Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and FFT

The examples below give a progression from the most simplistic analysis up to a proper practical treatment. Careful study of these examples will teach you a lot about how spectrum analysis is carried out on real data, and provide opportunities to see the Fourier theorems in action.

---

Subsections

• FFT of a Simple Sinusoid
• FFT of a Not-So-Simple Sinusoid
• FFT of a Zero-Padded Sinusoid
• Use of a Blackman Window
  • Applying the Blackman Window
  
  
• Hann-Windowed Complex Sinusoid
  • Hann Window Spectrum Analysis Results
  • Spectral Phase

---

Order a Hardcopy of Mathematics of the DFT

Previous: Why a DFT is usually called an FFT in practice
Next: FFT of a Simple Sinusoid

---

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.