Digital Filter Frequency Response Correction for Oscilloscope Sampling
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Solution Overview
Problem
Conventional equivalent time oscilloscopes fail to accurately preserve the frequency content of asynchronous components in sampled signals, leading to aliasing issues that affect digital filtering, resulting in the removal of noise and jitter frequencies that should not be affected by low-pass filters.
Innovation Solution
A method involving a digital filter with multiple filter regions applies corrections to the frequency response of a sampler, transitioning from a reference frequency response to the actual frequency response across different frequency ranges to preserve the statistics of asynchronous components, including a first region for correction, a second region for gradual transition, and a third region for compensating excess gain.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-affected harmful factors
If a conventional low-pass filter is applied to the sampled signal, then high frequency noise is removed, but asynchronous components (noise and jitter) at frequencies below the data rate are incorrectly removed due to aliasing
Solution Approach 1:
The frequency spectrum is divided into multiple segments: aliased asynchronous components (below data rate), deterministic synchronous components (at data rate harmonics), and high frequency noise (above Nyquist). Each segment is handled by a dedicated filter transfer function that applies appropriate correction factors, allowing selective preservation or removal of specific frequency components based on their origin and characteristics
Solution Approach 2:
The filter transfer function dynamically adjusts frequency-dependent correction factors based on the relationship between signal frequency and data rate. By calculating the ratio of signal frequency to data rate and applying appropriate correction factors, the system transforms the filtering approach from a static frequency threshold to a dynamic parameter-based correction that accounts for aliasing effects
2Measurement precision
If the sampler frequency response is corrected across all frequency ranges, then frequency accuracy is improved, but excess gain is introduced that distorts signal statistics
Solution Approach 1:
Different correction strategies are applied to different frequency regions: full frequency response correction is applied to aliased asynchronous components where accuracy is critical, gradual transition is applied in the intermediate region to avoid abrupt changes, and no correction (with excess gain compensation) is applied to high frequency deterministic components where original sampler characteristics should be preserved
3Measurement precision
If deterministic synchronous components are accurately reproduced, then trigger-synchronous signal integrity is maintained, but asynchronous components suffer from frequency aliasing
Solution Approach 1:
The filter transfer function acts as an intermediary that processes the sampled signal through multiple stages: first correcting frequency response for aliased asynchronous components, then gradually transitioning to preserve deterministic synchronous components, and finally compensating for excess gain. This intermediary processing layer reconciles the conflicting requirements of synchronous accuracy and asynchronous fidelity
Data Source
AI summary
A method of filtering a signal sampled by a sampler, for example, in an equivalent time oscilloscope includes applying a correction to an actual frequency response of the sampler, with respect to a reference frequency response, to a first frequency range of the sampled signal, and transitioning across a second frequency range of the sampled signal from the correction applied to the first frequency range to no correction of the actual frequency response of the sampler, the second frequency range being higher than the first frequency range. The method further includes compensating in a third frequency range of the sampled signal for excess gain incurred while applying the correction and transitioning from the correction to no correction in the first and second frequency ranges, respectively, so that statistics of asynchronous components of the sampled signal are preserved, the third frequency range being higher than the second frequency range.