Siriya Fourier na Trigonometri

Tambayar da muna so kuɗi Fourier series a cikin hanyar exponent. A cikin takardun wannan, za a iya tattaunawa wata tsarin Fourier series, yana nufin Trigonometric Fourier series.

Abubuwan da Fourier series ke ciki a cikin hanyar trigonometri

Trigonometric Fourier series zai iya samun da ita daga hanyar exponent. Cikakken abubuwan da Fourier series ke ciki a cikin hanyar exponent na signal din x(t) da kungiyar lokaci To ya ba da shi

Saboda sine da cosine suna iya bayyana a cikin hanyar exponent. Saboda haka, tun daga cikakken abubuwan da Fourier series ke ciki a cikin hanyar exponent, zan iya samun da ita a cikin hanyar trigonometri.

Cikakken abubuwan da Fourier series ke ciki a cikin hanyar trigonometri na signal din x (t) da kungiyar lokaci T, ya ba da shi

Daga baya, ak da bk su ne koefisientsu na Fourier da za a ba da shi

a0 shine komponentin dc na signal da za a ba da shi

Muhimmanci na Fourier series

1. Idan x(t) shine function mai gaba yana nufin x(- t) = x(t), maka bk = 0 da

2. Idan x(t) shine function mai gaba yana nufin x(- t) = – x(t), maka a0 = 0, ak = 0 da

3. Idan x(t) shine function mai gaba yana nufin x (t) = -x(t ± T0/2), maka a0 = 0, ak = bk = 0 don kafin kafin kafin,

4. Linearity

5. Time shifting

6. Time reversal

7. Multiplication

8. Conjugation

9. Differentiation

10. Integration

11. Periodic Convolution

Rashin aikinsu a cikin hanyar exponent da aikinsu a cikin hanyar trigonometri

Idan x (t) shine real, maka a, da b, suna real, za a iya tattaunawa

Tsari da ya faruwa a cikin axis na signal

• A cikin tsari da ya faruwa a cikin axis na signal zuwa hagu masu waɗanda a cikin axis na lokaci t = 0, haske aikin da za a ba da shi kawai ce ma a yi amfani da shi, amma aikin da za a ba da shi kawai ce ma a yi amfani da shi.

• A cikin tsari da ya faruwa a cikin axis na signal zuwa hagu masu waɗanda a cikin axis na lokaci, haske aikin da za a ba da shi kawai ce ma a yi amfani da shi.

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