Abstracting Transformations.........

 

  In the signal processing we have to learn the transformation from time domain to frequency domain. The very popular transformations are Laplace and Fourier transformations. We engineers learn the transform and solve the problems, but there is more than solving question in these transforms. These transform gives very much idea about the systems, which are processing the signals.

  The first thing comes in mind that why we have to convert the signal into frequency domain, can't we manipulate the signal in time domain ? And what are these domains actually are ?

  The time is base of everything, without time nothing can happen. To happen anything there must presence of time, same is true for the signal also, a signal must have time. And the amplitude, phase or/and frequency of signal vary according to time. So for a signal time domain is value of amplitude and phase at every instance of time, and frequency domain is amplitude and phase present in the signal at every fraction of frequency.

  For a periodic signal it is easy to see how signal is behaving, because it repeats itself after some time and we totally analyze the signal, but when the repetition period of signal is too high or it is non periodic signal then it is impossible to analyse signal fully. So we need a power tool to analyse such signals. Another limitation of time domain is most of systems are band limited i.e. they don't allow signal exceeding the frequency limitation, so when we deal with time domain the actual frequency can't be seen.

 Hence we have to convert the signal in frequency domain, it doesn't mean that the actual signal is converting into frequency domain. A frequency domain is just a representation of actual signal for manipulations.

  A Kernel is required for inter-conversion between time and frequency domain. These Kernel are Laplace and Fourier.