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The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one hertz is the reciprocal of one second. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon, via the Planck relation E = hν, where E is the photon's energy, ν is its frequency, and h is the Planck constant. The hertz is equivalent to one cycle per second. The International Committee for Weights and Measures defined the second as "the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9192631770hertz, νhfs Cs = 9192631770Hz." The dimension of the unit hertz is 1/time (T−1). Expressed in base SI units, the unit is the reciprocal second (1/s). In English, "hertz" is also used as the plural form. As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, e3Hz), MHz (megahertz, e6Hz), GHz (gigahertz, e9Hz) and THz (terahertz, e12Hz). One hertz simply means "one event per second" (where the event being counted may be a complete cycle); 100Hz means "one hundred events per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1Hz, or a human heart might be said to beat at 1.
[2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will design and use filters to extract specific
audio frequencies from a music file.
In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import IPython
import scipy.signal as sp
from scipy.io import wavfile
infringment...)
In [2]:
IPython.display.Audio(s, rate=SF)
Out[2]:
Your browser does not support the audio element.
[2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will explore various ways to implement a system
that changes the voice of a speaker. Typical applications for these
techniques, strictly sorted by plausibility, include international spy
missions and prank telephone calls, and devices such as the one
displayed here can be easily bought on the web... or in a novelty shop.
No description has been provided for t [2]Paolo Prandoni, [3]LCAV, EPFL
The Karplus-Strong algorithm is a simple method to generate synthetic
sounds with arbitrary pitch. In this notebook we will explore a few
variations of the method to illustrate some basic notions of
discrete-time signal processing.
In [1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import IPython
In [2]:
plt.rcParams["figure.figsize"] [2]Paolo Prandoni, [3]LCAV, EPFL
This simple notebook lets you interactively explore the intermodulation
effects of two superimposed sinusoids.
In [1]:
"I defy anybody to find a record... unless it is some old blues
record from 1922... that uses feedback that way. So I claim it for
the Beatles. Before H