Frequency Response Analysis

This chapter discusses frequency-response analysis of digital filters. The frequency response is a complex function which yields the gain and phase-shift as a function of frequency. Useful variants such as phase delay and group delay are defined, and examples and applications are considered.

---

Subsections

• Frequency Response
• Amplitude Response
• Phase Response
• Polar Form of the Frequency Response
  • Separating the Transfer Function Numerator and Denominator
  
  
• Frequency Response as a Ratio of DTFTs
  • Frequency Response in Matlab
  • Example LPF Frequency Response Using freqz
  
  
• Phase and Group Delay
  • Phase Delay
  • Phase Unwrapping
  • Group Delay
    • Derivation of Group Delay as Modulation Delay
  • Group Delay Examples in Matlab
  • Vocoder Analysis
  • Numerical Computation of Group Delay
  
  
• Frequency Response Analysis Problems

---

Order a Hardcopy of Introduction to Digital Filters

Previous: Problems
Next: Frequency Response

---

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.