# Converting complex baseband signal to passband signal

I have to convert baseband signal (BW-20MHz) to passband signal centred at 20MHz. I am implementing this in matlab. so, this is how I tried it. I have already generated LTE Waveform BW- 20MHz , fs =30.72e6, size(LTE Waveform)= 307200 samples.

n = [0:size(LTE_Waveform)-1]';
x = exp(1i*2*pi*20e6*(1/30.72e6)*n);

z =LTE_Waveform.*x;

fvtool(z, 'fs',30.72e6)

This is the LTE waveform

and the passband spectrum I got looks like this How can I get the spectrum properly centred around 20MHz?

• You can follow the diagram of Figure 2.8 of this book Tse and Viswanath, Fundamentals of Wireless Communication, stanford.edu/~dntse/wireless_book.html Section 2.2.2 could provide some useful details. – AlexTP Dec 28 '18 at 9:17

## 1 Answer

Your signal $$z$$ is centered at 20 MHz, but because your sampling rate is 30.72 MHz, 20 MHz is beyond the Nyquist frequency of $$f_s/2$$ = 15.36 MHz and therefore aliases to 20-30.72 = -11.72 MHz. The signal straddles $$\pm f_s/2$$, which is not what you want. To center a 20 MHz wide signal at 20 MHz, you must sample at least $$2*(20+20/2)=60$$ MHz, or roughly twice your current sample rate. Thus you want to interpolate the signal to a higher sample rate first.

The other issue is that your signal is still complex. Maybe that is what you want, but typically if you convert to passband it is because you need a real signal - e.g., for D/A conversion. In that case you also need to take the real component of the signal after the complex upconversion.

If you do need a passband signal for D/A conversion, then you might want to interpolate by more than 2 to make your D/A reconstruction filter easier - but that is another topic entirely.

• I believe that for a baseband signal from $-f_m/2$ to $f_m/2$, the Nyquist frequency to avoid aliasing is just $f_s > f_m = 20\textrm{MHz}$, hence this sampling rate $30.72\textrm{MHz}$ should be a good one, shouldn't it? – AlexTP Dec 28 '18 at 9:10
• The 30.72 MHz sample rate is good for the original complex baseband signal. But the passband signal has been shifted to a center frequency of 20 MHz, and therefore no longer extends from $-f_m/2$ to $f_m/2$. As long as the signal remains complex, shifting it in frequency hasn't led to any loss of information, but we can't unambiguously represent at carrier frequency of 20 MHz with a sample rate of 30.72 MHz. – Ill-Conditioned Matrix Dec 28 '18 at 16:18
• ok then, misread the OP's question :) – AlexTP Dec 28 '18 at 16:49