# Create a custom spectral modelΒΆ

This use case illustrates how the User can define his own density spectral function from parametric models. The library allows it thanks to the object *UserDefinedSpectralModel* defined from:

a frequency grid with step , stored in the object

*RegularGrid*,a collection of hermitian matrices stored in the object

*HermitianMatrixCollection*, which are the images of each point of the frequency grid through the density spectral function.

The library builds a constant piecewise function on , where the intervals where the density spectral function is constant are centered on the points of the frequency grid, of length . Then, it is possible to evaluate the spectral density function for a given frequency thanks to the method *computeSpectralDensity*: if the frequency is not inside the interval , an exception is thrown. Otherwise, it returns the hermitian matrix of the subinterval
of that contains the given frequency.

In the following script, we illustrate how to create a modified low pass model of dimension with exponential decrease defined by: where

Frequency value should be positive,

for , the spectral density function is constant: ,

for , the spectral density function is equal to .

The frequency grid is with Hz. The figure draws the spectral density.

```
[1]:
```

```
from __future__ import print_function
import openturns as ot
import math as m
```

```
[2]:
```

```
# Create the frequency grid:
fmin = 0.1
df = 0.5
N = int((10.0 - fmin)/ df)
fgrid = ot.RegularGrid(fmin, df, N)
```

```
[3]:
```

```
# Define the spectral function:
def s(f):
if(f <= 5.0):
return 1.0
else:
x = f - 5.0
return m.exp(-2.0 * x * x)
```

```
[4]:
```

```
# Create the collection of HermitianMatrix:
coll = ot.HermitianMatrixCollection()
for k in range(N):
frequency = fgrid.getValue(k)
matrix = ot.HermitianMatrix(1)
matrix[0, 0] = s(frequency)
coll.add(matrix)
```

```
[5]:
```

```
# Create the spectral model:
spectralModel = ot.UserDefinedSpectralModel(fgrid, coll)
# Get the spectral density function computed at first frequency values
firstFrequency = fgrid.getStart()
frequencyStep = fgrid.getStep()
firstHermitian = spectralModel(firstFrequency)
# Get the spectral function at frequency + 0.3 * frequencyStep
spectralModel(frequency + 0.3 * frequencyStep)
```

```
[5]:
```

[[ (2.50622e-15,0) ]]

```
[6]:
```

```
# Draw the spectral density
# Create the curve of the spectral function
x = ot.Sample(N, 2)
for k in range(N):
frequency = fgrid.getValue(k)
x[k, 0] = frequency
value = spectralModel(frequency)
x[k, 1] = value[0, 0].real
# Create the graph
graph = ot.Graph('Spectral user-defined model', 'Frequency', 'Spectral density value', True)
curve = ot.Curve(x, 'UserSpectral')
graph.add(curve)
graph.setLegendPosition('topright')
graph
```

```
[6]:
```