Howtosignalprocessing
- What is the relation between time-domain and frequency domain?
- What is infinite support?
- What is frequency domain in time series?
- Why do we use frequency domain instead of time-domain?
What is the relation between time-domain and 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 infinite support?
The sinc has infinite support. Support being defined as the smallest interval in which the function has non-zero values, it's trivial to see that sinc(x)=sin(x)/x (for all x but a single point) becomes arbitrarily small for large x, but never actually constantly sinc(x>ξ)=0 for any finite ξ.
What is frequency domain in time series?
Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies.
Why do we use frequency domain instead of time-domain?
The frequency domain representation of a signal allows you to observe several characteristics of the signal that are either not easy to see, or not visible at all when you look at the signal in the time domain. For instance, frequency-domain analysis becomes useful when you are looking for cyclic behavior of a signal.
