A new signal is formed by summing two signals of different frequencies. The low frequency signal may be the data that should have been obtained, but the high frequency signal, as noise, has altered the measurement.
By summing several signals of different frequencies, complex waveforms can be created. Whether it's speech, music or the sound produced by any object, lots of frequencies make up the sound. But it is not only in sound engineering where the analysis of different frequencies in waveforms are important, as medical diagnostics, meteorology and countless other scientific fields work with such data.
The goal of filtering is to remove unwanted frequencies from signals. Instead of removing a single frequency, filters are only able to filter ranges. The task may be to remove all frequencies greater or less than a specific frequency, or to remove and retain only one range, called a band in this context.
The output signal of a filter is usually measured on the Decibel scale, as it allows the comparison of high and low values on the same scale, which in this case is the ratio of the output to input power or voltage.
$ [dB] = 10 ⋅ lg \left(\dfrac{P_{out}}{P_{in}} \right) $
$ [dB] = 20 ⋅ lg \left(\dfrac{V_{out}}{V_{in}} \right) $
A useful tool for evaluating filters is the Bode plot, which consists of two sub-diagrams. The horizontal axis in both diagrams is the frequency on a logarithmic scale, the vertical axes are different. On the top the output signal in decibels is plotted, below it is the phase angle in degrees.