Band-Split Noise Generator With Interpolated Sample-Rate Scaling
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Solution Overview
Problem
Existing noise generators face challenges in simulating the real phase noise spectrum over a wide frequency range (1 Hz to 10 MHz) with high dynamics, requiring high sample rates and storage depths, leading to inefficient resource usage and long calculation times, while existing methods like IIR and FIR filters are either numerically unstable or consume excessive resources.
Innovation Solution
A noise generator that subdivides the frequency response into individual bands, using digital filters with increasing sample rates and interpolators to adjust and combine signals, allowing for a realistic simulation with reduced resource consumption and optimized filter edges for seamless transitions between bands.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If IIR filters are used to generate colored noise with high dynamics, then the filter order must be increased to achieve the desired frequency response, but this leads to numerical instability
Solution Approach 1:
The frequency spectrum is divided into multiple frequency bands, each processed by a separate digital filter with appropriate sample rate. This segmentation allows each filter to operate within a manageable frequency range, avoiding the numerical instability that would occur with a single high-order IIR filter covering the entire wide frequency range.
Solution Approach 2:
The sample rate is varied across different frequency bands, with higher sample rates used for higher frequency bands. This parameter change allows each filter to be optimized for its specific frequency range, achieving accurate frequency response without requiring excessively high filter orders that would cause numerical instability.
2Reliability
If FIR filters are used to generate colored noise, then the coefficients can be estimated reliably, but the number of coefficients required is very high (like 224), consuming much calculating time and memory
Solution Approach 1:
The wide frequency range is divided into multiple narrower frequency bands, each processed by a separate FIR filter. Each individual filter requires far fewer coefficients (e.g., 32 coefficients per filter) compared to a single filter covering the entire frequency range (224 coefficients), significantly reducing calculating time and memory consumption while maintaining reliable coefficient estimation.
3Measurement precision
If arbitrary generators use high sample rate (like 20 Msamples/sec) and high storage depth (like 1000 seconds corresponding to 40 gigabytes) to simulate phase noise over wide frequency range, then the simulation realism is improved, but the amount of time for calculating the noise sequence and loading the arbitrary generator becomes inacceptable (in the range of minutes)
Solution Approach 1:
The noise generation is divided into multiple frequency bands processed in parallel by separate digital filters. Each filter operates at an optimized sample rate appropriate for its frequency range, generating noise sequences that are much shorter and require minimal loading time. The filtered outputs are then combined to produce the final phase noise signal, achieving realistic simulation without the excessive calculation and loading times associated with single high-sample-rate arbitrary generators.
Solution Approach 2:
The sample rate is adapted to match the frequency band being processed, with higher sample rates used for higher frequency bands and lower sample rates for lower frequency bands. This parameter optimization reduces the overall data volume and processing time while maintaining simulation realism across the entire frequency range.
4Duration of action of stationary object
If two noise signals with prime lengths are generated and combined in separate arbitrary generators to improve repetition rate, then the repetition rate appears improved, but in the frequency range where signals overlap, there are frequently deviations from the desired frequency response and the autocorrelation function of the sum signal is bad
Solution Approach 1:
Instead of combining complete noise signals from separate arbitrary generators, the frequency spectrum is segmented into bands that are processed separately through digital filters. Each band is generated and filtered independently, then combined in the frequency domain. This ensures that the desired frequency response is maintained across the entire spectrum without the deviations that occur when combining signals with different repetition periods.
Data Source
AI summary
A noise generator for generating a noise signal over a frequency spectrum has a first noise source and a first digital filter for a first frequency band, a second noise source and a second digital filter for a second frequency band, and an interpolator and a combiner. The first digital filter has a first sample rate and the second digital filter has a second sample rate, wherein the ratio between the second sample rate and the first sample rate, with regard to a sign, corresponds to a ratio between center frequencies of the second frequency band and the first frequency band, wherein an edge of the second digital filters which determines a lower frequency band limit is steeper than an edge of the first digital filter which determines an upper frequency band limit. The interpolator is configured to adjust an output signal of the first digital filter, with regard to its sample rate, to a sample rate of the second digital filter, wherein the combiner is configured to combine the adjusted output signal from the interpolator and the output signal of the second digital filter.