CTFT from CTFS ¾ Aperiodic Construct periodic signal for which one period is

# Ctft from ctfs ¾ aperiodic construct periodic signal

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CTFT from CTFS ¾ Aperiodic Construct periodic signal for which one period is has a Fourier series As period for increase, and Fourier series of become Fourier transform of 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 12

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DTFT from DTFS ¾ Aperiodic Construct periodic signal for which one period is has a Fourier series As period for increase, and Fourier series of become Fourier transform of 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 13
Example 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 14 - N 1 N 1 0 - N 1 N 1 0 N -N - N 1 N 1 0 N -N - N 1 N 1 0 N -N

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As Fourier Transform: DTFT Algebraic Explanation 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 15
Discrete-Time Fourier Transform 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 16 Notation: or Synthesis equation Analysis equation

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Example 5.1 One-sided Exponential 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 17 a > 0
Example 5.1 One-sided Exponential 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 18 a < 0

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Example 5.2 Two-sided Exponential 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 19
Example 5.3 Rectangular Pulse 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 20

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Convergence 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 21
Example 5.4 ¾ Consider the unit impulse 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 22

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DTFT for Periodic Signals ¾ Recall for CTFT on x ( t ) being periodic We defined Write the CT Fourier series representation ¾ For DTFT on x [ n ] being periodic We define Write the DT Fourier series representation 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 23 or
Example 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 24

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Example 5.5 ¾ Consider the following periodic signal 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 25
Example 5.6 ¾ Consider the discrete-time infinite impulse train 20-Mar-19 EIE3001 Sig & Sys, Spring 2019 26

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