# How is quadrature mixing done?

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?

• 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. – Matt L. Jun 7 '16 at 10:26
• 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'? – anonymous Jun 7 '16 at 10:39
• 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. – Matt L. Jun 7 '16 at 13:39
• 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? – anonymous Jun 7 '16 at 19:38
• 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/… – Dan Boschen Jun 16 '16 at 11:05

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.