Design of filtering and control systems is usually easier in the frequency domain than in the time domain.
time domain is respected to the time and frequency domain is respected to the frequency
to find their ESD and PSD
Convolution in the time domain is equivalent to multiplication in the frequency domain.
We need small values of delta t as the smaller is the time interval better resolution of signal is possible. Also, the highest frequency in frequency domain is inversely proportional to delta t. So higher delta t in time domain results in higher the maximum frequency in frequency domain.
Convolution in the time domain is equivalent to multiplication in the frequency domain.
If we need to add two signals in time domain, we perform convolution. A better way, is to convert the two signals from time domain to frequency domain. This can be achieved by FAST FOURIER TRANFORM. Once both the signals have been converted to frequency domain, they can simply be multiplied. Since Convolution in time domain is similar to multiplying in Frequency domain. Once both the signals have been multiplied, they can be converted back to time domain by Inverse Fourier Transform method. Thus achieving accurate results.
with the help of laplace transform the calculation part can be reduced in frequency domain .In time domain differential equations are used and solution is cumbersome.
freguency domain concept
the use of frequency domain will prove better results were the latency is not a problem. also u can do batch processing in frequency domain hence the overall efficiency of hardware can be effectively used.....
Frequency Analysis is much easier. Some equations can't be solved in time domain while they can be solved easily in frequency domain. When moving to frequency domain you change the differential equation into algebric equation. Also, in frequency domain it is easy to apply filters and compute their specifications. In telecommunications, using multiple frequencies enables more than one user to use the service at the same time if having different frequency, this enables less delay for the signal. Also, it would be easier, when using frequency domain- to give each user, or each standard (GSM, Satellite ...) it's own frequency range without interfering. This can't be done in time domain
frequency transfer function deals with transfer in frequency domain, transfer function alone can be referring to any type of transfer in different domain e.g time domain
Fourier series analysis is useful in signal processing as, by conversion from one domain to the other, you can apply filters to a signal using software, instead of hardware. As an example, you can build a low pass filter by converting to frequency domain, chopping off the high frequency components, and then back converting to time domain. The sky is the limit in terms of what you can do with fourier series analysis.