Final answer:
The Fourier transform of the signal x(t) = cos(ω0t)u(t) can be found using the Fourier transform definition for continuous time signals, and it involves the Dirac delta function to represent the frequency content of the signal.
Step-by-step explanation:
The student is asking for the Fourier transform of the signal x(t) = cos(ω0t)u(t), where ω0 is the angular frequency and u(t) denotes the unit step function. This is a standard problem in signal processing, which comes under electrical engineering and, specifically, the field of communications. The Fourier transform is a mathematical tool used to transform signals between time and frequency domains, providing a frequency spectrum representation of the signal.
To find the Fourier transform of the given signal, you should use the definition of the Fourier transform for continuous time signals:
- F(δ(ω - ω0)) + δ(ω + ω0))
where δ represents the Dirac delta function, and we consider the Fourier transform of the cosine function multiplied by the step function. In practice, this method is a common approach to analyze the frequency content of signals in engineering.