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Language change is variation over time in a language's features. It is studied in several subfields of linguistics: historical linguistics, sociolinguistics, and evolutionary linguistics. Traditional theories of historical linguistics identify three main types of change: systematic change in the pronunciation of phonemes, or sound change; borrowing, in which features of a language or dialect are altered as a result of influence from another language or dialect; and analogical change, in which the shape or grammatical behavior of a word is altered to more closely resemble that of another word. All living languages are continually undergoing change. Some commentators use derogatory labels such as "corruption" to suggest that language change constitutes a degradation in the quality of a language, especially when the change originates from human error or is a prescriptively discouraged usage. Modern linguistics rejects this concept, since from a scientific point of view such innovations cannot be judged in terms of good or bad. John Lyons notes that "any standard of evaluation applied to language-change must be based upon a recognition of the various functions a language 'is called upon' to fulfil in the society which uses it". Over a sufficiently long period of time, changes in a language can accumulate to such an extent that it is no longer recognizable as the same language. For instance, modern English is the result of centuries of language change applying to Old English, even though modern English is extremely divergent from Old English in grammar, vocabulary, and pronunciation. The two may be thought of as distinct languages, but Modern English is a "descendant" of its "ancestor" Old English. When multiple languages are all descended from the same ancestor language, as the Romance languages are from Vulgar Latin, they are said to form a language family and be "genetically" related. Economy: Speech communities tend to change their utterances to be as efficient and effective (with as little effort) as possible, while still reaching communicative goals.
[2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will use the adaptive LMS filter to estimate the
impulse response of a reverberating room.
A typical use case is handsfree telephony: since the received signal,
amplified and played by the speaker, is picked up by the microphone, we
need to eliminate it from the signal that is transmitted back in order
to avoid a feedback loop. The signal picked up by the microph [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
In this notebook we will look at the practical issues associated to
plotting the DFT and in particular the DFT of real-world signals. We
will examine how to map the DFT coefficients to real-world frequencies
and we will investigate the frequency resolution of the DFT and the
effects of zero padding.
In [1]: