6
votes
Accepted
What wavelength do we use when calculating the array manifold vector when transmitting LFM waveforms?
As with many questions like these...it depends. We won't concentrate on LFM waveforms, the following is true for any waveform transmitted.
Virtually all of the introductory material to steering a ...
- 2,936
6
votes
Accepted
Why does frequency sweeping double the frequency?
You're calculating the parameters into the sinusoid incorrectly. By simply plugging in a linear frequency ramp into the sinusoid, you do not get the appropriate quadratic phase that is needed to ...
- 2,936
5
votes
Accepted
Circular Convolution and FFT of power 2
Circular convolution is just linear convolution aliased by DFT length $n$. The length of linear convolution of $a$ and $b$ will be $2n-1$. So take $FFTs$ of $a$ and $b$ , padding each of them to ...
- 2,303
5
votes
Accepted
Complex nature of chirped signal
Depending on the context, the use of the complex form could be for mathematical convenience or for a no-kidding need for both real and imaginary parts.
When you factor the expression, you get
$$u(t) = ...
- 2,936
4
votes
How to implement an RF Mixer for chirp signal in python?
What you're seeing is correct. When mixing two chirps as you're doing, you will get a doubling of the frequency.
Consider two chirps with a bandwidth $B$ and pulse length $\tau$. We'll use the complex ...
- 2,936
3
votes
Chirp zero crossings
Assuming that T is the length of the chirp, a linear chirp is given by
$$x(t) = \sin\left[2\pi \cdot \left( t\cdot f_1+ \frac{t^2}{2T}(f_2-f_1)\right)\right] $$
A zero crossing occurs when the phase ...
- 48.2k
3
votes
Accepted
Confused with filtering linear chirp signal using band-pass filter
You are seeing the difference between "wide band FM" and "narrow band FM" in your modulated waveform. Observe your modulation index for each case and then review the sideband levels versus mod index ...
- 55k
3
votes
Does chirp have constant magnitude frequency response?
The book is not wrong, but it does present the concepts on LFM in a clunky manner and can be misleading. The book presents the analytical expression for the LFM spectrum, which is an approximation. It ...
- 2,936
3
votes
Accepted
Wrong matched filter sidelobe level for linear chirp despite (invalid ?) energy normalization
You used the wrong logarithm function. The one in your code is the natural logarithm, not base-10 as intended. The following code produces what is expected:
...
- 2,936
2
votes
Equation of wave in Linear frequency modulation?
If you have a signal
$$g(t)=\cos(2\pi \hat{f}(t)t)\tag{1}$$
then the function $\hat{f}(t)$ is not the instantaneous frequency of $g(t)$ (unless $\hat{f}(t)$ is constant).
If you want an ...
- 92.5k
2
votes
Accepted
Designing a Chirp in the Frequency Domain
Instead of phase delay $td(f)$, use group delay $\tau(f)$:
$$\tau(f) = -\frac{d}{d\omega}\phi(f),\tag{1}$$
calculated as the negative of the derivative of the phase $\phi(f)$ with respect to the ...
- 13.7k
2
votes
Radar Imaging Method
You still only get one range and one velocity line per radar observation.
You can, however, "scan" a region (that's why airport towers and ships have these rotating antennas) and get another axis ...
- 32.5k
2
votes
Complex nature of chirped signal
$i$ is the symbol for $\sqrt{-1}$
There is a very important formula called Euler's Equation.
$$ e^{i\theta}=\cos(\theta) + i \sin(\theta) = (e^i)^\theta$$
"$ e^i $" is a point on the unit ...
- 7,600
2
votes
Accepted
2
votes
Accepted
Do PSK/QAM modulators (e.g. 4G/5G) fundamentally use more energy per packet than CSS modulators (e.g. LoRa)?
Yes PSK/QAM modulators fundamentally use more energy than LoRa chirp spread spectrum (specifically it is the transmit power required for transceivers using PSK/QAM modulators in order to close the ...
- 55k
2
votes
Chirp pulse train FFT
The spectrum of a single chirps is fairly straight forward. It should roughly be 1 between the start end and end frequency of the chirp and 0 everywhere else. On top of that there are some wiggle ...
- 48.2k
2
votes
Can you please help me in generating a chirp signal in GNU radio by creating a module of your own?
Your code works correctly. I have validated it against MATLAB's implementation and the results are the same down to numerical errors. You can see the results in the following figure.
The only ...
- 1,484
1
vote
Chirped vs. unchirped pulse and Fourier Transform intuition
I wouldn't say that your intuition is wrong, but you can't just look at the oscillations in a time domain signal and try to deduce from it the signal's frequency content. Think of an impulse or a step:...
- 92.5k
1
vote
Accepted
Add chirp to time domain pulse
Couple points that may be helpful:
The command plt.plot(I) is only plotting the real component.
The command phase = freq**0 ...
- 55k
1
vote
I am working on chirp signal generation using DDS in verilog . To generate the chirp signal do I need to change the limit of the 8 bit counter?
The step input should control the rate of the counter, which would then control the rate at which the sine table is traversed and therefore the frequency of the output. Therefore to implement a chirp,...
- 55k
1
vote
Accepted
Can someone help me with chirp signal generation using direct digital synthesizer(DDS) in verilog?
What you are creating is typically called a "Numerically Controlled Oscillator" or NCO, and when integrated with a D/A Converter would form a Direct Digital Synthesizer (DDS), but these are ...
- 55k
1
vote
Accepted
guidance for designing a pilot signal
An ideal pilot signal for channel estimation (without any apriori further knowledge of the channel) would transmit power uniformly across the channel and be easy to replicate in the receiver for ...
- 55k
1
vote
How to implement an RF Mixer for chirp signal in python?
Wouldn't mixing them give you a sum and difference frequency and you have to lowpass filter to get the difference frequency only? Also your chirps are the same frequency, just out of phase? So the ...
- 16k
1
vote
Detect playback position in swept sine sweep
Attached Matlab sample code to apply an matched filter to a sine sweep for finding the playback position (the playback position estimate can be derived as the position of the peak in the matched ...
- 31
1
vote
Radar SNR for a LFM Waveform
With pulse compression, the SNR improves by a factor equal to the time-bandwidth product (synonymous with pulse compression gain).
In the equation you listed, $\tau$ can be interpreted as the ...
- 2,232
1
vote
Accepted
Exponential Chirp
The Python implementation looks almost exactly like the definitions in Wikipedia. One will need to define functions in order to make it work, like this:
...
- 26
1
vote
Doppler Shifting A Chirp Signal
Rather than re-sampling, this is best accomplished by re-creating the signal after it is Doppler shifted. This allows any arbitrary waveform to have Doppler imparted on it. See Mark A. Richards, &...
1
vote
Accepted
Doppler Shifting A Chirp Signal
You need to resample the signal to simulate the Doppler induced dilation. The resampling factor is I=Td/Ts
where
Td = Duration ...
- 477
1
vote
Accepted
Cross-correlation peaks in acoustic multi-path conditions
I assume by "shift" you mean "shift in time".
No, the first correlation peak should not be shifted in time, you should just get multiple peaks, assuming the time difference of arrival is not much ...
- 12.2k
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