distance under Coefficient Quantization
Frequently Asked Questions
What does this calculator calculate?
The FPGA IIR Filter Minimum Pole-to-Unit-Circle Distance under Coefficient Quantization Calculator estimates Minimum pole-to-unit-circle distance based on the input parameters you provide
Why is real part of dominant pole (quantized) important in this calculation?
real part of dominant pole (quantized) is directly proportional to minimum pole-to-unit-circle distance. When you enter real part of dominant pole (quantized) in dimensionless, the calculator uses it in the engineering formula to compute the output
How should I interpret the result minimum pole-to-unit-circle distance?
The calculator outputs minimum pole-to-unit-circle distance in dimensionless. The result is computed directly from the input values using the defined engineering formula
What units should I use for the inputs?
Enter each value in the units shown next to the input field: Real part of dominant pole (quantized) (dimensionless), Imaginary part of dominant pole (quantized) (dimensionless), Coefficient quantization step size (dimensionless). Make sure all inputs use the specified units for consistent results
What assumptions does this calculator use?
This calculator uses automatically validated engineering formulas. Results are approximate and should be validated against site-specific conditions, applicable codes, and professional engineering judgment
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