6

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 ...


5

Wow, I'm honored by Matt L. doing what I'm often doing: Referring people to GNU Radio. The project actually has a list of recommended literature, but I don't know how well that'd fit you. It's probably still worth looking into. Then, regarding QPSK: Well, it's one of the basic constellations, and you'd probably be best off reading a textbook intro to ...


5

First, when you're talking angles, in DSP pretty much all angles are $\mod 2\pi$. So $2\pi \equiv 0$. Usually it's more convenient to keep angles on the interval $\left [-\pi, \pi \right )$, because we're usually most interested in angles around $0$. You don't have to do this, however -- if your problem at hand is easier to solve if your angle lies on $[-...


5

It is just a convention, but it is useful in some cases. For example, the phase of the DFT of a real discrete-time signal is odd only if the angles are expressed in the range $[-\pi, \pi)$. Sometimes you just have to adapt to the convention used by your tools -- for example, MATLAB functions like angle and atan2 return angles in $[-\pi, \pi)$. Note that the ...


4

First and foremost, I would recommend against over the air testing for this given the significant challenge in really being able to provide the same signal to each radio (since you have both temporal and spatial constraints that you cannot simultaneously meet). I would instead use one GNU radio as a transmitter (or any other repeatable high quality source) ...


3

Is this an entirely stupid idea? No, but you've just came to the conclusion that instead of sampling complex, with Nyquist rate being the bandwidth, you should do twice as many samples. That simply means you're not doing IQ sampling, but low-IF or direct-RF sampling. Mix the signal with a higher intermediate frequency and filter it in such a way that ...


3

If you are "observing" the source, this implies there is some sort of information you are looking to get out of it, whether it be the total background noise, interference levels etc. Do you find "value and use" in the RF signal's magnitude versus time? What about the RF signal's phase versus time? The IQ representation gives us both of ...


3

If the above is a good representation you should just try to infer when there is energy in the signal to align them. As it seems they start with nothing (Zero value). Then all needed is just to find where "Something" happens. This could be easily done with high resolution (Few samples). Regarding Cross Correlation, try to normalize both signal to have the ...


2

It will work when you take the 2nd gradient of the signals: import numpy as np from scipy import signal s0 = np.gradient(np.gradient(s0)) s1 = np.gradient(np.gradient(s1)) np.argmax(signal.correlate(s0, s1)) -> 525358 That corresponds to a shift of 1071 which is close to your expected 1069 Interestingly the minimum (most negative correlation) is close ...


2

This can be implemented, without needing to access the real and imaginary parts of $z$ individually, by writing $$\operatorname{Re}(z) + \operatorname{Im}(z) = \frac{(1 + i)(z^* - iz)}{2},$$ where $i$ is the imaginary unit and $z^*$ is complex conjugation. Factoring out a complex constant, $\xi = 1/2 + i/2$, turns this into a slightly tidier expression, $...


2

The high-frequency (RF) section of an SDR is all analog. Typically, the analog receiver downconverts the RF signal to an intermediate frequency that is within the Nyquist range of the ADC. As Stanley points out, you can also do bandpass sampling, though that is less common, in my experience.


2

If you postulate that receiever's clock is perfect, then you want to make the transmitter send symbols every $T_s \pm \varepsilon$ seconds, where $T_s$ is the symbol period according to the receiver. This is easily achieved by using a very high sampling rate in the transmitter. Let's assume $T_s=1$ and you need a deviation of $\pm 0.01$. This deviation ...


1

No you cannot change the carrier frequency of your local oscillator instantaneously. The RF local oscillator will be in a Phase-Lock Loop (PLL) circuit to a low frequency reference (to provide frequency stability and tunability) and the switching time can be approximated from the loop bandwidth of that PLL when operating within the linear range of the PLL (...


1

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 ...


1

I have thought about some points which could help find the answer: 1- I think there might be something related to $\operatorname{arctan}(x)$ which is continuous in $(-\pi/2 \ \ \pi/2 )$ but I am not sure how. 2- We almost always work with phase DIFFERENCE rather than the absolute phase itself. Phase difference could be both positive and negative. So, it ...


1

SDR is not applying a lowpass (baseband) sampling on its RF input, instead it effectively employs a band-pass signal sampling. According to Shannon-Nyquist baseband sampling criteria, the bandwidth of the signal to be sampled should be less than half the sampling frequency. That's what you are talking about. However for narrowband modulated signals bandbass ...


1

RF direct sampling architecture? Will there be DC offset? No, since the center of your signal doesn't end up on DC, so there's no DC offset. If not, then is it okay not to insert a DC null? yes. However, you might want to use quadrature mixers for the other end, so you might not want to do that. Also note that instead of direct sampling, superhet / low-IF ...


1

The sensible way here is to realize that each complex sample has a magnitude $|z|=\left\lvert \Re z + j \Im z\right\rvert = \sqrt{\left(\Re z\right)^2+\left(\Im z\right)^2}$. In your case, the maximum non-clipping amplitude is $2^{15}$ (the maximum-power samples are on a circle around the origin). Therefore, you'd calculate the magnitude of a sample, and ...


1

When working with such an RF signal, numerically transformed to a stochastic timeseries, to which extent can I consider the signal to be stationary? That depends on your signal model. We can't tell you that – but for example, in time-slotted system, obviously the received signal can't be stationary – its variance (which is basically its power) depends on ...


1

For those given specs, without additional hardware (upconverters) or modifications to the SDR circuit, it's not possible to detect AM or FM (88-108 MHz) range of frequencies. As you might have also seen, there are frequency range extenders (especially on the low frequency range) available as kits. Also, the sampling rate determines the maximum bandwidth of ...


1

After some thinking, I would could this a cartesian sum. It borrows from the notion of cartesian sum of two sets, here $\mathbb{R}$ (real part) and $i\mathbb{R}$ (imaginary part): if $x\in X$ and $y\in Y$, the sum is the set of $x+y$. This question initially sounded odd to me, until I saw the recent Matlab code contest at MatlabCentral on this issue: ...


1

There's no specific term, as far as I know, but it's a very common operation with quadrature mixing. It's the result of taking the real part of an analytic signal. You have a complex baseband signal $x(t)$, you modulate it with a complex carrier resulting in an analytic band pass signal, and then you take the real part to obtain the real-valued band pass ...


1

this is John BG 1.- GFSK is not same as single tone According to the CC1101 specs you refer to, the C1101 uses GFSK. GFSK varies the varrier frequency, therefore the spectrum cannot be a delta. Call it a 'shifting delta' but it cannot be same spectrum as just a tone. 2.- you want the carrier frequency to vary ISM are crowded bands, the carrier has ...


1

In terms of visualization, I think you may be confusing phase shift and delay. In the case of a single-frequency complex exponential , a plot of the imaginary part appears to be delayed from the real part by T/4, where T = 1/f. However, if you have a complex waveform which is the sum of two or more complex exponentials at different frequencies, the imaginary ...


1

Let's start from the beginning. Given a real signal to a quadrature circuit, two components are generated, I, the real component, and Q, the imaginary component, which is the same as I, only it has a 90º phase shift. So, we have I and Q, which are the same signal but 90º shifted from each other. I understand this, it's simple. What you are talking about is ...


1

You are mistaken in your 2nd paragraph. The I and Q components are not always identical with a 90 degree phase offset. Instead, they are usually generated by multiplying some real or complex signal with two sinusoids that offset by 90 degrees. Only if the input is a constant (e.g. carries zero information) does the IQ output fit your description. A ...


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