The Dirac delta function, often written as formula_1, is a made-up concept by mathematician Paul Dirac. It is a really pointy and skinny function that pokes out a point along a wave. Loosely speaking, it has the value of zero everywhere except at formula_2, in such a way that the area between the function and the "x"-axis adds up to 1. The delta function is often used in sampling theory, where its pointiness is useful for getting clean samples.
ð ə WORD_BOUNDARY d ɜː ɹ æ k WORD_BOUNDARY d ɛ l t ə WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ɔ f ə n WORD_BOUNDARY ɹ ɪ t ə n WORD_BOUNDARY æ z WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY w ʌ n WORD_BOUNDARY ɪ z WORD_BOUNDARY ʌ WORD_BOUNDARY m eɪ d ʌ p WORD_BOUNDARY k ɑ n s ɛ p t WORD_BOUNDARY b aɪ WORD_BOUNDARY m æ θ ɪ m ʌ t ɪ ʃ ə n WORD_BOUNDARY p ɔ l WORD_BOUNDARY d ɜː ɹ æ k WORD_BOUNDARY ɪ t WORD_BOUNDARY ɪ z WORD_BOUNDARY ʌ WORD_BOUNDARY ɹ iə l i WORD_BOUNDARY p ɔɪ n t i WORD_BOUNDARY æ n d WORD_BOUNDARY s k ɪ n i WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ð æ t WORD_BOUNDARY p oʊ k s WORD_BOUNDARY aʊ t WORD_BOUNDARY ʌ WORD_BOUNDARY p ɔɪ n t WORD_BOUNDARY ʌ l ɔ ŋ WORD_BOUNDARY ʌ WORD_BOUNDARY w eɪ v WORD_BOUNDARY l uː s l i WORD_BOUNDARY s p iː k ɪ ŋ WORD_BOUNDARY ɪ t WORD_BOUNDARY h ʌ z WORD_BOUNDARY ð ə WORD_BOUNDARY v æ l j uː WORD_BOUNDARY ʌ v WORD_BOUNDARY z iə ɹ oʊ WORD_BOUNDARY ɛ v ɹ ɪ w ɛ ɹ WORD_BOUNDARY ɛ k s ɛ p t WORD_BOUNDARY æ t WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY t uː WORD_BOUNDARY ɪ n WORD_BOUNDARY s ʌ t̠ʃ WORD_BOUNDARY ʌ WORD_BOUNDARY w eɪ WORD_BOUNDARY ð æ t ð ɪ WORD_BOUNDARY ɛ ɹ iə WORD_BOUNDARY b ɪ t w iː n WORD_BOUNDARY ð ə WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY æ n d WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɛ k s WORD_BOUNDARY æ k s ɪ s WORD_BOUNDARY æ d z WORD_BOUNDARY ʌ p WORD_BOUNDARY t ə WORD_BOUNDARY w ʌ n WORD_BOUNDARY ð ə WORD_BOUNDARY d ɛ l t ə WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ɪ z WORD_BOUNDARY ɔ f ə n WORD_BOUNDARY j uː z d WORD_BOUNDARY ɪ n WORD_BOUNDARY s æ m p l ɪ ŋ WORD_BOUNDARY θ iə ɹ i WORD_BOUNDARY w ɛ ɹ WORD_BOUNDARY ɪ t s WORD_BOUNDARY p ɔɪ n t i n ə s WORD_BOUNDARY ɪ z WORD_BOUNDARY j uː s f ə l WORD_BOUNDARY f ɔ ɹ WORD_BOUNDARY ɡ ɛ t ɪ ŋ WORD_BOUNDARY k l iː n WORD_BOUNDARY s æ m p ə l z WORD_BOUNDARY