# Tag Info

### What's the difference between frequency shift, frequency offset, phase offset, and phase noise?

To complement Dan's answer, this is the way I usually use these terms. Frequency shift: a change in the frequency of a bandpass signal. It can be intentional, as when downconverting a signal in the ...
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### Maximum cross-correlation coefficient value for time delay estimation

As your plot shows, the second form allows for the correlation peak to be negative. Now, what does a strong negative cross correlation mean? It means the signals are very similar, except one has a ...
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### Digital PLL loses lock every time mesage crosses zero

You are having trouble because that's not a Costas loop. A Costas loop uses demodulated data in some form to change the phase that's expected from the signal. You're just taking the I/Q ...
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### Actual Sample Rate slightly off?

If you calculate the error, 44102/44100 is only about 45 parts per million. That is well within operating tolerance of many crystal oscillators used in consumer equipment to generate audio sampling ...
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### Why is phase range between $-\pi$ and $+\pi$ (instead of $0$ and $2\pi$)?

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 ...
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### Why is phase range between $-\pi$ and $+\pi$ (instead of $0$ and $2\pi$)?

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 ...
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### Synchronizing 2 time series signals at slightly different sampling frequencies

If you are confident that the relationship is a ratio of integers, then resampling would be a fine approach. One would be matched to the other by upsampling by 1008 and then downsampling by 996 which ...
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### What's the difference between frequency shift, frequency offset, phase offset, and phase noise?

Frequency shift and frequency offset could reasonably refer to the same thing, but a shift suggests something that has moved (from one frequency to the next as would occur in a changing Doppler) while ...
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### Trouble with time-syncing two radio signals using cross-correlation

It will work when you take the 2nd gradient of the signals: ...
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### Loop bandwidth for symbol timing recovery

There is an optimum loop BW that maximizes the SNR, and this applies to both Symbol Timing Recovery as you inquire about as well as Carrier Recovery. The specific answer depends on the characteristics ...
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### Acceptable Carrier Frequency Offset for Specific BPSK system

Bottom line: Either implement a (simple) carrier recovery algorithm or use DBPSK instead of BPSK if you are ok with the 3 dB SNR penalty in performance. If you want to do synchronous detection of ...
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### Symbol Synchronization for GFSK/FSK signals in GNU Radio

The Symbol Synchronizer block is a PLL-based synchronizer that is trying to estimate the symbol clock period and symbol clock phase (aka timing offset) based on the samples coming in that represent ...
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### Why are preambles repeated in communication systems

In case of IEEE802.11a, that's Schmidl&Cox synchronization. I go into a few effects of having that in this answer; and as I say there, If in doubt, read the original Schmidl&Cox Paper Robust ...
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### Find out time offset between two substantially same audio tracks

Cross-correlation is definitely the answer. And it is basically a one-liner in any common DSP package (MATLAB, Python, Julia...). To make it more practical for your particular scenario, I would ...
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### What is the name of this FFT technique for carrier recovery?

You can find very similar implementations as part of a "squaring loop" for carrier recovery, and this would be the closest name related to the fundamental operation provided - which is not ...
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### Symbol Sync blocks in GNU Radio seem to use PID (well, PI) for their clock sync feedback loops. Why not IIR/FIR?

Keep in mind that we are talking about a clock synchronization loop, so you need to think of the behavior from a control-systems perspective. FIR Just discard that notion right out. There are good ...
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### Phase locking value / phase synchronization

If you have two numpy arrays of phase data theta1 and theta2 (in radians), you can calculate phase locking value in numpy without too much effort: ...
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### Band edge filter for raised cosine impulse

It looks like the filter you want is indeed $-ith(t)$. Here is some Octave code to get a visualization in the frequency domain: ...
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### How to find the time instant where my sent signal and received signal can synchronize?

This is usually addressed via looking for a known pattern in the data frame. The modulation scheme is not mentioned but when synchronisation is required, a Phase Locked Loop (PLL) is most commonly ...
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### FFT based symbol synchronization for digital demodulation

Symbol timing synchronization seems to be a complex topic although once you get some basic principles right, it all makes simple sense. The method you have referred to is known as Digital Filter and ...
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### OFDM synchronization using training symbols

Claim In OFDM receivers, special OFDM training symbols for which the data content is known, can be used to perform the synchronization process. Be a bit careful about that statement. There's ...
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### Frequency Hopping Spread Spectrum Synchronization Methods

This can be accomplished by changing the carrier frequency using a Numerically Controlled Oscillator (NCO) which maintains an accurate and continuous phase versus time trajectory via the phase ...
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### OFDM: How to do the carrier recovery of the quadrature(I/Q) demodulation

I can't find any way to make the carrier recovery, I don't think you can or should really talk "carrier recovery" in OFDM systems; after all, OFDM is a multi-carrier system. So, you'd need to recover ...
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### GNU Radio loop bandwidth normalization

I can only answer your second question: "How can the loop bandwidth in GNU Radio synchronization be configured as a percentage of the symbol rate?" The tracking loop in the symbol synchronizer block ...
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It seems like your error jumps to -$\pi$ and then to $\pi$ I think you need to unwrap your phase. Let me explain with an example Say that the output of atan2 block is $\pi - 0.001$ and then the ...