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## Fourier analysis in diffraction and image formation

*Christopher Hammond*

### in The Basics of Crystallography and Diffraction

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198738671
- eISBN:
- 9780191801938
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198738671.003.0013
- Subject:
- Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter starts with the Fourier series and Fourier transforms, and the representation of periodic functions. It then looks at Fourier analysis in crystallography. It details electron density, ... More

## Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

*Bas Edixhoven and Jean-Marc Couveignes (eds)*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691142012
- eISBN:
- 9781400839001
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142012.001.0001
- Subject:
- Mathematics, Number Theory

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's ... More

## Digital Filters

*Ilya Polyak*

### in Title Pages

- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195099997
- eISBN:
- 9780197560938
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195099997.003.0003
- Subject:
- Computer Science, Mathematical Theory of Computation

In this chapter, several systems of digital filters are presented. The first system consists of regressive smoothing filters, which are a direct consequence of the least squares polynomial ... More

## Capabilities and Merits of Long-term Bio-optical Moorings

*John Marra*

### in Ocean Optics

- Published in print:
- 1994
- Published Online:
- November 2020
- ISBN:
- 9780195068436
- eISBN:
- 9780197560235
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195068436.003.0014
- Subject:
- Earth Sciences and Geography, Oceanography and Hydrology

There are primarily three ways in which the ocean can be sampled. First, depth profiles of water properties can be collected. The sampling resolution for depth profiles can be very high (<1 m), and ... More

## Electron-density maps

*David Blow*

### in Outline of Crystallography for Biologists

- Published in print:
- 2002
- Published Online:
- November 2020
- ISBN:
- 9780198510512
- eISBN:
- 9780191919244
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198510512.003.0016
- Subject:
- Chemistry, Crystallography: Chemistry

When everything has been done to make the phases as good as possible, the time has come to examine the image of the structure in the form of an electron-density map. The electron-density map is the ... More

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