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I've a Gaussian modulated signal whose quadrature and in phase components are separated. I'm multiplying these components with quadrature and in phase components of a signal of 10MHz frequency, respectively. Then i added the two products.This sum is quadrature mixed data.Right?

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  • $\begingroup$ What exactly do you mean by "a Gaussian modulated signal"? Is your signal modulated twice? My answer below refers to quadrature modulation of a complex baseband signal. $\endgroup$ – Matt L. Jun 7 '16 at 10:26
  • $\begingroup$ Let me try to explain..i have an NRZ signal which i convolved with a Gaussian filter to get a Gaussian signal. I separated its in phase and quadrature components by multiplication with in phase and quadrature component of a signal with 25KHz frequency. Then i perform quadrature mixing with these components and a signal of 10MHz frequency. What does it mean by 'quadrature modulation of a complex baseband signal'? $\endgroup$ – S.G.K Jun 7 '16 at 10:39
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    $\begingroup$ The standard way to use quadrature modulation is to generate a complex baseband signal (i.e., two real-valued baseband signals), which is easy if your data are digital (just use a complex symbol constellation such as QPSK). If you only have a single signal, you can get the same bandwidth efficiency by using SSB (single sideband) modulation. $\endgroup$ – Matt L. Jun 7 '16 at 13:39
  • $\begingroup$ I've two real valued baseband signals of 10MHz frequency,i.e., sine and cosine of 10MHz. Multiplying the earlier quadrature components with sine and cosine of 10MHz respectively should give signal around -10MHz and 10MHz..Right? $\endgroup$ – S.G.K Jun 7 '16 at 19:38
  • $\begingroup$ Comment to tie this question to similar question by OP: dsp.stackexchange.com/questions/31355/…. In that diagram shown $\omega_c$ is the 10MHz carrier which is split in quadrature, the other two mixer inputs are your I and Q Gaussian filtered data. Also with regards to implementation of the Gaussian filter, see dsp.stackexchange.com/questions/31483/… $\endgroup$ – Dan Boschen Jun 16 '16 at 11:05
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If your signal's in-phase and quadrature components are $x_I(t)$ and $x_Q(t)$, respectively, then your quadrature mixed signal is

$$s(t)=x_I(t)\cos(\omega_ct)-x_Q(t)\sin(\omega_ct)\tag{1}$$

where $\omega_c$ is the carrier frequency in radians per second. You can also use a '$+$' sign in $(1)$, that's just a matter of convention.

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  • $\begingroup$ I read somewhere that quadrature mixing is unique as it can shift all the frequencies to another range, creating a single sideband..what does this mean? $\endgroup$ – S.G.K Jun 7 '16 at 10:33
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    $\begingroup$ @S.G.K: Quadrature modulation shifts a baseband signal to a frequency range around a chosen carrier frequency. It is unique in the sense that it can transmit 2 signals (or 1 complex-valued signal) in the same frequency range, because of the use of two orthogonal carriers (which are phase shifted by 90 degrees, e.g., sine and cosine). $\endgroup$ – Matt L. Jun 7 '16 at 13:34
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    $\begingroup$ To answer your question about SSB, consider multiplying two cosines: cos a * cos b = cos (a+b) + cos (a-b). This shows you how that process creates two sidebands ((a+b) and (a-b)). Now consider a complex signal exp(j a) * exp(jb) = exp(j(a+b))-- this created only one sideband, and you can change the sign to get upper or lower. Now in the "real world" to create exp(j a) we use the relationship: exp(j a) = cos (a) + jsin(a), and split the signal into quadrature components, with each output having a 90 degree phase to each other. It takes two real signals to implement one complex signal. $\endgroup$ – Dan Boschen Jun 7 '16 at 13:40

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