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What is Spectral leakage?

In a DFT, the phenomenon in which the energy of a component at one frequency appears spread over many surrounding bins rather than only its own. The DFT treats the observation interval as a repeating signal, so when the interval does not hold a whole number of signal periods, the computation behaves as if the two ends of the interval joined discontinuously. Leakage from a strong component can hide nearby weak components or make amplitudes read too small. A window function that brings both ends of the interval smoothly toward 0 greatly reduces leakage into distant bins. Zero padding does not remove leakage.

Japanese name: スペクトル漏れ

Spectral leakage appears in 2 practice questions across 1 topic, including Digital Signal Processing Basics.

Field: Digital Signal Processing Basics

Try it: questions about Spectral leakage

Which of the following is the main cause of spectral leakage in a DFT?

  1. AThe sampling frequency is lower than twice the highest signal frequency, so high frequencies fold back onto low frequencies
  2. 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
  3. 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.

Spectral leakage in the explanations

Questions that mention Spectral leakage (2)

  1. Which of the following is the main cause of spectral leakage in a DFT?
  2. Let k = 0 be the DC bin. When a 1 kHz sine wave sampled at 8 kHz is analyzed with a 256-point DFT, which of the following is the index k of the bin where the peak appears on the positive-frequency side?

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Related terms

Window function Aliasing Convolution Decimation Difference equation Discrete Fourier transform Fast Fourier transform (FFT) FIR filter Frequency resolution Group delay

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