8/19/2019 The Nyquist Theorem

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Hi, my name is vinícius Bernucci. I live in Brazil, Minas Gerais, Belo

Horizonte. I work with studio for over ten years. Also I make music school at the

Universidade ederal !e Minas Gerais. In this work, I want to talk a little a"out the

ny#uist theorem.

The Nyquist Theorem

Accordin$ to the ny#uist %heorem, in order to di$itally encode the desired

fre#uency "andwidth, the selected sam&le rate must "e at least twice as hi$h as the

hi$hest recorded fre#uency 'sam&le rate ( ) hi$hest fre#uency*. %hus, as +udio si$nal

with a "andwidth of ( -Hz would re#uire a sam&lin$ rate of at least .

sam&les/second. In addition, it0s of e#ual im&ortance that no +udio si$nal $reater than

half the sam&lin$ fre#uency enter into the di$itization &rocess. If fre#uencies $reater 

than one1half the sam&le rate are allowed to enter into the conversion &rocess,

erroneous fre#uencies 1 -nown as alias fre#uencies 2 would enter into the audi"le

+udio si$nal "and as false fre#uencies and &roduce audi"le harmonic distortion.

In order to eliminate the effects of aliasin$, a low1&ass filter is &laced "efore

the analo$1to1di$ital 'A/!* conversion sta$e. In theory, a filter that would &ass all

8/19/2019 The Nyquist Theorem

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fre#uencies u& to the ny#uist cutoff fre#uency and have infinite attenuation thereafter 

would "e ideal.

In the real world, however, such a 3"rick wall4 filter doesn0t e5ist. or the

reason, a sli$htly hi$her sam&le rate must "e chosen in order account for the

attenuation slo&e re#uired for the filter to "e effective. A sam&le rate of .6 -Hz, for 

e5am&le, has "een chosen in order to accurately encode an effective "andwidth u& to

( -Hz.