Task 2: Your supervisor asked you to analyse the following signal processing system that exists in an advanced communication system. The transfer function of this system is expressed in the Laplace domain as follows: Y(s)/X(s) = 1 / s^5 + 15s^4 + 85s^3 + 225s^2 + 274s + 120. For this system, we are interested in finding the roots of the denominator of H(s). This is needed to find the inverse Laplace transform and to understand the function behaviour in the time domain. However, it's hard to find an analytical solution for high order systems using trivial methods, therefore, you need to solve such systems using numerical methods. Y(s) H(s) = X(s) 1 s5 + 15s* + 85s3 + 225s? + 274s + 120 Sketch the function of the denominator (s5 + 15s* + 85s3 + 225s² + 274s + 120) and estimate the roots of the sketched function using a graphical estimation method. Find the value of the first root of the denominator using bisection technique with 5 iterations knowing that the first root exists in the interval [0, -1.25]. (Show the numerical solution using both, hand-solution, and MATLAB). i) ii)
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.
![Task 2:
Your supervisor asked you to analyse the following signal processing system that exists in an
advanced communication system. The transfer function of this system is expressed in the Laplace
domain as follows: Y(s)/X(s) = 1/ s^5 + 15s^4 + 85s^3 + 225s^2 + 274s + 120. For this system, we are
interested in finding the roots of the denominator of H(s). This is needed to find the inverse Laplace
transform and to understand the function behaviour in the time domain. However, it's hard to find an
analytical solution for high order systems using trivial methods, therefore, you need to solve such
systems using numerical methods.
Y(s)
H(s) =
1
X(s) s5 + 15sª + 85s3 + 225s? + 274s + 120
Sketch the function of the denominator (s5 + 15s* + 85s³ + 225s² + 274s + 120) and
estimate the roots of the sketched function using a graphical estimation method.
Find the value of the first root of the denominator using bisection technique with 5
iterations knowing that the first root exists in the interval [0, -1.25]. (Show the numerical
solution using both, hand-solution, and MATLAB).
i)
ii)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc48aa633-e054-48b9-8cd1-6f9a62dc3af2%2Fa246a7d8-a474-4ca4-9c03-3bf3ced14afd%2F5c9rux_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
