page_title: Negative frequency
section_title: Sampling of positive and negative frequencies and aliasing
hierarchical_section_title: Negative frequency / Sampling of positive and negative frequencies and aliasing
context_page_description: The concept of negative and positive frequency can be as simple as a wheel rotating one way or the other way: a signed value of frequency can indicate both the rate and direction of rotation. The rate is expressed in units such as revolutions per second or radian/second.
caption: This figure depicts two complex sinusoids, colored gold and cyan, that fit the same sets of real and imaginary sample points.  They are thus aliases of each other when sampled at the rate (fs) indicated by the grid lines.  The gold-colored function depicts a positive frequency, because its real part (the cos function) leads its imaginary part by 1/4 of one cycle.  The cyan function depicts a negative frequency, because its real part lags the imaginary part.