Euclidean geometry

Related notebooks (32)

Basic Example of Anderson Localization in a 1D System

Demonstration of Anderson localization[1]¶ This notebook is intended to show a very basic example of the Anderson localization in one-dimensional system. In [1]: import numpy as np from numpy import linalg as LA import matplotlib.pyplot as plt

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib inline To show the idea of Anderson localization, we can consider 1D chain of

N

atoms with perio

Modeling and Analysis of a PN-Junction in Inhomogeneous Semiconductors.

In [1]: import matplotlib.pyplot as plt import matplotlib.ticker as mtick import numpy as np import ipywidgets as widgets import scipy.integrate as integrate from ipywidgets import interact, fixed from scipy.interpolate import interp1d from textwrap import dedent from bokeh.io import push_notebook, show, output_notebook, output_file, curdoc from bokeh.plotting import figure from bokeh.layouts import column, row from bokeh.themes import built_in_themes from bokeh.models import Range1d, BasicTickFormatter, L

Designing FIR Filters Using the Parks-McClellan Algorithm

The Parks-McClellan Filter Design Method[1]¶

                                      [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

Adaptive Echo Cancellation using LMS Filter

Adaptive Echo Cancellation[1]¶

                                      [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

Investigating the Effect of Phase on Sound Perception

Hearing the phase of a sound[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

In this notebook we will investigate the effect of phase on the perceptual quality of a sound. It is often said that the human ear is commercial-grade audio equipment takes place in the magnitude domain only. In [1]: %matplotlib inline import matplotlib import matplotlib.pyplot as plt import numpy as np import IPython from scipy.io import wavfile In [2]: plt.rcParams["figure.fig

Building a Dual-Tone Multi-Frequency (DTMF) Decoder using Short-Time Fourier Transform

Dual-tone multi-frequency (DTMF) signaling[1]¶

                                      [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]:

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.pyplot as plt import numpy as np import IPython In [2]: plt.rcParams["figure.figsize"] = (14,4)

Introduction[4]¶ DTMF signaling is the way analog phones send the n

Implementing a Fractional Resampler using Local Lagrange Interpolation

FIR Resampling[1]¶

                                      [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

Drude Model

::: {role="main"} ::: {.jp-Cell .jp-MarkdownCell .jp-Notebook-cell} ::: {.jp-Cell-inputWrapper tabindex="0"} ::: {.jp-Collapser .jp-InputCollapser .jp-Cell-inputCollapser} ::: ::: {.jp-InputArea .jp-Cell-inputArea} ::: {.jp-InputPrompt .jp-InputArea-prompt} ::: ::: {.jp-RenderedHTMLCommon .jp-RenderedMarkdown .jp-MarkdownOutput mime-type="text/markdown"}

Drude Model¶{.anchor-link} {#Drude-Model}

Plots the dielectric function and loss function in the Drude model ::: ::: ::: ::: ::: {.jp

Understanding and Plotting the Discrete Fourier Transform (DFT)

Plotting the DFT[1]¶

                                      [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]:

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.p

Calculation and plotting of some important quantities relative to the electron s properties in a conventional TEM

Classical Monte Carlo Simulations of the Ising Model on Square Lattice

"## Classical Monte-Carlo simulations of the Ising model on square lattice\n", "\n", "The Ising model considers the following Hamiltonian\n", "\n", "

\\hat{\\mathcal{H}} = -J\\displaystyle\\sum_{}\\sigma_i \\sigma_j

,\n", "\n", "in which spins

\\sigma_i

can take only two discrete values

\\sigma_i \\in \\{-1,+1\\}

. Below, we will consider spins on two-dimensional square lattice taking into account couplings

J

only for the nearest neighbor sites. For

J > 0

the ferromagneti

Constructing Brillouin Zones of the 2D Square Lattice

Brillouin zones of the two-dimensional square lattice¶{.anchor-link} {#Brillouin-zones-of-the-two-dimensional-square-lattice}

This notebook demonstrates construction of the first three Brillouin zones of square lattice

Constrution of the first Brillouin zone¶{.anchor-link} {#Constrution-of-the-first-Brillouin-zone}

The first Brillouin zone is the Wigner-Seitz cell of the reciprocal lattice. Hence

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Related notebooks (32)

Basic Example of Anderson Localization in a 1D System

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib inline To show the idea of Anderson localization, we can consider 1D chain of

N

atoms with perio

Modeling and Analysis of a PN-Junction in Inhomogeneous Semiconductors.

Designing FIR Filters Using the Parks-McClellan Algorithm

The Parks-McClellan Filter Design Method[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

Adaptive Echo Cancellation using LMS Filter

Adaptive Echo Cancellation[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

Investigating the Effect of Phase on Sound Perception

Hearing the phase of a sound[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

Building a Dual-Tone Multi-Frequency (DTMF) Decoder using Short-Time Fourier Transform

Dual-tone multi-frequency (DTMF) signaling[1]¶

                                      [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]:

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.pyplot as plt import numpy as np import IPython In [2]: plt.rcParams["figure.figsize"] = (14,4)

Introduction[4]¶ DTMF signaling is the way analog phones send the n

Implementing a Fractional Resampler using Local Lagrange Interpolation

FIR Resampling[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

Drude Model

Drude Model¶{.anchor-link} {#Drude-Model}

Plots the dielectric function and loss function in the Drude model ::: ::: ::: ::: ::: {.jp

Understanding and Plotting the Discrete Fourier Transform (DFT)

Plotting the DFT[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.p

Calculation and plotting of some important quantities relative to the electron s properties in a conventional TEM

Classical Monte Carlo Simulations of the Ising Model on Square Lattice

"## Classical Monte-Carlo simulations of the Ising model on square lattice\n", "\n", "The Ising model considers the following Hamiltonian\n", "\n", "

\\hat{\\mathcal{H}} = -J\\displaystyle\\sum_{}\\sigma_i \\sigma_j

,\n", "\n", "in which spins

\\sigma_i

can take only two discrete values

\\sigma_i \\in \\{-1,+1\\}

. Below, we will consider spins on two-dimensional square lattice taking into account couplings

J

only for the nearest neighbor sites. For

J > 0

the ferromagneti

Constructing Brillouin Zones of the 2D Square Lattice

Brillouin zones of the two-dimensional square lattice¶{.anchor-link} {#Brillouin-zones-of-the-two-dimensional-square-lattice}

This notebook demonstrates construction of the first three Brillouin zones of square lattice

Constrution of the first Brillouin zone¶{.anchor-link} {#Constrution-of-the-first-Brillouin-zone}