The 2-sample wide triangular pulse (Eq.(4.4)) can be expressed as a convolution of the one-sample rectangular pulse with itself.

The one-sample *rectangular pulse* is shown in Fig.4.8
and may be defined analytically as

where is the

Convolving with itself produces the two-sample triangular pulse :

While the result can be verified algebraically by substituting for , it seen more quickly via graphical convolution.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University