Which of the following statements is NOT true?\ 1) Laplace transform of a non-causal signal can not be used for the analysis of a linear time invariant system. 2) Laplace transform changes differential equation into algebraic equation for a linear time invariant system with causal input signal. 3) Electrical circuit analysis can be carried out using Laplace transform where each circuit element is converted to its equivalent impedance with additional source characterizing the initial condition. 4) Laplace transform can be greatly simplified for a causal system with causal input signal where the region of convergence becomes irrelevant.
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
Which of the following statements is NOT true?\
1) Laplace transform of a non-causal signal can not be used for the analysis of a linear time invariant system.
2) Laplace transform changes differential equation into algebraic equation for a linear time invariant system with causal input signal.
3) Electrical circuit analysis can be carried out using Laplace transform where each circuit element is converted to its equivalent impedance with additional source characterizing the initial condition.
4) Laplace transform can be greatly simplified for a causal system with causal input signal where the region of convergence becomes irrelevant.
1) Laplace transform of a non-causal signal can not be used for the analysis of a linear time invariant system.
2) Laplace transform changes differential equation into algebraic equation for a linear time invariant system with causal input signal.
3) Electrical circuit analysis can be carried out using Laplace transform where each circuit element is converted to its equivalent impedance with additional source characterizing the initial condition.
4) Laplace transform can be greatly simplified for a causal system with causal input signal where the region of convergence becomes irrelevant.
Which statement is false and explain it
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