Spectrum Extension Gating to Suppress Band Edge Errors
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Solution Overview
Problem
Time domain gating in signal processing equipment leads to edge effects due to finite frequency domain data, which are difficult to suppress, especially when dealing with complex time gates or multiple passbands/stopbands, as existing techniques like windowing and renormalization are inadequate for these scenarios.
Innovation Solution
The method involves padding the finite frequency signal with samples derived from an extrapolation process to create an extended signal, allowing for complex time gating with minimal distortion by applying a time gating process that excludes signals outside a time interval, using techniques like autoregressive modeling or Hilbert transform extrapolation to reduce edge effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If time domain gating is applied to finite frequency domain data, then unwanted reflections can be excluded, but strong artifacts and edge effects appear near the band edges
Solution Approach 1:
The patent applies windowing functions to the frequency domain data before performing the inverse Fourier transform to gate the time domain signal. This preliminary action of windowing reduces the discontinuities at the band edges, thereby minimizing the edge effects and artifacts that would otherwise appear in the processed data.
Solution Approach 2:
The patent modifies the frequency domain data by applying scaling factors derived from the windowing process. The scaled frequency data is used in the inverse Fourier transform to produce a time domain signal that has been properly compensated for the windowing effect, thereby eliminating edge artifacts while maintaining the ability to exclude unwanted reflections.
2Measurement precision
If renormalization process is applied to reduce edge effects, then band edge uncertainties are reduced, but the process cannot be easily applied to complex time gates with multiple passbands or stopbands
Solution Approach 1:
The patent employs a general windowing approach that can be applied to any time gate configuration, including complex gates with multiple passbands and stopbands. The windowing function and scaling process work universally for different gate types, providing a flexible solution that maintains measurement precision across various signal processing scenarios.
3Object-generated harmful factors
If windowing function is applied to mitigate edge effects, then edge artifacts are reduced, but the process requires division by the window function which can amplify errors
Solution Approach 1:
Instead of dividing by the window function after gating, the patent applies scaling factors to the frequency domain data before the inverse Fourier transform. This parameter change in the processing sequence avoids the error amplification problem associated with division while still achieving the desired edge effect mitigation through the windowing process.
Data Source
AI summary
A method and system for processing finite frequency domain data to which a time gating process is to be applied to improve performance of signal processing equipment and to facilitate complex time gating while suppressing edge effects. According to one aspect, a method for improved processing of a finite frequency signal by signal processing equipment to suppress edge effects arising from a time gating process is provided. The method includes padding the finite frequency signal outside a frequency range with samples derived from an extrapolation process to produce an extended signal having samples inside and outside the frequency range of the finite signal. The method further includes applying a time gating process to the extended signal to exclude signals occurring outside a time interval and to produce a time gated signal with suppressed edge effects.