Sign in

Not a member? | Forgot your Password?

Search Online Books

Search tips

Free Online Books

Free PDF Downloads

A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

C++ Tutorial

Introduction of C Programming for DSP Applications

Fixed-Point Arithmetic: An Introduction

Cascaded Integrator-Comb (CIC) Filter Introduction


FIR Filter Design Software

See Also

Embedded SystemsFPGA
Chapter Contents:

Search Spectral Audio Signal Processing


Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?


Bartlett (``Triangular'') Window


$\displaystyle w(n) = w_R(n)\left[1 - \frac{\vert n\vert}{\frac{M-1}{2}}\right],
\quad n\in\left[-\frac{M-1}{2},\frac{M-1}{2}\right]


$\displaystyle W(\omega) = \left(\frac{M-1}{2}\right)^2\hbox{asinc}_{\frac{M-1}{2}}^2(\omega)


  • Convolution of two length $ (M-1)/2$ rectangular windows
  • Main lobe twice as wide as that of a rectangular window of length $ M$
  • First side lobe twice as far down as rectangular case (-26 dB)
  • Often applied implicitly to sample correlations of finite data
  • Also called the ``tent function''
  • Can replace $ M-1$ by $ M+1$ to avoid including endpoint zeros

Previous: Conclusions
Next: Matlab for the Bartlett Window:

Order a Hardcopy of Spectral Audio Signal Processing

About the Author: 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 (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 for details.


No comments yet for this page

Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )