Howtosignalprocessing
- What is the relationship between time domain and the frequency domain?
- What is time and frequency domain representation?
- How does a time shift affect frequency domain?
- What is the correlation between time and frequency response?
What is the relationship between time domain and the frequency domain?
Parseval's theorem gives the relationship between the squared integral of a time function and that of its Fourier transform, namely, the energy in the time domain is equal to the energy in the frequency domain.
What is time and frequency domain representation?
Time domain representation – In frequency domain, a signal is represented by its frequency spectrum. To obtain frequency spectrum of a signal, Fourier series and Fourier transformation are used. Fourier series is used to get frequency spectrum of time-domain signal, when the signal is periodic function of time.
How does a time shift affect frequency domain?
Apparently, a shift in the time domain corresponds to a phase rotation in the frequency domain. In particular, when the time-shift equal 1s (or in general: t0), the period of the phase rotation in frequency domain amounts 1Hz (or in general 1/t0Hz).
What is the correlation between time and frequency response?
The overshoot of the time response can be related to the resonant peak of the frequency response. This resonant peak also indicates the relative stability of the systems. The bandwidth is related to the natural frequency ωn of the system. For a given ξ greater the value ωn faster is the response.
