Type theory

Related notebooks (15)

Exploring Quantization and Oversampling through One-Bit Music

One-Bit Music[1]¶ In this notebook we will talk about quantization and oversampling and we will do so by taking a trip down memory lane to revisit the early from monophonic square waves, introduce polyphony by way of pulse-width modulation and finish with the basics of sigma-delta quantization. pacman In [1]: import matplotlib import matplotlib.pyplot as plt import numpy as np import scipy.signal as sp from scipy.io import wavfile import IPython In [2]: import sys ! wget -q -O mus

Powder X-Ray Diffraction Analysis: Exploring Crystal Structures.

XRay Diffraction[1]¶ The purpose of this notebook is to study the powder XRay diffraction spectra of some systems. When the crystal is hit with an XRay wave, the wave is diffracted only for specific case where the Bragg condition is satisfied for one of the lattice planes in the material. For single crystal diffraction, the condition is satisfied only for specific orientation of the crystal, such that the incident ray has the correct

\theta

value for the plane. In powder XRay data, however, any plane ori

Introduction to Reciprocal Lattices with Periodic Boundary Conditions.

Real vs. Reciprocal Space in 2D[1]¶ Introduction[2]¶ In this short notebook, we will introduce the lattice with periodic(Born- von Karman) boundary condition. Following the boundary condition, there is a transformation from real lattice to the reciprocal lattice. In the code below, we define a1 and a2 through cartesian vectors. Hence, the reciprocal vectors will be the original rotated by 90 degrees multiplied by 2pi and divided by the area of the unit cell (|a1xa2|) In [1]: i

Voice Transformation Techniques Using Digital Signal Processing

A Gallery of Voice Transformers[1]¶

                                      [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

Exploring the Karplus-Strong Algorithm for Sound Synthesis

The Karplus-Strong Algorithm[1]¶

                                      [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"]

Safety Week 2: Content Recommendation – Solutions

{#Introduction} You are a software engineer working on Memeverse, an application where people can share and explore memes. Memes are cultural ideas, jokes, or trends that rely on humor, relatability, or commentary on current events, which make them spread rapidly online. They can take various forms such as images, videos, or short texts. Memeverse is specialized in images. Memeverse includes a smart recommendation system that personalizes the

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

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

Fairness Week 1: University Admissions – Solutions

Fairness Week 1: University admissions¶{.anchor-link} {#Fairness-Week-1:-University-admissions}

How to use this notebook Simply read the text and follow the instructions.
This notebook contains code cells, which can be modified and must be executed to see the result of their content.
To execute a cell, select it and click on the play button (▶) in the tool bar, or type Shift + Enter or Ctr + Enter. As the variables contained in a cell are stor

Filtering Music: Extracting Audio Frequencies Using Filters

Filtering Music[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.

Extracting the bas

Empowerment Week 2: Explainable AI and Model Interpretability – Solutions

Empowerment Week 2 Exercise: Explainability and Transparency¶{.anchor-link} {#Empowerment-Week-2-Exercise:-Explainability-and-Transparency}

Cylindrical Coordinates Visualization

::: {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"}

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

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

Modeling Epidemics with Signal Processing Techniques

Epidemics and Signal Processing[1]¶

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

In [1]: import matplotlib.pyplot as plt import numpy as np import scipy.signal as sp import seaborn as sns sns.set() In [2]: plt.rcParams["figure.figsize"] = (14,4) The basic reproduction number[4]¶ The propagation mechanism of an epidemic such as the one caused by SARS-CoV-2 virus can be roughly modeled, at least in its inital phase, as a process in which each infected individ

Ewald Sphere

Ewald Sphere¶{.anchor-link} {#Ewald-Sphere}

Play with the Ewald Sphere This schematics represent the Ewald sphere for a typical high

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