Roadmap to complex signals

[f-brinkmann]

Problem: We want to allow signals with complex time data

Required changes in audio classes:

• [x] TimeData: add complex argument in init and make it a class property
• [x] Signal.domain: check complex and chose FFT accordingly
• [x] Signal.freq: Call normalization according to complex property
• [x] FFT module: wrap fft and ifft and fft_frequencies in analogy to the real parts
• [x] Frequencies in complex signals will go from -fs/2 to fs/2
• [x] check arithmetic operations on audio class, with one complex and one real-valued signal.

Changes in plot module (good first issues)

• [x] Plot functions time domain: add parameter ??? to plot 'real', 'imag', or 'abs' values
• [x] Plot functions frequency domain: add parameter side to plot 'left' or 'right' sided spectrum
• [ ] Add plot interaction for both parameters

Add tests in dsp module (good first issues)

• [x] average
• [x] convolve
• [x] decibel
• [x] deconvolve
• [x] fractional_time_shift
• [x] phase
• [x] pad_zeros
• [x] regularized_spectrum_inversion
• [x] resample (depends on scipy implementation)
• [x] spectrogram
• [x] time_shift
• [x] time_window
• [x] filter classes

Throw errors in dsp module - we decided to implement energy, power, and rms for complex signals

• [x] energy
• [x] power
• [x] rms

Possibily change functionality

• [x] find_impulse_response_delay:
• [x] find_impulse_response_start: detect separately for real and imag and return earliest or use absolute value (test with gammatone filters and decide later, probably absolute value because this is the envelope)
• [x] group_delay (check because the estimation is FFT based)
• [x] normalize (some modes like rms not supported)
• [ ] smooth_fractional_octaves
• [x] update concatenate function (see comment in #452)

Open question (throw errors for now)

• [ ] linear_phase
• [ ] minimum_phase
• [ ] zero_phase

To discuss:

• arithmetic operation that casts a real to complex valued signal, with invalid ftt_norm. Cast to none or error?

To do:

• check docstrings for all above methods