The discussion focuses on analyzing the response of a linear system described by the differential equation y' + y = x, where the input x is a sine wave function, x = sin(t). The Fourier Transform is utilized to derive the system's response, represented by the relationship Y(jω) = H(jω)X(jω), where H(jω) is the system's transfer function. The convolution theorem is applied to express the output y(t) as the convolution of the system's impulse response h(t) and the input x(t). Additionally, the Fourier Transform of the derivative y'(t) is addressed, emphasizing the need to understand its implications in the context of linear systems.
PREREQUISITESStudents and professionals in engineering, particularly those specializing in signal processing, control systems, and applied mathematics. This discussion is beneficial for anyone looking to deepen their understanding of linear system responses to sinusoidal inputs using Fourier analysis.
If the FT of y(t) is [tex]Y(j\omega)[/tex] what is the FT of y'(t)?jaguar515 said:Find the response of the of the linear system at rest
y' + y = x , where x = sin(t)
using the Fourier transform and formulas :
Y(jw)=H(jw)X(jw)
y(t)=h(t)*x(t) convolution