Continuous Wavelet Transform Mirrored Inversion Signal Decoding
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Solution Overview
Problem
Existing signal processing methods, such as Fast Fourier Transform (FFT) and Continuous Wavelet Transform (CWT), face limitations in resolving transient features and frequency components across an entire frequency band, leading to poor temporal and frequency resolution at certain frequencies.
Innovation Solution
A computer-implemented method that involves pre-processing the input waveform to generate a mirrored inverted waveform, followed by applying a Continuous Wavelet Transform (CWT) to this pre-processed waveform. This approach reverses the time and frequency resolution of the CWT, achieving good temporal resolution with poor frequency resolution at low frequencies and vice versa at high frequencies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a continuous wavelet transform is applied to the input waveform directly, then good frequency resolution is achieved at low frequencies, but poor temporal resolution is achieved at low frequencies
Solution Approach 1:
The patent applies a mirrored inverted waveform transformation before the continuous wavelet transform. This inversion reverses the resolution characteristics: poor frequency resolution with good temporal resolution at low frequencies becomes good frequency resolution with good temporal resolution after the inversion, effectively resolving the contradiction through mathematical transformation of the input signal.
2Loss of time
If a continuous wavelet transform is applied to the input waveform directly, then good temporal resolution is achieved at high frequencies, but poor frequency resolution is achieved at high frequencies
Solution Approach 1:
The mirrored inversion of the input waveform before applying the continuous wavelet transform reverses the resolution trade-off at high frequencies. The transformation converts the inherent poor frequency resolution with good temporal resolution into good frequency resolution while maintaining good temporal resolution, resolving the contradiction through the inverted transformation approach.
3Loss of information
If the input waveform is processed with a continuous wavelet transform, then transient features can be decoded, but frequency components across the entire frequency band cannot be resolved accurately
Solution Approach 1:
The patent applies mirrored inversion to the input waveform before the continuous wavelet transform, which reverses the resolution characteristics and enables both transient feature detection and accurate frequency component resolution across the entire frequency band to be achieved simultaneously.
Data Source
AI summary
A computer implemented method of decoding a signal. The method includes receiving a signal (which may be an electromagnetic signal), sampling the received signal to generate an input waveform having magnitude and phase components, applying a transform operation to the input waveform to generate a first decoded signal, and outputting the first decoded signal. The transform operation includes pre-processing the input waveform to generate a mirrored inverted waveform and applying a continuous wavelet transform to the mirrored inverted waveform to generate the first decoded signal. This allows inversion of the frequency and temporal resolution of the continuous wavelet transform, thereby enabling improved temporal and frequency decoding of a signal. The method is particularly suitable for signal filters and filtering units.