Complex Spectrogram Signal Inversion Phase Recovery
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing signal processing methods, such as those described in U.S. patent Ser. No. 11/867,733, have limitations in accurately representing time-frequency-amplitude information and reintroducing phase information during signal inversion, which affects the precision and efficiency of signal analysis and synthesis.
Innovation Solution
The method involves constructing a complex-valued spectrogram from a digital signal by integrating the signal with respect to time, applying filters, and computing the discrete Fourier transform. This process ensures that time-frequency-amplitude bands represent physically meaningful information and allows for the correct reintroduction of phase information during signal inversion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If phase information is removed during spectrogram construction to improve observation of time-frequency-amplitude values, then measurement precision of amplitude values is improved, but loss of information occurs because phase information cannot be reintroduced during inversion
Solution Approach 1:
The patent introduces a complex exponential function as an intermediary carrier to embed phase information indirectly. By representing phase as the angle of a complex number on the unit circle, the system can remove phase for amplitude observation while preserving it in the complex structure, allowing recovery during inversion through the relationship: phase = angle(exp(j*phase))*j
Solution Approach 2:
The patent transforms phase information from a direct parameter to an encoded form using complex exponentials. By changing the representation parameter from direct phase angle to complex exponential form (magnitude and angle), the system enables selective removal and recovery of phase components while maintaining the ability to reconstruct the original signal
2Ease of manufacture
If all peaks in the spectrogram are treated as very-short-time-interval pulses, then simplicity of processing is improved, but manufacturing precision of signal representation deteriorates because very-long-time-interval information cannot be correctly observed
Solution Approach 1:
The patent segments peaks into different types based on their temporal characteristics: very-short-time-interval pulses and very-long-time-interval bands. This segmentation allows different processing methodologies to be applied to each type, maintaining simplicity for pulses while achieving precision for bands through specialized grouping and representation techniques
Data Source
AI summary
A method for generating an analog signal for signal analysis, which includes the steps of receiving analog spectrogram data that characterizes one or more bands, constructing an analog signal from the analog spectrogram data, discretely sampling the analog signal for a time period comprised of a sequence of equal time intervals to create a digital signal with values that characterize the analog signal for each of the time periods, constructing a digital spectrogram from the digital signal, wherein the digital spectrogram represents the rate of change of amplitude with respect to time and frequency; and computing an analog spectrogram from the digital spectrogram, wherein an analog spectrogram represents the one or more bands in units of time, frequency and amplitude for the time period.