Summary

This article analyzes how time reversal of finite-length discrete-time sequences affects their DFT/FFT representations, filling a gap in standard DSP literature. It presents derivations and examples that reveal how indexing, zero-padding, and circular versus linear reversal change spectral magnitude and phase, with implications for communications and acoustic/radar systems.

Key Takeaways

• Derive the mathematical relationship between the DFT of a finite-length sequence and the DFT of its time-reversed version.
• Predict how time reversal alters spectral phase and magnitude, and how circular indexing introduces mirroring and phase shifts.
• Apply zero-padding and indexing strategies to control aliasing and spectral interpolation when reversing sequences before FFT processing.
• Use time-reversal insights to improve matched-filtering, channel compensation, or signal reconstruction in communications and underwater acoustic systems.

Who Should Read This

Intermediate-to-advanced DSP engineers, researchers, and system designers in communications, sonar, or radar who analyze spectra or design FFT-based algorithms and need practical understanding of time-reversal effects.

TimelessAdvanced

Topics