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Questions and Answers
What is the purpose of Z-transform in analysing discrete time signals and systems?
What is the purpose of Z-transform in analysing discrete time signals and systems?
- To converge for all signals
- To represent continuous time signals
- To generalize the Discrete-Time Fourier Transform (DTFT) (correct)
- To simplify the notation of Fourier Transform
Which transform does not converge for all the signals?
Which transform does not converge for all the signals?
- Fourier Transform
- Z-transform
- Discrete-Time Fourier Transform (DTFT) (correct)
- Laplace transform
In analytical problems, why is the notation of Z-transform more convenient than Fourier Transform?
In analytical problems, why is the notation of Z-transform more convenient than Fourier Transform?
- It represents continuous time signals better
- It converges for a broader class of signals (correct)
- It simplifies the notation of Laplace Transform
- It is applicable only for specific types of systems
Which transform is a generalization of the Discrete-Time Fourier Transform (DTFT)?
Which transform is a generalization of the Discrete-Time Fourier Transform (DTFT)?
What is the purpose of the Z-transform in analyzing discrete time signals and systems?
What is the purpose of the Z-transform in analyzing discrete time signals and systems?
Which transform is a generalization of the Discrete-Time Fourier Transform (DTFT)?
Which transform is a generalization of the Discrete-Time Fourier Transform (DTFT)?
Why is the notation of Z-transform more convenient than Fourier Transform in analytical problems?
Why is the notation of Z-transform more convenient than Fourier Transform in analytical problems?
Which transform does not converge for all the signals?
Which transform does not converge for all the signals?
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Study Notes
Discrete-Time Signals and Systems
- The Z-transform is a powerful tool for analyzing discrete-time signals and systems, enabling the conversion of difference equations into algebraic equations.
Convergence of Transforms
- The Z-transform does not converge for all signals, unlike the Fourier Transform which converges for all signals.
Notation Convenience
- The notation of the Z-transform is more convenient than the Fourier Transform in analytical problems due to its ability to handle rational functions of z, making it easier to manipulate and analyze.
Generalization of DTFT
- The Z-transform is a generalization of the Discrete-Time Fourier Transform (DTFT), providing a more comprehensive and flexible approach to analyzing discrete-time signals and systems.
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