Question

Synthesize a strategy for minimizing leakage effect in the DFT analysis of signals with finite duration. The most effective approach is:

• A. Applying a rectangular window to the signal before computing the DFT
• B. Increasing the length of the DFT to include more zero-padding
• C. Utilizing a window function that tapers the beginning and end of the signal
• D. Reducing the sample rate to decrease the resolution of the DFT

Hint:

Use Hamming, Hanning, or Blackman windows to smooth signal edges and minimize DFT leakage.

Answer 1

The Correct Option is C

The leakage effect in Discrete Fourier Transform (DFT) analysis occurs when a signal that is not perfectly periodic within the observation window is transformed, leading to spectral spreading.
To mitigate this, the best method is to apply a tapered window function (such as Hamming, Hanning, or Blackman windows) to the signal. These functions gradually reduce the signal amplitude at the edges, thereby:

• Minimizing abrupt discontinuities at boundaries,
• Reducing spectral leakage by smoothing out edge effects,
• Improving the frequency domain representation.

Why the other options are not effective:

• (A) A rectangular window does not taper the signal, so it worsens leakage.
• (B) Zero-padding increases resolution but doesn't reduce leakage.
• (D) Lowering the sample rate reduces bandwidth and can introduce aliasing without addressing leakage.

Hence, using a window that tapers the signal edges is the most effective strategy to reduce DFT leakage.