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Propiedades de la Transformada de Fourier Discreta en el Tiempo

Module by: Don Johnson Translated By Fara Meza, Erika JacksonBased on: Discrete-Time Fourier Transform Properties by Don Johnson

Summary: Da varias propiedades de la Transformada de Fourier Discreta en el Tiempo.

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Figura 1: Propiedades de la Transformada de Fourier Discreta en el Tiempo y sus relaciones.
Propiedades de la Transformada de Fourier Discreta en el Tiempo
Dominio de la Secuencia Dominio de la Frecuencia
Linearidad a1s1n+a2s2n a1 s1 n a2 s2 n a1S1ⅇⅈ2πf+a2S2ⅇⅈ2πf a1 S1 2f a2 S2 2f
Simetría del Conjugado sn sn real Sⅇⅈ2πf=Sⅇ-ⅈ2πf¯ S 2f S 2f
Simetría Par sn=s-n sn sn Sⅇⅈ2πf=Sⅇ-ⅈ2πf S 2f S 2f
Simetría Impar sn=-s-n sn s n Sⅇⅈ2πf=-Sⅇ-ⅈ2πf S 2f S 2f
Retrazo del Tiempo sn−n0 s n n0 ⅇ-ⅈ2πfn0Sⅇⅈ2πf 2 f n0 S 2f
Modulacion Compleja ⅇⅈ2πf0nsn 2 f0n sn Sⅇⅈ2πf−f0 S 2 f f0
Modulación de Amplitud sncos2πf0n sn 2 f0n Sⅇⅈ2πf−f0+Sⅇⅈ2πf+f02 S 2 f f0 S 2 f f0 2
snsin2πf0n sn 2 f0n Sⅇⅈ2πf−f0−Sⅇⅈ2πf+f02ⅈ S 2 f f0 S 2 f f0 2
Multiplicación por n nsn n sn 1-2ⅈπddfSⅇⅈ2πf 1 2 f S 2f
Suma ∑n=-∞∞sn n sn Sⅇⅈ2π0 S 20
Valor en el Origen s0 s0 ∫-1212Sⅇⅈ2πfdf f 12 12 S 2f
Teorema de Parseval ∑n=-∞∞|sn|2 n sn 2 ∫-1212|Sⅇⅈ2πf|2df f 12 12 S 2f 2

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