The impulse response of a linear, time-invariant system is described by the following equation and shown in the accompanying figure. The transform can be easily computed by using the Table of Fourier Transforms and applying the linearity property.
Decibels are a convenient way of plotting magnitudes which cover a wide range of values.
Note that the frequency scale in both plots is a logarithmic scale. Major changes in magnitude and phase generally occur on a log scale rather than a linear scale in most Fourier or Laplace Transforms. Now, we will apply 3 different pure sinusoids as inputs to the system, one at a time. Note the relative magnitudes and phases of the input and output signal at that frequency, and compare them with the magnitude and phase plots in the frequency domain. Now we will look at an input signal which has a multitude of frequencies in it, namely the unit step signal.