Negative frequency

The negative frequency occurs as a component in simple harmonic motion if the mathematical description in the complex plane is done with complex numbers. Physically, the sign has no meaning; it specifies the right or left manoeuvrable circulation of pointers in the complex plane.

The concept of negative frequency plays in the field of signal theory and signal processing, a role, especially in technical modulation method.

Definition

A frequency f is the number of events within a certain time period and is typically a positive number. A harmonic vibration S (t) of frequency f and an amplitude A has a sinusoidal curve over the time t:

The term 2? F is usually summarized to the angular frequency ω. As a phasor diagram in the complex plane can be as shown in the adjacent diagram, map onto the real axis of the sinusoidal profile over time t during the rotation of the pointer r. The illustration on the imaginary axis cosine curve is equivalent to and provides a phase shift of π / 2 dar.

The harmonic oscillation can be specified as equivalent to complex vibration of the Euler identity:

With the real part of s (t):

And with A * the conjugate to A amplitude. The second expression is equivalent to the vibration as a sum of a positive and a negative frequency in the vector diagram is a graphical way of expression by two oppositely rotating pointer representable, the direction of rotation of the pointer is determined by the sign of the frequency.

Applications

The distinction between positive and negative frequencies has, in particular in technical modulation method and signal processing meaning. If a signal as an information carrier by the amplitude modulation of the baseband modulated for transmission in a higher frequency range, resulting from the positive and negative frequencies of the signal, an upper or lower sideband. These two sidebands both carry the same signal information of the baseband.

An ability to suppress one of the two side bands, is to form an analytical signal by means of the Hilbert transform of the real signal. An analytical signal is a complex signal, the negative frequency components are equal to 0, consisting only of positive frequencies.