# How to calculate the upsampling rate (sample per symbol) for a recorded raw IQ .wav file?

I am not familiar with raw IQ wave files. For tetra-1 signal, the bit rate is $$36$$ k bps (or $$18$$ k as the symbol rate). If the Fs saved in the .wav file is $$48000$$ Hz, what should be the SPS (sample per symbol)? Remember that if SPS is 4 for QPSK, then both I&Q components need to be upsampled by $$4$$. In this case, should it be calculated as $$(48000/2)/18000$$?

• Is this a homework problem?
– MBaz
Nov 20, 2020 at 14:18
• It is a general question. If you are using GNU radio USRP to record the raw IQ data, you will need the upsampling rate (or sps) to process the recorded signal. Nov 20, 2020 at 18:12

It is a unit conversion. You have the sampling rate given, $$F_s$$, and it has units of $$\frac{\text{samples}}{\text{second}}$$. You also have the symbol rate, $$F_{sym}$$, and it has units of $$\frac{\text{symbols}}{\text{second}}$$. You are trying to figure out what is the $$\frac{\text{samples}}{\text{symbol}}$$ so it is this division:
\begin{align} \frac{\text{samples}}{\text{symbol}} &= \frac{ F_s }{ F_{sym} } \\ &= \frac{ \big(\frac{\text{samples}}{\text{second}} \big)}{ \big(\frac{\text{symbols}}{\text{second}} \big) } \\ &= \frac{\text{samples}}{\text{symbol}} \checkmark \end{align}