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Commit 86cb36d8 authored by Erik Strand's avatar Erik Strand
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Don't use default posts structure

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collections:
authors:
psets:
output: true
notes:
output: true
defaults:
- scope:
path: ""
type: "authors"
type: "psets"
values:
layout: "author"
layout: "pset"
- scope:
path: ""
type: "posts"
type: "notes"
values:
layout: "post"
layout: "note"
- scope:
path: ""
values:
......
......@@ -2,3 +2,5 @@
link: /
- name: Problem Sets
link: /psets.html
- name: Notes
link: /notes.html
......@@ -3,8 +3,4 @@ layout: default
---
<h1>{{ page.title }}</h1>
<p>
{{ page.date | date_to_string }}
</p>
{{ content }}
---
layout: default
---
<h1>{{ page.title }}</h1>
{{ content }}
---
title: Chapter 2 Notes
title: Fourier Transforms
---
This page contains some proofs that I needed to review to make sense of the material in chapter 2.
It's based on my prior knowledge and some helpful websites:
To really make sense of chapter 2 I needed to review the properties of Fourier Transforms. These
notes are based on my prior knowledge and some helpful websites:
- [Properties of Fourier Transform](http://fourier.eng.hmc.edu/e101/lectures/handout3/node2.html)
- [symmetry.pdf](https://www.cs.unm.edu/~williams/cs530/symmetry.pdf)
......
File moved
......@@ -95,13 +95,14 @@ visible light?
Note: in the previous problem I used $$\lambda$$ as the expected number of events of a Poisson process.
Here I'll use $$N$$ to avoid confusion with wavelength.
We have already found that $$\sigma = \sqrt{N}$$. For large $$N$$, the Poisson
distribution is very close to the normal distribution. So about two thirds of the probability mass
lies between $$N - \sigma$$ and $$N + \sigma$$. Thus if $$\sigma \leq 0.01 N$$, in
any given second it's more likely than not that the number of photons emitted is within one percent
of the true mean. Thus we'd need $$\sqrt{N} \leq 0.01 N$$, i.e. $$N \geq 10^4$$.
To have the same probability that the number of observed photons is within $$10^{-6} N$$ of
the true value, we need $$N \geq 10^{12}$$.
Since the photons are generated independently and with a constant average rate, it's reasonable to
model their creation as a Poisson process. We have already found that $$\sigma = \sqrt{N}$$. For
large $$N$$, the Poisson distribution is very close to the normal distribution. So about two thirds
of the probability mass lies between $$N - \sigma$$ and $$N + \sigma$$. Thus if $$\sigma \leq 0.01
N$$, in any given second it's more likely than not that the number of photons emitted is within one
percent of the true mean. Thus we'd need $$\sqrt{N} \leq 0.01 N$$, i.e. $$N \geq 10^4$$. To have the
same probability that the number of observed photons is within $$10^{-6} N$$ of the true value, we
need $$N \geq 10^{12}$$.
The wavelength of visible light is about $$\num{500e-9} \si{m}$$, so the energy of each photon will
be
......
---
title: Notes
---
<h1>Notes</h1>
<ul>
{% for note in site.notes %}
<li>
<h2><a href="{{ note.url | real_relative_url }}">{{ note.title }}</a></h2>
</li>
{% endfor %}
</ul>
......@@ -4,10 +4,9 @@ title: Problem Sets
<h1>Problem Sets</h1>
<ul>
{% for post in site.posts %}
{% for pset in site.psets %}
<li>
<h2><a href="{{ post.url | real_relative_url }}">{{ post.title }}</a></h2>
<p>{{ post.excerpt }}</p>
<h2><a href="{{ pset.url | real_relative_url }}">{{ pset.title }}</a></h2>
</li>
{% endfor %}
</ul>
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