Complex analysis

Related notebooks (32)

Simulating Electron Motion in 2D Materials Using the Drude Model - Advanced

Drude model considers electrons small solid particles traveling through lattices as a stationary array of heavier and bigger atoms. The model use "mean free time" as a measure of the frequency an electron gets scattered. This jupyter notebook makes use of this concept and uses stochastic method to simulate electrons traveling through a 2D material of finite width but infinite length."

First we setup the simulation parameters such as the external electric field, number of electrons (default to 1)

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

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

Interactive Wave Visualization: Transverse and Longitudinal Modes.

"First, we define a 2D lattice as follow:"

"Next, we define a function that updates the atomic positions in the lattice at each call"

Digital Simulation of Guitar Feedback in I Feel Fine by The Beatles

I Feel Fine, Digitally[1]¶ This notebook is a little musing inspired by the "internal mechanics" of a very famous audio snippet, namely the guitar sound at the beginning of the song "I Feel Fine", written and recorded by the Beatles in 1964. The historical significance of the record lies in the following claim by John Lennon:

 "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

Whistle-Activated Keylock System Implementation

Whistling Keylock[1]¶ In this notebook we will implement a simple "whistle-activated" keylock, that is, an access control system where the password is a pre-defined melody. To program the lock, you record your musical passphrase and then, to open the lock, you whistle it back. Although the implementation will be simple and skip most of the fine details that would be necessary to produce a truly robust system, we need to take into account at least the following points: * The syste

Cylindrical Coordinates Visualization

Important note¶{.anchor-link} {#Important-note}

This notebook is obsolete and not maintained. For an interactive display of cylidri

Temperature Dependence of the Fermi-Dirac Distribution

This notebook serves to show how the Fermi-Dirac distribution and its derivative change with temperature.\n", " \n", "The Fermi-dirac distribution is

f(E)=\\frac{1}{e^{(E-\\mu)/k_bT}+1}

\n", "\n", "For the purpose of simplicity, we will plot the graph of

f(E-\\mu)

. This allows us to avoid complications connected with

\\mu

being a function of temperature (consult the other notebook for this week or section 2.2.3 in the notes for more details)\n", "\n", "We first define the r

Spherical Coordinates Visualization

Important note¶{.anchor-link} {#Important-note}

This notebook is obsolete and not maintained. For an interactive display of polar coordinates, please use

def rotation_matrix(d):
    """
    Calculates a rotation matrix given a vector d. The direction of d
    corresponds to the rotation axis. The length of d corresponds to 
    the sin of the angle of rotation.

    Variant of: http://mail.scipy.org/pipermail/numpy-discuss

Wave Interference

The plotted function is the superimposition of $n$ 2d-sine functions centered in $(0,Y_i)$: $$f(x,y)=\sin\big(p\cdot\sqrt{x^2+(y-Y_i)^2}\big)$$ The parameters that can be changed are: -- $n$ the number of sources (start with 2) -- $d$ the distance between sources -- $p$ the periodicity. Higher periodicity means shorter wavelength. $p =2\pi / \lambda$. Note that in electron microscopy the usual convention is to define the wave vector as $k=1/\lambda$. -- $f$ the field o

Simulating a Telephone Channel using FIR Filter Design

A Telephone Channel Simulator[1]¶ In this notebook we will develop a filter that simulates the effect of a standard telephone channel. 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 In [2]: plt.rcParams["figure.figsize"] = (14,4) implicit sampling rate will be the internal "clock" of our simulation. In [3]: IPython.display.Audio(s, rate=SF) Out[3]: Your browser does not support

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

Exploring Frequency Beatings and Intermodulation Effects with Sinusoids

Feel the Beat(s)[1]¶

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

This simple notebook lets you interactively explore the intermodulation effects of two superimposed sinusoids. In [1]:

standard bookkeeping

%matplotlib inline import matplotlib.pyplot as plt import numpy as np from IPython.display import Audio, display

interactivity library:

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets In [2]: plt.rcParams[

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Related notebooks (32)

Simulating Electron Motion in 2D Materials Using the Drude Model - Advanced

Drude model considers electrons small solid particles traveling through lattices as a stationary array of heavier and bigger atoms. The model use "mean free time" as a measure of the frequency an electron gets scattered. This jupyter notebook makes use of this concept and uses stochastic method to simulate electrons traveling through a 2D material of finite width but infinite length."

First we setup the simulation parameters such as the external electric field, number of electrons (default to 1)

Drude Model

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

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

Interactive Wave Visualization: Transverse and Longitudinal Modes.

"First, we define a 2D lattice as follow:"

"Next, we define a function that updates the atomic positions in the lattice at each call"

Digital Simulation of Guitar Feedback in I Feel Fine by The Beatles

 "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

Whistle-Activated Keylock System Implementation

Cylindrical Coordinates Visualization

Important note¶{.anchor-link} {#Important-note}

This notebook is obsolete and not maintained. For an interactive display of cylidri

Temperature Dependence of the Fermi-Dirac Distribution

This notebook serves to show how the Fermi-Dirac distribution and its derivative change with temperature.\n", " \n", "The Fermi-dirac distribution is

f(E)=\\frac{1}{e^{(E-\\mu)/k_bT}+1}

\n", "\n", "For the purpose of simplicity, we will plot the graph of

f(E-\\mu)

. This allows us to avoid complications connected with

\\mu

being a function of temperature (consult the other notebook for this week or section 2.2.3 in the notes for more details)\n", "\n", "We first define the r

Spherical Coordinates Visualization

Important note¶{.anchor-link} {#Important-note}

This notebook is obsolete and not maintained. For an interactive display of polar coordinates, please use

def rotation_matrix(d):
    """
    Calculates a rotation matrix given a vector d. The direction of d
    corresponds to the rotation axis. The length of d corresponds to 
    the sin of the angle of rotation.

    Variant of: http://mail.scipy.org/pipermail/numpy-discuss

Wave Interference

Simulating a Telephone Channel using FIR Filter Design

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

Exploring Frequency Beatings and Intermodulation Effects with Sinusoids

Feel the Beat(s)[1]¶

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

This simple notebook lets you interactively explore the intermodulation effects of two superimposed sinusoids. In [1]:

standard bookkeeping

%matplotlib inline import matplotlib.pyplot as plt import numpy as np from IPython.display import Audio, display

interactivity library:

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets In [2]: plt.rcParams[