The Laplace transform of two functions is equal. The functions are equal. 2. Laplace transform is a linear operator. 3. The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero.
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.
TRUE OR FALSE
1. The Laplace transform of two functions is equal. The functions are equal.
2. Laplace transform is a linear operator.
3. The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero.
4. L(f*g) = L(f).L(g).
5. Every function f(t) has a Laplace transform.
6. Taking the inverse Laplace transform gives us a function that is in the time domain.
7. Inverse Laplace transform is a linear operator.
8. The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function.
9. If the denominator of a Laplace transform has degree 4, you should expect to find 4 items in the table to use for writing the transform as a sum of terms.
10. L(f(t)/t) = -F’(s).
11. L(3y+5w)=3∙L(y)+5∙L(w).
12. Daniel Bernoulli is the original author of Laplace Transform.
13. The Laplace transform of the sum of two functions is equal to the sum of the Laplace transform of the functions.
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