Question

For part (a), repeat the derivation using linearity and time shift properties of the Fourier transform. Show that your answers for part (a) are the same. What does this demonstrate?

A) Consistency in Fourier series expansion
B) Orthogonality of wave functions
C) Validity of Fourier transform properties
D) Symmetry in time-domain signals

Answer 1

The answers for part (a) using linearity and time shift properties of the Fourier transform are the same, which demonstrates the validity of the Fourier transform properties.

Step-by-step explanation:

When two wave functions are solutions to the linear wave equation, their sum is also a solution to the wave equation. This property is known as the principle of superposition. To show that the answers obtained by using linearity and time shift properties of the Fourier transform are the same, we can express the two wave functions in terms of the Fourier transform, apply the linearity property to obtain the sum, and then use the time shift property to shift the resulting wave function. This demonstrates the validity of the Fourier transform properties.