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)

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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)
Transcribed Image Text: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)
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