Oh, my professor never mention this, i will check this and seeBvU said:
Yes i have tried this before, but it didn't match the solution that my professor gave, that's why i ask in here to checkMathematicalPhysicist said:
The purpose of finding x(t) from X(ω) is to understand the relationship between a signal in the time domain and its representation in the frequency domain. This allows for the analysis and manipulation of signals using mathematical techniques in the frequency domain, which can be more efficient and intuitive than working in the time domain.
To find x(t) from X(ω), you can use the inverse continuous-time Fourier transform (CTFT) formula: x(t) = ∫X(ω)e^(jωt)dω, where X(ω) is the frequency domain representation of the signal and x(t) is the time domain representation. This formula can be calculated using calculus or by using tables of common transforms.
The continuous-time Fourier transform (CTFT) is used to analyze signals that are continuous in time, while the discrete-time Fourier transform (DTFT) is used for signals that are discrete in time. The CTFT uses continuous variables (such as frequency ω) while the DTFT uses discrete variables (such as frequency in radians/sample). The inverse transforms for CTFT and DTFT also differ in their formulas.
In theory, yes, you can find x(t) from X(ω) for any signal using the inverse CTFT formula. However, in practice, this may not always be possible due to the complexity of the signal or limitations in the analysis tools available. In some cases, it may be more practical to approximate the signal using a simpler function or to use other techniques for signal analysis.
Finding x(t) from X(ω) is useful in many real-world applications, such as in signal processing, telecommunications, and audio and image processing. It allows for the analysis and manipulation of signals in the frequency domain, which can be more efficient and intuitive than working in the time domain. This can lead to improved signal quality, increased data transmission rates, and more efficient data storage and compression techniques.