In-phase and quadrature components

The I and Q process ( in-phase and quadrature - method) is one way to preserve the phase information for demodulation of a radio-frequency carrier signal. So you can, for example, moving the radar distinguished from non- moving objects.

In a simple demodulation of only the real part of a complex signal is determined, ie a signal at the input of the demodulator has an amplitude size, and a phase position at the output of the demodulator circuit, only the amplitude size, the phase information is lost.

However, the evaluation of the phase information is a prerequisite for a MTI circuit that detects the signal in a Doppler shift of the carrier frequency, and thus can distinguish moving objects from non-moving.

With simple demodulation may even happen that the instantaneous value ( the real part R ), the amplitude is zero and the phase information (imaginary part: -jX ) has its maximum value. At the output of the demodulator so simple, no signal will be measured in this case. This has fatal consequences in radar devices, operating according to the monopulse method, which therefore only these need a pulse for target recognition. Therefore it must be phase-shifted by 90 °, the entire signal, in order to obtain in this case in general a demodulated signal.

Since, however, is not known at which phase the signal is received, both ways of demodulation must be carried out:

The signal is therefore divided into two paths, one path of the demodulation to the original phase angle (English: in -phase ) is performed and results in the I data, the second path is carried out with phase-shifted by 90 ° reference frequency and provides the Q data (English: quadrature ).

Now both components of the input signal are available. The I signal is the original amplitude, the Q signal is also amplitude, but represents the size of the phase angle. From these two signals can now, as they relate to each other in the original at a right angle, the absolute amplitude value can be calculated with the Pythagorean theorem.

In practice, however, the technical realization of a root calculation is complicated. In addition to possible yet available in real time at this stage of signal processing, the radar data. Therefore, most continued to work here with an approximation method.

The length of the longer cathetus A plus half the length of the shorter cathetus b is approximately the length of the hypotenuse c. This formula, however, can be easily realized with an assembler program or even with extremely fast hardware wiring. The approximation is greater than or equal to the true value, with a maximum error of 12% at 26 ° ..

In addition to the approximation Pythagorean a more exact calculation of using the CORDIC algorithm is possible, the often used in digital signal processing and in the mobile communications and also comes into consideration for real-time applications. The CORDIC offers a resource efficient implementation for the iterative rotation of pointers, that maps the trigonometric functions using simpler functions. In concrete use of CORDIC in the field of I & Q demodulation, the pointer of the input signal is turned on with the cover unit pointer ( CORDIC vector mode ), resulting in the length ( amplitude ) and the phase angle.

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