Introduction

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Introduction

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Introduction

Inside computers and modern “digital” synthesizers, (as well as music CDs), sound is sampled into a stream of numbers. Each sample can be thought of as a number which specifies the position of a loudspeaker at a particular instant. When sound is sampled, we call itdigital audio. The sampling rate used for CDs is 44,100 samples per second. That means when you play a CD, the speakers in your stereo system are moved to a new position 44,100 times per second, or once every 23 microseconds. Controlling a speaker this fast enables it to generate any sound in the human hearing range because we cannot hear frequencies higher than around 20,000 cycles per second, and a sampling rate more than twice the highest frequency in the sound guarantees that exact reconstruction is possible from the samples.



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