Digital Signal Processing Basics
A 256-point signal is followed by 768 zeros (zero padding) and a 1024-point DFT is computed. Compared with computing the DFT of the 256 points as they are, which of the following is correct?
- AThe spectrum is interpolated at finer spacing, but the ability to tell apart two sine waves of close frequencies does not change
- BThe bin spacing becomes 1/4, and the ability to tell apart two sine waves of close frequencies also improves fourfold
- CThe added zeros join the two ends of the interval smoothly, so spectral leakage disappears and peak heights can be read accurately
Show answer and explanation
Answer: A. The spectrum is interpolated at finer spacing, but the ability to tell apart two sine waves of close frequencies does not change
Zero padding makes the bin spacing finer, fs/1024, and gives values interpolated between those of the 256-point spectrum. No new information is added, however, so the ability to tell two frequencies apart (the frequency resolution) is set by the 256 samples actually observed and stays at about fs/256. Truly improving it requires recording data over a longer time. Zero padding is used to make peak positions easier to read or to bring the number of points to a power of two for the FFT.
- A. Correct. The spectrum only looks smoother through interpolation; the ability to tell frequencies apart does not change.
- B. The bin spacing becomes 1/4, but the ability to tell frequencies apart is set by the 256 samples observed and does not improve.
- C. Leakage comes from how the observation interval is cut out, and appending zeros does not remove it.