Chirp

As a chirp (English chirp " chirping " ) or a cicada is called a signal whose frequency changes over time in the signal processing. A distinction is made between positive chirp, in which the frequency increases in time, and negative chirp having a frequency decrease.

Industrial applications are in the transmission of microwaves in the synthetic aperture radar and bandspreizenden modulation methods such as Chirp Spread Spectrum (CSS). In nature put bats for locating a chirp pulses.

Be strong, short laser pulses, " chirped " to them - thereby enlarged with pulse duration - can strengthen ( Chirped Pulse Amplification ).

Chirp Description

A typical example is a signal x (t) with the following timing:

In this case, f (t ) is interpreted as a time-dependent frequency of the indefinite integral has a specific fixed root function f (t) use. This interpretation requires a more detailed explanation, since according to the uncertainty principle of the Fourier transform ( see also Heisenberg's uncertainty principle ) it is not possible, the time and frequency to determine exactly together.

The frequency data is to be understood that in a time interval about full periods of the sine are run, the average frequency is so. By the mean value theorem of integral calculus, there is at least one time at which this value also takes. To speak of the instantaneous frequency, the time interval should encompass a plurality of full periods, but the change of f ( t) in this interval may be small, so that the average frequency is always close to the value of f ( t).

Examples and Applications

Reducing the pulse power in radar

In order to hear answers from distant radar reflections from the noise, a certain minimum energy must be received. For accurate distance measurements, but you need the shortest possible transmit pulses that on a 0.1 microseconds short transmission pulse, the wave packet is already 30 m long. The combination of both requirements leads to immense power levels of 10 MW, the production of aircraft or satellite causes problems. As a way out, a low-power chirped - pulse longer total duration will be sent the pulse compression method, which is compressed when received by special filters or mathematical methods to a much shorter pulse. This can then be detected in the noise well.

Linear chirp

For the special case of a linear chirp, the frequency increases linearly by the constant K to:

And it is the timing for x (t):

Acoustic Example: Linear Chirp ( 5 reps ) / i?

Exponential chirp

For radar or sonar often exponential chirps are used. Here is the frequency dependency of the time when the fixed fundamental frequency f 0, and k is a constant:

And thus the time course x (t):

Acoustic Example: Exponential chirp ( 5 reps ) / i?

Gravity

In a more general definition of a chirp has the form

The parameters a and b. This waveform occurs in practice for the detection of gravitational waves.

Dispersion at light

In the optical light pulses will be a wavelength-dependent refractive index of the so-called dispersion distorted:

In the generation and transmission of ultra-short pulses of light, it is necessary to compensate for this phase shift. Besides prisms also called Chirpspiegel (English: chirped mirrors ) are used, which can compress extended and distorted pulses again due to a frequency-dependent reflection. Chirpspiegel are reflection diffraction grating. They are (see pulse laser ) used in pulse power lasers, high to expand the pulses prior to amplification, and to re-compress the end.

With the direct modulation of the semiconductor lasers, the most unwanted laser chirp arises see Distributed_Feedback_Laser