Windows, Harmonic Analysis and the Discrete Fourier Transform
Research and development May-Aug 1976
NAVAL UNDERSEA CENTER SAN DIEGO CA
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The discrete Fourier transform implemented by means of the fast Fourier transform has become a primary processing tool for harmonic detection and harmonic analysis. The relationships between bandwidth and sample rate and between resolution and observation interval are supposedly well known to the practicing engineer. Real-world harmonic analysis requires the use of a window other than the rectangle to assure consistency and confidence in the harmonic estimates. Applying a window to observed data affects the detectability, resolution, confidence, and bias of the estimates. We have observed that the trade-offs available through the use of windows are not well understood nor popularly appreciated in the literature or by the practitioner. In addition, the requirement to apply windows to sampled data often leads to subtle misapplications of the windows. This paper, tutorial and informational, will identify the major considerations, effects, and pitfalls of which the signal processor should be aware. We will also identify and clarify points of common misunderstanding concerning sampled windows.
- Theoretical Mathematics