Representation of Aperiodic Signals: the Continuous-Time...

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Feng-Li Lian © 2015 NTUEE-SS4-CTFT-18 Outline 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

Transcript of Representation of Aperiodic Signals: the Continuous-Time...

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

Feng-Li Lian © 2015Feng-Li Lian © 2015NTUEE-SS2-LTI-38Midterm 2012-7