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

eeeeeeeeee

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

eeeeeeeeeeeeeee

 

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

eeeeeeeeeeee

Solution:

eeeeeeeeeeeeee

Time shifting property of DTFT states that

eeeeeeeeeeeee

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

eeeeeeeeeeeee

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

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


Difference Equations - Natural Response (Zero Input Response), Complete Response y(n),

Impulse Response Properties - Causality of LTI Systems, Stability of LTI Systems, Memoryless and with Memory Systems, Invertible Systems and DE - Convolution, Step Response, Problems based on Impulse response properties

Block Diagram Representation - Direct Form I Structure, Direct Form - II Structure,

Cascade Form Structure for IIR Systems - Parallel Form Structure for IIR Systems

Discrete Time Fourier Transform Analysis of DT Systems

Z Transform Analysis of DT Systems - Pole Zero Plots, Transfer Function of the Linear Time Invariant (LTI) System, Causality and Stability

Example Problems Based on z Transform Analysis of Discrete Time Systems

Convolution Sum - Discrete Time Signal as Weighted Impulses, Convolution Sum Formula,

Problems Based on Convolution Sum

Properties of Convolution and System Interconnections

Two Mark Questions with Answers of Linear Time Invariant-Discrete Time Systems

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