Thanks for your feedback @tupui . Complex chirp uses both complex and real part of the signal(I and Q). If anyone wants to obtain more bandwidth while maintaining the same sample rate, this will be very helpful. From Nyquist theorem, bandwidth is limited to F_s/2. However, if we use the complex part of the signal as well, bandwidth will be limited to F_s.

I'll add the missing tests.

Another thing about complex chirp is that it's possible to sweep from negative frequency to positive frequency or otherwise.

It would be good to have a reference to the definition of a complex chirp, as well as give some idea of applications (in electronic and electrical engineering I think at least radar, power systems, and communication).

I'd expect the function to be something like the below, which has the property that the real part of the output when complex_chirp=True is equal to the output when complex_chirp=False.

I also don't have a reference to support this, though.

def chirp(t, f0, t1, f1, method='linear', phi=0, vertex_zero=True, *, complex_chirp=False):
    phase = _chirp_phase(t, f0, t1, f1, method, vertex_zero)
    phi *= pi / 180
    if complex_chirp:
        return exp(1j * (phase + phi)) # exp already imported in _waveforms.py
    else:
        return cos(phase + phi)

There's no need to limit it to just linear and quadratic - you just can't get a sign change in frequency with a logarithmic sweep. I'm not familiar with hyperbolic sweep, but

If chirp were changed like this, sweep_poly should probably be changed too, in much the same way. I don't think _chirp_phase or _sweep_poly_phase need to be changed at all.

It would be good to have a reference to the definition of a complex chirp, as well as give some idea of applications (in electronic and electrical engineering I think at least radar, power systems, and communication).

Good point, the only reference I could find for complex chirp waveform is the Matlab user manual. I think we shouldn't limit this specifically to complex chirp. My change is adding complex baseband (sort of) support to the chirp waveform. There is a good post about this at DSP StackExchange link. Proakis's digital communications book might be a good reference for this.

Please let me know what I can do for this PR to be merged.

PS. Once again, sorry for the delay. I finally had time to look at this.

Thanks,
A.

The STFT plot of a complex chirp using scipy.signal.ShortTimeFFT can be found here. Perhaps it would make sense to put an adapted version into the docstring. I think it is pretty self-explanatory.

Note that creating arbitrary chirps is straightforward, if you remember that the instantaneous frequency is derivative of the phase, e.g.,

n, T = 1000, 1e-3  # number of samples and sampling interval
t = np.arange(n)*T  # time stamps
f_i = 5*t +10  # arbitrary function for instantaneous frequency f_i(t)
phi = np.cumsum(f_i)*T  # numeric integration
z = np.exp(2j*np.pi*phi)  # sinusoid with instantaneous frequency f_i(t)

(I did not investigate the given code)

Thanks for your comment @DietBru. The document you shared generates the chirp waveform from scratch. Therefore, it might not be too relevant to our case here but it's helpful to compare the approach.

Regarding the documentation, I can add the FFT output of complex chirp, similar to Matlab's example. Does it sound reasonable?

Any chirp will do. 😃 But why use an FFT if there's a shiny new STFT?
My motivation to write down the derivation in the comment was to hint that the docstring could use some love. I think adding the explicit formulas of the chirp (e.g., $x(t)=\cos(\phi(t)+\phi_0), f_i(t) = \phi'(t)/(2\pi)$, ... ) would add a lot more clarity. Also the Python code could be a bit more expressive, e.g.:

 phase = _chirp_phase(t, f0, t1, f1, method, vertex_zero) + np.deg2rad(phi)
 return np.exp(1j*phase) if complex else np.cos(phase)

Oh, it makes more sense now 😅. Let me add those details to the docstring. Thanks for the feedback!

Well, I realized something strange with the new spectrogram function. Maybe this is not a place to discuss but I will create a separate pull request to fix it if needed. It doesn't support complex numbers. Am I missing something? @DietBru do you have an idea?

TypeError: x must be a real sequence

Well, I realized something strange with the new spectrogram function. Maybe this is not a place to discuss but I will create a separate pull request to fix it if needed. It doesn't support complex numbers. Am I missing something? @DietBru do you have an idea?

TypeError: x must be a real sequence

Nice to see the new functionality get some use. fft_mode='onesided' does not work for complex signals. Use fft_mode='centered' instead. Addressed in #20010

Thanks for the suggestion! I finished the documentation part and other things. Let me know if something missing.

@anilgurses it's probably time to put this to the mailing list now

In the rendered documentation, I noticed four unwanted blocks with gray highlighting, which is caused of blocks being indented too far, e.g.:

This highlighting appeared due to the updating of the sphinx theme. If you want, you can remove one space from the indentation from those four blocks.

Is there any update on this? It's almost 2 years since my commit :) If the indentation in the document is the problem, I can easily fix it. I believe indentation helps highlight the description of the point.

The main point is that your addition is hard to understand, as commented here.
Concerning the indentation: It is helpful if the documentation layout is consistent across all functions.

Gentle ping to @anilgurses : Do you still have interest in finishing this PR? If not, that is fine as well. I would be happy to take up the remaining work.

Yes, I am still interested. I was busy with other things. I will try to finish it this week.

I just pushed some changes, which:

• Improved signal.chirp() docstr—rendered version can be found here
• Simplified signal.chirp() code
• Used xp_assert_allclose() in _waveforms.py
• Manually rebased onto main to resolve conflicts

I hope it also addresses your change request, @j-bowhay, @tupui

PS: The test failures seem unrelated.

Thanks for the feedback, @j-bowhay. On this subject matter is not a lot to know—just that any signal can be represented by real-valued amplitude $a(t)$ and a real-valued phase $ϕ(t)$, i.e., $z(t) = a(t)\ \exp\big(j 2 π ϕ (t)\big)$ (with instantaneous frequency $f_i(t)=dϕ/dt$). A great opportunity to deepen the knowledge is to review PR #20097 😁

Also, thank you @anilgurses for your contribution! I squashed the commits again, to be able to add you as author.
Will merge after the tests complete.

Thanks for your help @DietBru!