Digital Signal Processing Basics
Which of the following correctly compares the rectangular window (no window applied) and the Hann (Hanning) window applied before a DFT?
- AThe Hann window makes the main lobe about half as wide as the rectangular window and also lowers the side lobes, so it is better in every respect
- BThe Hann window has lower side lobes and less leakage into distant bins, but its main lobe is about twice as wide as that of the rectangular window
- CThe Hann window narrows the main lobe, but in exchange its side lobes are higher than those of the rectangular window
Show answer and explanation
Answer: B. The Hann window has lower side lobes and less leakage into distant bins, but its main lobe is about twice as wide as that of the rectangular window
The rectangular window has a narrow main lobe of ±1 bin (to the first nulls), but its highest side lobe is high, about −13 dB, so leakage spreads to distant bins. The Hann window brings both ends of the interval smoothly to 0, lowering the highest side lobe to about −31 dB, but its main lobe widens to ±2 bins, about twice as wide. The choice depends on the purpose: a window like Hann to see a weak signal near a strong one, and the rectangular window to tell apart signals of similar strength at close frequencies.
- A. The main lobe actually becomes wider. There is a trade-off: lowering the side lobes widens the main lobe.
- B. Correct. The side lobes drop from about −13 dB to about −31 dB, and the main lobe widens from ±1 bin to ±2 bins.
- C. It is the other way round: the Hann window has lower side lobes and a wider main lobe.