# Bandwidth of a modulated signal in analog domain

If i am using QPSK modulation with data rate 4 Mbps with rolloff factor $$0.5$$, then the bandwidth will be symbol $$\rm rate\times (1 + rolloff\ factor)$$. So here it will be $$\rm 2\ MHz\times 1.5 = 3\ MHz$$

This is baseband data bandwidth.

So should I use analog filter of bandwidth $$\rm 3\ MHz$$ or should it be more? or should it be more than that?

## 1 Answer

The analog filter will be more than that such as to minimize further distortion to the passband. The analog filter bandwidth will depend on its purpose (Tx DAC reconstruction, Rx ADC and mixer anti-alias, interference rejection) while the fine passband filtering would be done by the pulse shaping filter in the Tx itself and the matched filter in the Rx, typically both implemented as digital filters.

• Yes i understand that but if i need to put a filter so that there is no loss of data is it enough if i consider the main lobe BW(i.e. 3 Mhz) for the above specifications? Jul 10, 2020 at 11:30
• "Main lobe" isn't a good description of pulse shaped data (that is typically used for the unfiltered waveform). I suggest adding a plot to your question showing your specific analog filter design, importantly both the amplitude AND phase response within your passband and then re-read my answer with that in mind. Typically the analog filter will NOT be so close to your passband because of the distortion that it will add to your signal, and such close filtering is done digitally. Jul 10, 2020 at 11:45
• What i meant was if my baseband data is 3 Mhz . can i use analog filter with any bandwidth more than 3 MHz? the whole idea is to have no distortion outside the bandwidth? so sould my analog filter be as close to 3 mhz as possible( assuming amplitude response is constant in this range) Jul 20, 2020 at 12:27
• @Susan Yes but be very careful to look at the phase response as well, and specifically any non-linearity in the phase within your passband. This will often cause much more distortion than a symmetric amplitude distortion. So you want the filter as tight as you reasonably can do without imparting distortion in your passband. Often it is easier and more effective to do the detailed filtering digitally and ultimately you want to have some requirements you are driving the filter design to. Analog filters can be more expensive and not as flexible in changing. Jul 20, 2020 at 12:35
• thanks. i got the complete picture now but if my bandwidth is more then noise floor also increases? does the analog filter bandwidth have any effect on the noise figure? Jul 20, 2020 at 12:43