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An academic degree is a qualification awarded to a student upon successful completion of a course of study in higher education, usually at a college or university. These institutions often offer degrees at various levels, usually divided into undergraduate and postgraduate degrees. The most common undergraduate degree is the bachelor's degree, although some educational systems offer lower level undergraduate degrees such as associate and foundation degrees. Common postgraduate degrees include master's degrees and doctorates. The doctorate (Latin: doceo, "I teach") appeared in medieval Europe as a license to teach (Latin: licentia docendi) at a medieval university. Its roots can be traced to the early church when the term "doctor" referred to the Apostles, church fathers and other Christian authorities who taught and interpreted the Bible. The right to grant a licentia docendi was originally reserved to the church which required the applicant to pass a test, take an oath of allegiance and pay a fee. The Third Council of the Lateran of 1179 guaranteed the access – now largely free of charge – of all able applicants, who were, however, still tested for aptitude by the ecclesiastic scholastic. This right remained a point of contention between the church authorities and the slowly emancipating universities, but was granted by the Pope to the University of Paris in 1231 where it became a universal license to teach (licentia ubique docendi). However, while the licentia continued to hold a higher prestige than the bachelor's degree (Baccalaureus), it was ultimately reduced to an intermediate step to the Magister and doctorate, both of which now became the exclusive qualification for teaching. At the university, doctoral training was a form of apprenticeship to a guild. The traditional term of study before new teachers were admitted to the guild of "Master of Arts", seven years, was the same as the term of apprenticeship for other occupations.
[2]Paolo Prandoni, [3]LCAV, EPFL
The Parks-McClellan (PM) algorithm is a clever application of advanced
polynomial fitting techniques to the problem of FIR filter design. In
this notebook we will explore the key ideas behind the method by
considering the design of a simple Type-I lowpass filter.
NOTE: This notebook uses interactive widgets. If the interactive
controls do not work or show up, please fo [2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will implement a simple fractional resampler that
uses local Lagrange interpolation. The resampler can be used to perform
any rational sampling rate change (but beware of aliasing when
downsampling!)
In [1]:
import numpy as np
import IPython
from scipy.io import wavfile
Local Lagrange interpolation[4]¶
To perform resampling we will need to compute subsample values and, in