# 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. Jun 7, 2016 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'? Jun 7, 2016 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. Jun 7, 2016 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? Jun 7, 2016 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/… Jun 16, 2016 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.

• 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? Jun 7, 2016 at 10:33
• @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). Jun 7, 2016 at 13:34
• 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. Jun 7, 2016 at 13:40