representation of aperiodic signals: the continuous-time...
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![Page 1: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/1.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-18Outline
Representation of Aperiodic Signals: the Continuous-Time Fourier Transform
The Fourier Transform for Periodic Signals
Properties of Continuous-Time Fourier Transform
The Convolution Property
The Multiplication Property
Systems Characterized by Linear Constant-Coefficient Differential Equations
![Page 2: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/2.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-19Problem 4.10 (p.336) – Convolution, Multiplication [SS4:70-71]
![Page 3: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/3.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-20Problem 4.11 (p.336) – Convolution, Multiplication [SS4:70-71]
![Page 4: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/4.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-21Problem 4.12 (p.336) – Convolution, Multiplication [SS4:70-71]
![Page 5: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/5.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-22Problem 4.13 (p.336) – Convolution, Multiplication [SS4:70-71]
![Page 6: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/6.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS2-LTI-23Midterm 2014-7
![Page 7: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/7.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-24Problem 4.14 (p.337) – Facts [SS4:70-71]
![Page 8: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/8.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-25Problem 4.15 (p.337) – Facts [SS4:70-71]
![Page 9: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/9.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-26Problem 4.16 (p.337) – Convolution, Multiplication [SS4:70-71]
![Page 10: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/10.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-27Problem 4.17 (p.337) – Rea, Imaginary, Even, Odd [SS4:35]
![Page 11: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/11.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-28Problem 4.18 (p.337) – Convolution, Multiplication [SS4:70-71]
![Page 12: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/12.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS3-FS-29Midterm 2014-10
![Page 13: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/13.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS3-FS-30Midterm 2013-6
![Page 14: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/14.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS2-LTI-31Midterm 2013-10
![Page 15: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/15.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS2-LTI-32Midterm 2012-8
![Page 16: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/16.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-33Outline
Representation of Aperiodic Signals: the Continuous-Time Fourier Transform
The Fourier Transform for Periodic Signals
Properties of Continuous-Time Fourier Transform
The Convolution Property
The Multiplication Property
Systems Characterized by Linear Constant-Coefficient Differential Equations
![Page 17: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/17.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-34Problem 4.19 (p.337) – Frequency Response [SS4:75]
![Page 18: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/18.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS4-CTFT-35Problem 4.20 (p.337) – RLC [SS4:75]
![Page 19: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/19.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS3-FS-36Midterm 2014-8
![Page 20: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/20.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS2-LTI-37Midterm 2013-7
![Page 21: Representation of Aperiodic Signals: the Continuous-Time ...homepage.ntu.edu.tw/.../103-2_ss04_CTFT_Problem_3... · NTUEE-SS4-CTFT-18 Outline Representation of Aperiodic Signals:](https://reader033.vdocument.in/reader033/viewer/2022041607/5e34c2ba3d88dc6fdd166c1b/html5/thumbnails/21.jpg)
Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS2-LTI-38Midterm 2012-7