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Windowing is required to analyze finite-duration signals with the DFT, but windows create spectral leakage where energy from one frequency bin spreads to others. Different windows trade main-lobe width against side-lobe magnitude: narrow main-lobes (good frequency resolution) produce high side-lobes (poor out-of-band rejection), and vice versa. The choice of window depends on whether closely-spaced components or weak components in noise are the priority.
Compare rectangular, Hann, and Hamming windows on a signal containing closely-spaced sinusoids and single weak sinusoid in noise. Observe main-lobe and side-lobe characteristics.
From your work with window functions and the DFT, you know that analyzing a finite-duration signal forces you to multiply it by a window before transforming. Even the "no window" choice is a choice: the rectangular window (all ones) abruptly truncates the signal to zero outside the analysis interval, creating sharp edges. Those edges look like high-frequency content to the DFT and cause energy from a single sinusoid to smear across many frequency bins — that smearing is spectral leakage. Every window design is an attempt to make this truncation less abrupt, but doing so always comes at a cost.
The trade-off lives between two competing properties of a window's frequency-domain shape: main-lobe width and side-lobe level. The main lobe is the central peak centered on a sinusoid's true frequency — its width determines how close two sinusoids can be before their spectral peaks blur together (this is frequency resolution). The side lobes are the ripples extending outward from the main lobe — their level determines how much a strong component masks nearby weak components. A narrow main lobe gives precise frequency resolution, but the side lobes must be high (energy conservation forces the trade-off). A window that suppresses side lobes does so by spreading its main lobe wider, sacrificing resolution.
The rectangular window has the narrowest possible main lobe, but its side lobes are only about 13 dB below the main peak — quite high. The Hann window (a raised-cosine shape) broadens the main lobe by roughly a factor of two but drops side lobes to about −32 dB, dramatically better for detecting weak signals near strong ones. The Hamming window optimizes the side-lobe level even further (around −43 dB) for a similar main-lobe width. The Blackman window extends this further still (~−58 dB side lobes), at the cost of a main lobe three times wider than rectangular. No window escapes the trade-off — it is a fundamental consequence of the time-frequency uncertainty principle.
Choosing a window means choosing which failure mode you can tolerate. If you need to distinguish two closely spaced sinusoids of similar amplitude, use the rectangular window: its narrow main lobe gives the best chance of resolving them as separate peaks. If you need to detect a weak sinusoid close to a strong one (say, a −40 dB signal 2 bins away from a full-scale signal), a rectangular window's side lobes will bury the weak signal; switch to Hann or Blackman. In practice, Hann is the default choice for most spectral analysis because its side-lobe suppression is good and its main-lobe broadening is modest.
A final point worth fixing: zero-padding does not reduce spectral leakage. Zero-padding the time-domain signal before the DFT interpolates the spectrum more finely — the DFT evaluates the continuous DTFT at more points — which makes the spectrum look smoother and the peaks more precise. But the underlying leakage pattern is set entirely by the window; zero-padding just reveals it at higher apparent resolution. You are not recovering information that was lost to leakage; you are simply zooming in on the same smeared spectrum. The only way to reduce leakage is to choose a window with lower side lobes, or to acquire more data.