# Dictionary:Comb

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An infinite sequence of impulses ${\displaystyle \delta (t-n\Delta t)}$ occurring at time intervals ${\displaystyle \Delta t}$:

${\displaystyle {\text{comb}}(t)=\sum _{n=-\infty }^{\infty }\delta (t-n\Delta t)}$,

called the sampling function because multiplying a function by a comb gives the sample values at the comb interval, and the replicating function because convolution with a waveform reproduces the waveform at the position of each comb spike. Also called a shah, named for the Cyrillic symbol ш. The Fourier transform of a comb is also a comb:

${\displaystyle {\text{comb}}(t)\leftrightarrow {\text{comb}}(f)}$,

where frequency f=1/t if t is time and ${\displaystyle \leftrightarrow }$ indicates a Fourier transform operation. See Figures C-8 and F-19.

If the impulses are spaced T apart,

${\displaystyle {\text{comb}}\left({\frac {t}{T}}\right)\leftrightarrow {\text{comb}}(Tf)}$.