be-7.py

import math
import scipy.signal
import numpy as np
import plotly.graph_objects as go # I prefer ployly over matplotlib
from scipy.ndimage import gaussian_filter1d

step = 0.01 # Defining the grid step for all further operations

# gaussian kernel on its own grid with the same step
def gauss(pos, sigma):
    guass_x = np.arange(-5*sigma, 5*sigma, step)
    return np.exp(-(guass_x/sigma)**2.0/2.0)/sigma/np.sqrt(2.0*math.pi)
        
# convolution operation
def convolve(spectrum, sigma):
    # Not an obvious point. We need to convert from grid cell number to actual x value.
    sigma_steps = sigma/step
    # We can also try to use numpy.convolve or scipy.signal.convolve, but result is more or less the same
    return gaussian_filter1d(spectrum, sigma_steps)

# peak definitions
k_base_prob = 0.864
k_base_energy = 112.0
k_ext_prob = 0.096
k_ext_energy = 83.0
l_base_prob = 0.036
l_base_energy = 55.0
l_ext_prob = 0.004   

ext_width = 28.0

# custom peak definition
def ext_value(x, pos, prob):
    if abs(x - pos) > ext_width:
        return 0.0 # PITFALL!
    else:
        return math.cos( (x-pos)/ext_width * math.pi/2.0) /2.0 *prob

# need to vectorize the function to make it work properly with numpy      
def vector_ext_func(pos, prob):
    return np.vectorize(lambda x: ext_value(x, pos,prob))
  
# define peaks
curve_x = np.arange(0, 130, step) # x values for the curve
curve = np.zeros(curve_x.size) # empty array initialization

# add two delta-peaks
curve[(int)(k_base_energy/step)] = k_base_prob
curve[(int)(l_base_energy/step)] = l_base_prob

# add a custom peak
curve = curve + vector_ext_func(k_ext_energy,k_ext_prob)(curve_x)

# generating curve and plotting with Plotly
convoluted = convolve(curve, 0.5)
fig = go.Figure(
    data = [
        go.Scatter(x=curve_x, y = curve, name = "initial"),
        go.Scatter(x=curve_x, y = convoluted, name = "convolved")
    ]
)
fig.update_yaxes(type="log")
fig.show()