# Translations:Frequency/13/en

Why is the use of sines and cosines of the time variable t relevant to the theory of digital filtering? The reason is that sines and cosines let us define frequency, and the concept of frequency is basic to what we mean by a filter, be it digital or analog. Let us think about a rotating wheel, as on an old-fashioned wagon or stagecoach. Consider, for example, a wheel that is rotating at a rate of 10 times a second. If we consider one spoke on this wheel to be a reference vector, this vector makes 10 complete rotations in every second. Each rotation through ${\displaystyle {\rm {36}}0^{\rm {o}}}$ (which is ${\displaystyle {\rm {2}}\pi }$ radians) represents one cycle, so we say that the vector has a cyclic frequency of 10 cycles per second. The word hertz (Hz) stands for cycles per second, so alternatively, we say that the vector has a frequency of 10 Hz. Up to this point, we have not specified in which direction the vector is rotating. As a matter of mathematical convention, we say that the vector has a frequency of +10 Hz if it is rotating in the counterclockwise direction, whereas it has a frequency of –10 Hz if it is rotating in the clockwise direction. The frequency customarily is denoted by the symbol f.