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In psychophysics, sensory threshold is the weakest stimulus that an organism can sense. Unless otherwise indicated, it is usually defined as the weakest stimulus that can be detected half the time, for example, as indicated by a point on a probability curve. Methods have been developed to measure thresholds in any of the senses. Several different sensory thresholds have been defined; Absolute threshold: the lowest level at which a stimulus can be detected. Recognition threshold: the level at which a stimulus can not only be detected but also recognized. Differential threshold: the level at which an increase in a detected stimulus can be perceived. Terminal threshold: the level beyond which any increase to a stimulus no longer changes the perceived intensity. The first systematic studies to determine sensory thresholds were conducted by Ernst Heinrich Weber, a physiologist and pioneer of experimental psychology at the Leipzig University. His experiments were intended to determine the absolute and difference, or differential, thresholds. Weber was able to define absolute and difference threshold statistically, which led to the establishment of Weber's Law and the concept of just noticeable difference to describe threshold perception of stimuli. Following Weber's work, Gustav Fechner, a pioneer of psychophysics, studied the relationship between the physical intensity of a stimulus and the psychologically perceived intensity of the stimulus. Comparing the measured intensity of sound waves with the perceived loudness, Fechner concluded that the intensity of a stimulus changes in proportion to the logarithm of the stimulus intensity. His findings would lead to the creation of the decibel scale. Defining and measuring sensory thresholds requires setting the sensitivity limit such that the perception observations lead to the absolute threshold. The level of sensitivity is usually assumed to be constant in determining the threshold limit.
[2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will build a dual-tone multi-frequency decoder
based on the short-time Fourier transform.
In [1]:
[2]Paolo Prandoni, [3]LCAV, EPFL
In [1]:
import matplotlib.pyplot as plt
import numpy as np
import scipy.signal as sp
import seaborn as sns
sns.set()
In [2]:
plt.rcParams["figure.figsize"] = (14,4)
The basic reproduction number[4]¶
The propagation mechanism of an epidemic such as the one caused by
SARS-CoV-2 virus can be roughly modeled, at least in its inital phase,
as a process in which each infected individ