1. Fourier Spectral Estimation Basics

When we estimate a signal’s spectrum using the Discrete Fourier Transform (DFT), we essentially project a finite-length signal segment onto complex exponentials. Because the DFT assumes the input is periodic in the chosen time window, truncating the signal introduces spectral leakage: energy from one frequency spreads into others.

2. Role of Windowing

A window function (Hamming, Hanning, Blackman, etc.) tapers the signal segment before taking the DFT. This tapering modifies the trade-off between:

• Main lobe width (frequency resolution)
• Side lobe level (spectral leakage suppression)

3. Accuracy Effects in Spectral Estimation

• Rectangular window (no tapering): Narrowest main lobe → best frequency resolution. But highest side lobes → severe leakage, especially for signals with closely spaced frequencies or large dynamic range.
• Tapered windows (Hamming, Hann, Blackman, etc.): Wider main lobe → reduced frequency resolution. Lower side lobes → much less leakage, so weak spectral components near strong ones can be detected more accurately.

Thus:

• If accuracy = frequency resolution → Rectangular window is best.
• If accuracy = suppression of leakage / detection of weak signals → Tapered windows are better.

4. In Time-Frequency Analysis

In short-time Fourier transform (STFT) or spectrograms:

• Windowing affects both time resolution and frequency resolution (uncertainty principle).
• A longer window = better frequency accuracy but poorer time localization.
• A shorter window = better time localization but poorer frequency resolution.
• Choice of window also determines leakage control across frequencies, directly affecting clarity of spectral ridges or transients.

✅ Summary: Windowing improves the accuracy of detecting true spectral content by reducing leakage, but at the cost of frequency resolution. In time-frequency analysis, it further influences the balance between time and frequency localization. The "best" window depends on whether your priority is resolving close frequencies, detecting weak signals, or capturing sharp time-localized events.

Your question corresponds to a point from a classic lecture course on periodic signal analysis. It's unclear why you're asking it in such a generalized form ;)