# Post-processing
ElectroacPy provides some tools for crossover-network / filter design. These are considered "post-processing" as they are applied on computation results. It might not be the best term, but we'll go with it for now.


## `.crossover[]`
Crossovers/filters are initialized through the `.filter_network()` method. Input parameters are:

- `name`, network reference,
- `ref2bem`, which BEM elements should be filtered,
- `ref2study`, which study (or list of study) should receive the filter network.

Available filters are:

- lowpass and highpass, both under their "analog" form and as biquads,
- low-shelf, high-shelf,
- peaking eq, 
- delay, gain and phase-flip,
- user-defined transfer functions.

In the code below, we define a crossover network using the available biquads:
```python
from electroacPy import gtb
import electroacPy as ep
import numpy as np

#%% load data
system = ep.load("06_acoustic_radiation_refined")

#%% LF filter
system.filter_network("LF_xover", ref2bem=[1, 2], ref2study="free-field")
system.filter_addLowPassBQ("LF_xover", "lf1", 300, 0.5)

#%% MF Filter
system.filter_network("MF_xover", ref2bem=3, ref2study="free-field")
system.filter_addHighPassBQ("MF_xover", "hp1", 300, 0.5)
system.filter_addLowPassBQ("MF_xover", "lp1", 3500, 0.5)
system.filter_addGain("MF_xover", "db", -2)
system.filter_addPhaseFlip("MF_xover", "pi")

#%% HF Filter
system.filter_network("HF_xover", ref2bem=4, ref2study="free-field")
system.filter_addHighPassBQ("HF_xover", "hp1", 3500, 0.5, dBGain=-4)
```

Networks will automatically update the frequency response of previously computed studies. The `.plot_results()` method will display updated data. If you want to have a better look at each network response, you can either use the `.plot_xovers()` method, or extract the transfer function with `.crossover["reference"].h` --- {numref}`xover` is made using the following code:

```python
#%% Transfer functions
H_lf = system.crossover["LF_xover"].h
H_mf = system.crossover["MF_xover"].h
H_hf = system.crossover["HF_xover"].h

gtb.plot.FRF(system.frequency, (H_lf, H_mf, H_hf, H_lf+H_mf+H_hf), 
             legend=("LF", "MF", "HF", "total"), transformation="dB",
             ylim=(-30, 10), xlim=(10, 10000), figsize=(6, 3),
             xticks=(10, 20, 50, 
                     100, 200, 500, 
                     1000, 2000, 5000, 10000),
             yticks=np.arange(-30, 12, 6))

```

```{figure} ./postP_images/crossovers_b.svg
        :name: xover

Crossover frequency-response.
```

It is also possible to extract and plot each individual pressure response using `.get_pMic()`, available through any loudspeaker system object. Here, we separate each acoustic radiator and look at the multiple contributions in {numref}`xover-pressure`.

```python
# get pressure
p_lf   = system.get_pMic("free-field", "polar_hor", radiatingElement=1)
p_port = system.get_pMic("free-field", "polar_hor", radiatingElement=2)
p_mf   = system.get_pMic("free-field", "polar_hor", radiatingElement=3)
p_hf   = system.get_pMic("free-field", "polar_hor", radiatingElement=4)
p_tot  = system.get_pMic("free-field", "polar_hor")

# plot pressure response
gtb.plot.FRF(system.frequency, (p_lf[:, 73//2], 
                                p_port[:, 73//2],
                                p_mf[:, 73//2],
                                p_hf[:, 73//2],
                                p_tot[:, 73//2]), 
             ylabel="SPL [dB]",
             legend=("woofer", "port", "midrange", "tweeter", 
                     "total contribution"),
             xlim=(10, 10e3), ylim=(35, 80))
```

```{figure} ./postP_images/pressure_xover_b.svg
        :name: xover-pressure

Filtered loudspeaker response.
```

It is important to note that electroacPy's crossover tools are considered as digital filters: interactions between speaker and supposed electrical components are not taken into account. In order to have a better understanding of the electrical behavior with passive components, it is either possible to use the **circuitSolver** class, or to export results to an external software for crossover design. 

## Export simulation data
For now, it is only possible to export directivity and impedance data. The following code extracts pressure and impedance with `.export_directivity()` and `.export_impedance()`. Results are then imported into VituixCAD as shown in {numref}`vituixcad-import`. In the import window, you can notice that the "Minimum phase" box is checked: this helps reducing the comb-filtering coming from VituixCAD re-calculation of radiated pressure. Keep in mind that the overall radiation will be slightly off; you can un-check this box if you want a better estimation (although "noisier").

The export syntax are:
```python
# directivity
system.export_directivity(folder_path,      # path to export folder (mkdir if doesn't exists)
                          file_name,        # file prefix (angles are added to it)
                          study,            # study to export
                          evaluation,       # evaluation setup to export
                          radiatingElement, # radiating elements to export, optional
                          bypass_xover,     # if crossovers need to be bypassed, optional
                          frd)              # if True, uses *.frd extension, optional

# impedance
system.export_impedance(folder_path, # path to export folder (mkdir if doesn't exists)
                        file_name,   # file name
                        objName,     # driver object or enclosure object to export
                        zma)         # if True, uses *.zma extension, optional
```

In our case:

```python
# export woofer data 

system.export_directivity("export/woofer", 
                           "polar_hor", "free-field", "polar_hor", 
                           radiatingElement=[1, 2], bypass_xover=True)
system.export_impedance("export_impedance", "ported_LF", "ported_LF")

# export midrange
system.export_directivity("export/midrange", 
                          "polar_hor", "free-field", "polar_hor", 
                          radiatingElement=3, bypass_xover=True)
system.export_impedance("export_impedance", "sealed_MF", "sealed_MF")

# export tweeter
system.export_directivity("export/tweeter", 
                           "polar_hor", "free-field", "polar_hor", 
                           radiatingElement=4, bypass_xover=True)
system.export_impedance("export_impedance", "TW29", "TW29")
```

```{figure} ./postP_images/vituixcad_parameter_import.png
        :name: vituixcad-import

Importing woofer simulation in VituixCAD. Because the directivity was estimated at 2 meters, a 6dB scaling is used to normalize it relative to 1 meter.
```

```{figure} ./postP_images/vituixcad_woofer_b.png
        :name: vituixcad-woofer
Frequency response, directivity and impedance plot without crossovers.
```

```{figure} ./postP_images/vituixcad_network_b.png
        :name: vituixcad-network
Frequency response, directivity and impedance plot of system with crossovers.
```

If you'd rather use Xsim for your design, it is possible to add the `frd=True` and `zma=True` to the directivity and impedance export functions. By doing that, `.export_directivity()` and `.export_impedance()` use`*.frd` and `*.zma` extensions instead of `*.txt`.

```python
# directivity export
system.export_directivity("export/woofer_FRD", 
                           "polar_hor", "free-field", "polar_hor", 
                           radiatingElement=[1, 2], bypass_xover=True, frd=True)

# impedance export
system.export_impedance("export_impedance_ZMA", "ported_LF", "ported_LF", zma=True)

```

```{figure} ./postP_images/xsim_network.png
        :name: xsim-network
        :width: 20cm
        
Crossover design with Xsim4.
```


As you'll see in section **{ref}`Application example <monitorCrossover>`**, it is possible re-create the above crossover using electroacPy's own Modified Nodal Analysis (MNA) tool: **circuitSolver**.