Signals and Systems: Unit V: Linear Time Invariant-Discrete Systems,,

Discrete Time Fourier Transform Analysis of DT Systems

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Discuss about Discrete Time Fourier Transform Analysis of DT Systems and Solved Problem

5.4 DISCRETE TIME FOURIER TRANSFORM ANALYSIS OF DT SYSTEMS

Magnitude / Phase transfer functions using fourier transform.

Output of LTI system is given by

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Let us consider the LTI system is excited by sinusoidal signal.

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H(ω) is the fourier transform of h(k). H(ω) is called transfer function of the system.

H(ω) in polar form is |H(ω)| e ^{j < H(ω)}

|H(ω)| ⇒ Magnitude of H(ω)

< H(ω) ⇒ Angle of H(w)

Problem 1:

Write a difference equation that characterizes a system whose frequency response is

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Solution:

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Time shifting property of DTFT states that

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Taking inverse DTFT of above equation and applying time shifting property.

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Signals and Systems: Unit V: Linear Time Invariant-Discrete Systems,, : Tag: : - Discrete Time Fourier Transform Analysis of DT Systems

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EC3354 - 3rd Semester - ECE Dept - 2021 Regulation | 3rd Semester ECE Dept 2021 Regulation