A novel algorithm for implementing time-frequency transform with low computation

Area of Science:

• Signal Processing
• Fourier Analysis
• Algorithm Development

Background:

• Traditional sliding discrete Fourier transform (DFT) algorithms can be computationally intensive.
• Detecting ultra-short pulses in mixed-domain oscilloscopes presents challenges due to frequency-domain limitations.

Purpose of the Study:

• To introduce a novel two-dimensional sliding fast Fourier transform (2D SFFT) algorithm.
• To demonstrate the computational efficiency and accuracy of the 2D SFFT algorithm.
• To apply the 2D SFFT algorithm for improved ultra-short pulse detection.

Main Methods:

• Organizing one-dimensional data into a two-dimensional structure.
• Calculating current spectrums using existing spectrums and new data.
• Comparing computational requirements against traditional sliding DFT and fast Fourier transform (FFT) algorithms.

Main Results:

• The 2D SFFT algorithm requires less computation than traditional sliding DFT for sliding rates >= 4/M.
• The 2D SFFT algorithm is computationally more efficient than FFT for sliding rates <= 6.25%.
• The spectral error between 2D SFFT and FFT is minimal, less than 10^-10.

Conclusions:

• The proposed 2D SFFT algorithm offers significant computational advantages.
• The 2D SFFT algorithm improves the detection of previously invisible ultra-short pulses.
• This advancement enhances the probability of intercept for mixed-domain oscilloscopes.