Howtosignalprocessing
- What is the consequence in the time domain for having samples in the frequency domain?
- What is the relation between time domain and frequency domain?
- Why is frequency domain sampling necessary?
- Why the conversion of signal from time domain to frequency domain is necessary?
What is the consequence in the time domain for having samples in the frequency domain?
The answer is: yes, sampling in the frequency domain causes aliasing in the time domain, exactly like the dual case: sampling in the time domain causes aliasing in the frequency 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.
Why is frequency domain sampling necessary?
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.
Why the conversion of signal from time domain to frequency domain is necessary?
For mathematical systems governed by linear differential equations, a very important class of systems with many real-world applications, converting the description of the system from the time domain to a frequency domain converts the differential equations to algebraic equations, which are much easier to solve.
