0
$\begingroup$

I am new in the signal processing. I hope I can get help. I want to ask a question regarding IQ modulation work .

Why can’t I simply multiply a complex base-band signal with a cosine to modulate it?

$\endgroup$
3
$\begingroup$

If you have a complex baseband signal and you modulate it with a cosine then you shift the signal in frequency but your passband signal is still complex-valued, so it cannot be transmitted over a single channel (you would need two channels, one for the real part and one for the imaginary part).

You can, however, transmit the same information over a single real-valued channel by modulating with a complex carrier and taking the real part of the result.

Let $x(t)$ be the complex baseband signal, and let $\omega_c$ be the desired carrier frequency (in radians). Your suggestion results in a passband signal

$$s_1(t)=x(t)\cos(\omega_ct)=\frac12 x(t)e^{j\omega_ct}+\frac12 x(t)e^{-j\omega_ct}\tag{1}$$

If $x(t)$ is complex-valued, then $s_1(t)$ is also complex-valued, and if $x(t)$ has bandwidth $B$, then for transmitting $s_1(t)$ you need two real-valued channels (for the real and imaginary part of $s_1(t)$) with bandwidth $2B$.

However, if you define a passband signal

$$s_2(t)=\text{Re}\left\{x(t)e^{j\omega_ct}\right\}=x_R(t)\cos(\omega_ct)-x_I(t)\sin(\omega_ct)\tag{2}$$

where $x_R(t)$ and $x_I(t)$ are the real and imaginary parts of $x(t)$, respectively, then you can transmit $s_2(t)$ over a single real-valued channel with bandwidth $2B$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.