Digital Signal Processing Basics
Which of the following is the main cause of spectral leakage in a DFT?
- AThe sampling frequency is lower than twice the highest signal frequency, so high frequencies fold back onto low frequencies
- BWhen the number of DFT points is not a power of two, rounding errors in the FFT computation grow and spread to the surrounding bins
- CThe observation interval does not contain a whole number of signal periods, so the waveform is treated as if its two ends joined discontinuously
Show answer and explanation
Answer: C. The observation interval does not contain a whole number of signal periods, so the waveform is treated as if its two ends joined discontinuously
The DFT treats the N observed points as one period of a repeating signal. If the interval holds exactly a whole number of periods of a sine wave, the peak fits in a single bin; otherwise the waveform is discontinuous where the ends of the interval meet, and that energy spreads into many surrounding bins. This is spectral leakage, and it can be reduced with a window function that brings both ends of the interval smoothly toward 0. Aliasing (folding) is a different phenomenon that occurs at sampling.
- A. This describes aliasing (folding), which is a different phenomenon from spectral leakage.
- B. DFTs with a number of points that is not a power of two can be computed; only the FFT speed changes. Leakage is not caused by rounding errors.
- C. Correct. The discontinuity at the ends of the interval spreads energy into the surrounding bins.