Frequency Resolution

The frequency resolution of a spectrum-analysis window is determined by its main-lobe width in the frequency domain, where a typical main lobe is illustrated in Fig.1.6 (top). For maximum frequency resolution, we desire the narrowest possible main-lobe width, which calls for the rectangular window, the tranform of which is shown in Fig.1.11. When we cannot be fooled by the large side-lobes of the rectangular window transform (e.g., when the sinusoids under analysis are known to be well separated in frequency), the rectangular window truly is the optimal window for the estimation of frequency, amplitude, and phase of a sinusoid in the presence of stationary noise [212,106,107].

The rectangular window has only one parameter (aside from simple amplitude)--its length. The next series of plots shows the effect that an increased window length has on our ability to resolve two sinusoids.

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Subsections

• Two Cosines (``In-Phase'' Case)
• One Sine and One Cosine ``Phase Quadrature'' Case

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Order a Hardcopy of Spectral Audio Signal Processing

Previous: Rectangular Window Side-Lobes
Next: Two Cosines (``In-Phase'' Case)

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.