# QPSK Modulation towards DAC

Modern DACs are able to accept 2 digital values (representing I and Q), multiply them internally by a Sine and Cosine waveforms and combining the result to form the output signal. When dealing with QPSK modulation textbooks show it like that:

To me this signal looks like it will have incredibly wide spectrum (because of the discontinuities). So what am I missing ? If we want to send a sequence of the symbols: "11" "00" "01" "10" do we really send to the DAC corresponding Phasor Diagram I and Q values and end up with a signal looking like this ?

• Usually, the quadrature encoded signal is fed to a bandpass and then to a PA. Aug 11, 2023 at 23:22
• When you say "bandpass" filter. Is it before the DAC ? Aug 12, 2023 at 11:52
• It can be either. Before the DAQ, it will be a digital filter, after, it will be analog components. Aug 12, 2023 at 12:20

Your missing piece of the puzzle is pulse shaping:

https://en.wikipedia.org/wiki/Pulse_shaping

Pulse shaping restricts the bandwidth of the baseband data, but usually at the expense of intersymbol interference (ISI). There are classes of filters that have no ISI:

https://en.wikipedia.org/wiki/Intersymbol_interference

for example, the ideal raised cosine filter:

https://en.wikipedia.org/wiki/Raised-cosine_filter

• So...if there's a digital filter between the QPSK constellation symbol mapping logic and the DAC - does this means that if we put a logic analyzer at the DAC's I/Q inputs we will never see the QPSK values directly (1,1) (1,-1),(-1,-1),(-1,1) ? Instead, we'll see some filtered version of them that yields a band constrained spectrum ? Aug 12, 2023 at 9:58
• @shaiko that depends on the pulse shaping filter chosen. Often, you design them to indeed not be free of inter-symbol-interference (so you do not ever see the pure constellation points at the DAC), to make it easier at the receiver to apply the matched filter and only after that be ISI-free. Aug 12, 2023 at 10:03

Modern DACs are able to accept 2 digital values (representing I and Q), multiply them internally by a Sine and Cosine waveforms and combining the result to form the output signal.

To avoid a terminology confusion, it might be safe to talk about DAC branches. For example, with proposed ultrafast optical WDM technology, DACs (and ADCs) are integrated with the DSP to avoid the data interface bottleneck. Inside the TX-side converter, we have a number of DACs and analog multiplexers.

When dealing with QPSK modulation textbooks show it like that...

When dealing with "modern DACs", it makes sense to learn from acclaimed textbooks. Introduction to Digital Communications by Prof. Wayne Stark explains QPSK (M-ary PSK with M=4, Quaternary PSK) signaling and spectra in chapter 6 Modulation Techniques.