Summary

This paper shows that eliminating ringing when filtering a rectangular pulse requires only that all FIR coefficients be positive, and that symmetric coefficients produce symmetric leading and trailing edges. It frames the result as a window-function perspective, connecting simple coefficient constraints to time-domain pulse behavior and trade-offs in spectral leakage.

Key Takeaways

• Recognize that all-positive FIR coefficients prevent ringing in the filtered rectangular pulse.
• Design symmetric coefficients to enforce identical leading and trailing edge shapes.
• Interpret common window functions as FIR filters whose sign and symmetry determine time-domain ringing and symmetry.
• Apply simple window choices to trade off transition width and sidelobe behavior while avoiding ringing.

Who Should Read This

DSP engineers and researchers (filter designers, communications or audio/radar engineers) who want quick, practical insight into designing FIR/window-based filters that avoid pulse ringing while preserving edge symmetry.

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