What is I/Q Data? - National Instruments
First, the digital data stream is processed so that two consecutive bits become two parallel bits. Both of these bits will be transmitted simultaneously; in other words, as mentioned in this pageQPSK allows one symbol to transfer two bits. The local oscillator generates the carrier sinusoid. The I and Q carriers are multiplied by the I and Q data streams, and the two signals resulting from these multiplications are summed to produce the QPSK-modulated waveform.
The I and Q data streams are amplitude-modulating the I and Q carriers, and as explained above, these individual amplitude modulations can be used to produce phase modulation in the final signal.
However, if the I and Q data streams are bipolar signals—i. Note that in the following plots the frequency of the waveforms is chosen such that the number of seconds on the x-axis is the same as the phase shift in degrees.
Multiplying -8 by j results in a further 90o rotation giving the -j8 lying on the negative imaginary axis. Whenever any number represented by a dot is multiplied by j, the result is a counterclockwise rotation of 90o. Conversely, multiplication by -j results in a clockwise rotation of o on the complex plane. Don't forget this, as it will be useful as you begin reading the literature of quadrature processing systems! Let's pause for a moment here to catch our breath.
Quadrature - Wikipedia
Don't worry if the ideas of imaginary numbers and the complex plane seem a little mysterious. It's that way for everyone at first—you'll get comfortable with them the more you use them. Remember, the j-operator puzzled Europe's heavyweight mathematicians for hundreds of years.
Granted, not only is the mathematics of complex numbers a bit strange at first, but the terminology is almost bizarre. While the term imaginary is an unfortunate one to use, the term complex is downright weird. When first encountered, the phrase complex numbers makes us think 'complicated numbers'.
This is regrettable because the concept of complex numbers is not really all that complicated. Just know that the purpose of the above mathematical rigmarole was to validate Eqs. Consider a number whose magnitude is one, and whose phase angle increases with time.
As time t gets larger, the complex number's phase angle increases and our number orbits the origin of the complex plane in a CCW direction. Figure 5 a shows the number, represented by the black dot, frozen at some arbitrary instant in time. A snapshot, in time, of two complex numbers whose exponents change with time. They each have quadrature real and imaginary parts, and they are both functions of time. We're going to stick with this phasor notation for now because it'll allow us to achieve our goal of representing real sinusoids in the context of the complex plane.
Don't touch that dial! We've added the time axis, coming out of the page, to show the spiral path of the phasor. Return to Figure 5 b and ask yourself: That's right, the phasors' real parts will always add constructively, and their imaginary parts will always cancel.
Implementations of modern-day digital communications systems are based on this property! To emphasize the importance of the real sum of these two complex sinusoids we'll draw yet another picture. A cosine represented by the sum of two rotating complex phasors. Thinking about these phasors, it's clear now why the cosine wave can be equated to the sum of two complex exponentials by Eq. We could have derived this identity by solving Eqs. Similarly, we could go through that same algebra exercise and show that a real sine wave is also the sum of two complex exponentials as Look at Eqs.
They are the standard expressions for a cosine wave and a sine wave, using complex notation, seen throughout the literature of quadrature communications systems.
To keep the reader's mind from spinning like those complex phasors, please realize that the sole purpose of Figures 5 through 7 is to validate the complex expressions of the cosine and sine wave given in Eqs. Those two equations, along with Eqs. We can now easily translate, back and forth, between real sinusoids and complex exponentials.
Again, we are learning how real signals, that can be transmitted down a coax cable or digitized and stored in a computer's memory, can be represented in complex number notation.
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Yes, the constituent parts of a complex number are each real, but we're treating those parts in a special way - we're treating them in quadrature. Representing Quadrature Signals In the Frequency Domain Now that we know something about the time-domain nature of quadrature signals, we're ready to look at their frequency-domain descriptions.
That way none of the phase relationships of our quadrature signals will be hidden from view. Figure 8 tells us the rules for representing complex exponentials in the frequency domain.
Interpretation of complex exponentials. We'll represent a single complex exponential as a narrowband impulse located at the frequency specified in the exponent. In addition, we'll show the phase relationships between the spectra of those complex exponentials along the real and imaginary axes of our complex frequency domain representation. With all that said, take a look at Figure 9. Complex frequency domain representation of a cosine wave and sine wave.
See how a real cosine wave and a real sine wave are depicted in our complex frequency domain representation on the right side of Figure 9. The directions in which the spectral impulses are pointing merely indicate the relative phases of the spectral components.
Because it's the tool we'll use to understand the generation modulation and detection demodulation of quadrature signals in digital and some analog communications systems, and those are two of the goals of this tutorial. However, before we consider those processes let's validate this frequency-domain representation with a little example.
Figure 10 is a straightforward example of how we use the complex frequency domain. There we begin with a real sine wave, apply the j operator to it, and then add the result to a real cosine wave of the same frequency.
Complex frequency-domain view of Euler's: This figure shows the big payoff: If you understand the notation and operations in Figure 10, pat yourself on the back because you know a great deal about the nature and mathematics of quadrature signals.What is QUADRATURE BOOSTER? What does QUADRATURE BOOSTER mean? QUADRATURE BOOSTER meaning
Bandpass Quadrature Signals In the Frequency Domain In quadrature processing, by convention, the real part of the spectrum is called the in-phase component and the imaginary part of the spectrum is called the quadrature component. The signals whose complex spectra are in Figure 11 aband c are real, and in the time domain they can be represented by amplitude values that have nonzero real parts and zero-valued imaginary parts.
We're not forced to use complex notation to represent them in the time domain—the signals are real. Real signals always have positive and negative frequency spectral components. For any real signal, the positive and negative frequency components of its in-phase real spectrum always have even symmetry around the zero-frequency point.
That is, the in-phase part's positive and negative frequency components are mirror images of each other. Conversely, the positive and negative frequency components of its quadrature imaginary spectrum are always negatives of each other. Out-of-phase waves Representation of phase comparison. Phase difference is the difference, expressed in degrees or radians, between two waves having the same frequency and referenced to the same point in time.
Two oscillators that have the same frequency and different phases have a phase difference, and the oscillators are said to be out of phase with each other. If two interacting waves meet at a point where they are in antiphase, then destructive interference will occur.
It is common for waves of electromagnetic light, RFacoustic sound or other energy to become superposed in their transmission medium. When that happens, the phase difference determines whether they reinforce or weaken each other.
Complete cancellation is possible for waves with equal amplitudes. Time is sometimes used instead of angle to express position within the cycle of an oscillation.