# OpenStax_CNX

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### Lenses

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#### Definition of a lens

##### Lenses

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##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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• Rice Digital Scholarship

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# Examples with Matched Filters

Module by: Behnaam Aazhang. E-mail the author

Summary: Examples with the use of matched filters.

The theory and rationale behind matched filter receivers can be found in Matched Filters.

## Example 1

s 1 t=t s 1 t t for 0tT 0 t T

s 2 t=t s 2 t t for 0tT 0 t T

h 1 t=Tt h 1 t T t for 0tT 0 t T

h 2 t=T+t h 2 t T t for 0tT 0 t T

t,0t2T: s 1 ˜ t= s 1 τ h 1 tτd τ t 0 t 2 T s 1 ˜ t τ s 1 τ h 1 t τ
(1)
s 1 ˜ t=0tτ(Tt+τ)d τ =12(Tt)τ2|0t+13τ3|0t=t22(Tt3) s 1 ˜ t τ 0 t τ T t τ 0 t 1 2 T t τ 2 0 t 1 3 τ 3 t 2 2 T t 3
(2)
s 1 ˜ T=T33 s 1 ˜ T T 3 3
(3)

Compared to the correlator-type demodulation

ψ 1 t= s 1 t E s ψ 1 t s 1 t E s
(4)
s 11 =0T s 1 τ ψ 1 τd τ s 11 τ 0 T s 1 τ ψ 1 τ
(5)
0t s 1 τ ψ 1 τd τ =1 E s 0tττd τ =1 E s 13t3 τ 0 t s 1 τ ψ 1 τ 1 E s τ 0 t τ τ 1 E s 1 3 t 3
(6)

## Example 2

Assume binary data is transmitted at the rate of 1T 1 T Hertz.

0(b=1)( s 1 t=st) 0 b 1 s 1 t s t for 0tT 0 t T

1(b=-1)( s 2 t=st) 1 b -1 s 2 t s t   for   0tT 0 t T

X t = i =PP b i stiT X t i P P b i s t i T
(7)

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

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My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks