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In my assignment I am provided with a recording of a radio signal that was supposedly done in the AM spectrum with a USRP, and I am told to process it in various ways with GNURadio. However, the assignment makes a statement about the recorded signal that I have slight difficulty understanding.

The assignment says that the signal was recorded with the USRP set to 710 kHz, yet it also says that the recording was sampled at 256 kHz, and that the 0 kHz component of the recording actually corresponds to 710 kHz in the original signal.

My understanding is that the only way for this to be the case is that the signal was recorded with a frequency well above 710 kHz, then the frequencies were translated so that the 710 kHz component was shifted to 0 kHz, and finally sampled at 256 kHz. Is my understanding correct?

In relation to that, what does it mean for a USRP to be set to a particular frequency, if the recorded signal seems to contain frequencies several tens of kHz above and below that frequency?

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  • $\begingroup$ Your understanding is generally right. When you say that the receiver is "set" to a particular frequency $f_c$, that normally means that $f_c$ would appear in the center of the spectrum (that is, at DC). Exactly how it got there can vary; sometimes an analog tuning step is involved, sometimes the signal is just sampled at a much higher rate and the tuning/decimation is done digitally. $\endgroup$
    – Jason R
    Sep 2, 2021 at 16:08
  • $\begingroup$ @JasonR Thanks. I'd give you an upvote, but I can't do it yet. $\endgroup$
    – Cosinux
    Sep 2, 2021 at 17:51
  • $\begingroup$ There's no USRP that actually supports a 256 kHz sampling rate without complaining (and rightfully so). $\endgroup$ Sep 2, 2021 at 22:29

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The USRP is taking a frequency band of width 256 kHz centered on 710 kHz, and downconverting it to baseband. Whatever is in that band will appear in the USRP output.

To be specific, the band that the USRP is capturing goes from 710-128 = 582 to 710+128 = 838 kHz.

Keep in mind that the band is 256 kHz wide (that is, equal to the sampling rate) because the USRP actually performs complex sampling.

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  • $\begingroup$ Is that last part the reason why the signal seems to be sampled at twice the frequency (AM sidebands are 10 kHz wide and the voice is slowed down by a factor of two when I demodulate it)? $\endgroup$
    – Cosinux
    Sep 2, 2021 at 17:50
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    $\begingroup$ Could be -- depends on how you process the signal. One easy thing to do with AM is to calculate the magnitude ("merging" two samples into one) and then doing envelope detection. $\endgroup$
    – MBaz
    Sep 2, 2021 at 18:39

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