High-speed coherence processing using the sectionalized Fourier transform

The sectionalized Fourier transform of a band-limited signal (defined as a Fourier transform which is computed over incremented temporal sections of the function) is equivalent to basebanding, filtering, and sampling the signal in time domain. Spectral windowing is employed, through appropriately summing a sequence of the Fourier transform bins, to control the passband and leakage characteristics of the resulting filter. This in turn controls the distortion of the signal induced as a result of the transform process. The use of the sectionalized Fourier transform is exploited to conveniently and rapidly map the cross-correlation envelope of narrow-band signals over the time-register Doppler-ratio (ambiguity) plane. By using the ambiguity kernel as an approximation of signal time compression (or expansion), the coherence between transformed signals (along the Doppler-ratio axis) may further be expedited through use of the discrete Fourier transform. The resulting error is negligible when the time-bandwidth product of the process is less than the inverse of the maximum Doppler ratio employed. The resulting algorithms have proved advantageous in underwater acoustic applications. It is concluded that the sectionalized Fourier Transform has many applications in time-domain signal processing using modern array digital computers.