# 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

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.
• 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