I've thinking about this for some time now and I was wondering why do we need to increase smapling rate in the transmitter? I will explain a bit more.

From the point of view of a software-defined radio, you convert bits to symbols (let's suppose I'm doing QPSK) and after pulse shaping with 4 samples per symbol, (which I know it also increase sampling frequency by 4 since it's another interpolation after all) I've seen it's quite common to do some multi-stage interpolation (or a single-stage interpolation, it doesn't matter) to increase the sampling frequency even more. Why is this beneficial? I mean, I can only think of one reason and that'd be because you have more samples per symbol, but if after you're upconverting to passband and send it to the channel, what was that for?

Then, when you get the signal at the receiver, you decimate it to decrease sampling frequency. This one, I think I understand it better, after doing synchronization (for example in symbol sync you might need more than 1 sample per symbol), you want to decrease the sampling frequency so you don't have to deal with so many samples and is less computational costly.

So my question is, why doing interpolation in the transmitter?

Correct me if I said something wrong, please. Thank you.


1 Answer 1


Three reasons to increasing the sampling rate further are

1) To relax the requirements of the post D/A conversion filtering for image rejection.

2) Increase signal SNR by spreading quantization noise for a fixed number of DAC bits across a wider frequency range.

3) Minimize passband droop in the D/A reconstruction.

Reason 1 is the most dominant one in my opinion. The complexity and cost of a low pass filter (either digital or analog, but in this case it is the analog filter) is driven by the width of the transition band. And the reason for filtering the images is usually spectral containment as limited by regulatory requirements (and given the value of spectrum this is a HUGE reason). Reason 2 is a solid consideration if your DAC is limited by the number of bits but has wider analog BW and sufficient Spurious-Free-Dynamic Range (SFDR) to allow for overssampling benefits. Reason 3 is of least impact but I mention it as it is indeed a benefit. To address reason 3 we can often optionally simply incorporate an inverse Sinc filter digitally to compensate for the passband droop from the D/A (and this can be quite simple- see how to make CIC compensation filter).

Note interpolating DAC architectures do this for you- increase the sampling rate prior to conversion to simplify the analog anti-imaging filter requirements and give you more bits effectively since the same total quantization noise power is spread across a wider frequency range, some of which is then filtered out by the anti-imaging filter.

These graphic by Walt Kester of Analog Devices in their App Note MT-017 (https://www.analog.com/media/cn/training-seminars/tutorials/MT-017.pdf) shows this very well (Thanks Walt!):
enter image description here

enter image description here

To add, there is no benefit to the performance (sideband rejection) of the pulse shaping filter by increasing the sampling rate. The pulse shaping filters rejection is completely driven by how many symbols it spans. Two samples per symbol are all that is needed. Having more samples per symbol in pulse shaping does however simplify subsequent digital filtering if a post shaping interpolator is used- but this is exactly the same benefit described above for simplifying the analog anti-imaging filter, for the same reason.

  • 3
    $\begingroup$ I'd add (and this really isn't enough to warrant an answer of my own) that often, you also have systems that simply have specific sample rate restrictions – for example, it's quite common that SDR transmitters simply can't be used with arbitrarily low sampling rates, or with sampling rates that aren't a divisor of some fixed reference rate and such. Or, you need to combine your digital baseband signal in some multiplexing scheme, so your sampling rate needs to match that of the other sources. $\endgroup$ Nov 15, 2019 at 17:10
  • $\begingroup$ Good one @MarcusMueller $\endgroup$ Nov 15, 2019 at 19:46

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