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A master's degree (from Latin magister) is a postgraduate academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice. A master's degree normally requires previous study at the bachelor's level, either as a separate degree or as part of an integrated course. Within the area studied, master's graduates are expected to possess advanced knowledge of a specialized body of theoretical and applied topics; high order skills in analysis, critical evaluation, or professional application; and the ability to solve complex problems and think rigorously and independently. The master's degree dates back to the origin of European universities, with a Papal bull of 1233 decreeing that anyone admitted to the mastership in the University of Toulouse should be allowed to teach freely in any other university. The original meaning of the master's degree was thus that someone who had been admitted to the rank (degree) of master (i.e. teacher) in one university should be admitted to the same rank in other universities. This gradually became formalised as the licentia docendī (licence to teach). Originally, masters and doctors were not distinguished, but by the 15th century it had become customary in the English universities to refer to the teachers in the lower faculties (arts and grammar) as masters and those in the higher faculties as doctors. Initially, the Bachelor of Arts (BA) was awarded for the study of the trivium and the Master of Arts (MA) for the study of the quadrivium. From the late Middle Ages until the 19th century, the pattern of degrees was therefore to have a bachelor's and master's degree in the lower faculties and to have bachelor's and doctorates in the higher faculties. In the United States, the first master's degrees (Magister Artium, or Master of Arts) were awarded at Harvard University soon after its foundation.
[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 [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