Bandlimited Digital Synthesis Using Phase-Based Alias Reducing Pulses
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Solution Overview
Problem
Existing methods for digital synthesis of analog waveforms, such as sawtooth and pulse waveforms, often result in aliasing due to discontinuities, which are not effectively addressed by current bandlimited synthesis techniques like MinBLEP and nonlinear waveshaping, leading to DC biases and frequency-dependent errors.
Innovation Solution
The method involves generating bandlimited digital signals by summing digital samples of waveforms with alias reducing pulses, which are phase and magnitude-based, and using table lookup or interpolation to create sets of digital samples that eliminate DC bias, applied to both hard sync and other modulation techniques like soft sync and ring modulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If digital synthesis of analog waveforms is performed without bandlimiting, then the synthesis process is simple and computationally efficient, but the resulting signal contains aliasing
Solution Approach 1:
The patent applies bandlimiting corrections (MinBLEP, MaxBLEP, or SINC corrections) in advance at the points of discontinuity in the waveform. By pre-calculating and applying these corrections before the aliasing artifacts fully manifest, the method effectively eliminates aliasing while maintaining computational efficiency. The correction values are determined based on the phase and magnitude of discontinuities, allowing proactive prevention of aliasing rather than reactive correction.
2Object-affected harmful factors
If MinBLEP is applied to introduce bandlimited discontinuity, then aliasing is reduced, but frequency-dependent DC error is introduced
Solution Approach 1:
The patent dynamically adjusts the parameters of the bandlimiting correction based on the phase and magnitude of each discontinuity. By changing the correction parameters adaptively rather than applying a fixed MinBLEP correction, the method eliminates frequency-dependent DC errors while maintaining aliasing reduction. The correction is scaled and positioned according to the specific characteristics of each discontinuity point.
3Adaptability or versatility
If hard sync technique is implemented with slave waveform reset, then modulation effect is achieved, but discontinuities with various amplitudes cause aliasing
Solution Approach 1:
The patent applies local bandlimiting corrections at each discontinuity point in the hard sync waveform. Instead of applying a uniform correction across the entire waveform, the method calculates and applies corrections specifically at the points where discontinuities occur, with the correction magnitude and phase tailored to each local discontinuity. This localized approach effectively handles the varying amplitude discontinuities introduced by hard sync modulation.
4Object-affected harmful factors
If nonlinear waveshaping filter is used for sawtooth waveform synthesis, then aliasing is reduced, but the method is complex and still produces perceptible aliasing
Solution Approach 1:
The patent extracts and corrects only the problematic high-frequency components at the discontinuity points of the waveform. Rather than applying complex nonlinear waveshaping filters to the entire waveform, the method identifies and removes the specific frequency components that cause aliasing at the discontinuities. This selective extraction approach simplifies the synthesis process while effectively eliminating perceptible aliasing.
Data Source
AI summary
A method for generating a bandlimited digital signal, includes generating a sequence of digital samples of a waveform, such as a sawtooth, square, or pulse waveform. The waveform has a discontinuity with a phase within a particular sampling interval. The digital samples in the sequence of digital samples of the waveform around the discontinuity are summed with a set of digital samples of an alias reducing pulse, which is based on the phase and magnitude of the discontinuity. The alias reducing pulse has essentially no DC bias, such as a pulse that is substantially odd symmetric relative to the phase of the discontinuity. The process is used in synthesis of analog synthesizer waveforms, hard sync and other waveform synthesis procedures.