What is the process of digital sampling in music?

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astro_kat
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The process known as sampling in reference to music is as follows:
A device called a sampler is used to convert an analog signal representing sound waves into digital information. This digital information is called a sample, artists often use samples in their music. however, this not the only function of a sampler, one might sample a LP and save the information, as a digital representation of the sound waves composing the song.
 
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astro_kat,
Your examples of "sampling" are of different time scales.

When an artist "samples" a song, the artist is copying a short portion (say, 3 sec) of the song... which could be done with analog tape or vinyl or with a digital method.

To encode live music on a CD, one has to digitally-"sample" or digitize (many samples at intervals of like 1/44100 s) the music.