The Fourier Transform

11/10/01


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Table of Contents

The Fourier Transform

The Fourier Transform

The Fourier Pair

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

1D Fourier Transform

2D Extension

2D Extension

Definitions

Full k Space Coverage

Only Centre of k Space

Only Edges of k Space

How to Picture k Space

Gradient-Echo Sequence

Gradient-Echo Sequence

Gradient-Echo Sequence

Gradient-Echo Sequence

Gradient-Echo Sequence

Gradient-Echo EPI Sequence

Interleaved EPI

Fast Spin Echo

Fast Spin Echo

Options that Alter how k Space is Filled

Zero Filling

Zero Filling

Nyquist Theorem

Nyquist Aliasing

No Phase Wrap

k Space Symmetry

Phase Correcting Images

Partial k Space Acquisitions

Fractional NEX

Partial k Space Acquisitions

Minimum TE

Field of View and Resolution

Field of View and Resolution

Field of View and Resolution

Rectangular Field of View

Slice Selection

2D Multi Slice Imaging

3D Imaging

3D Imaging

PPT Slide

Author: Peter Jezzard

Email: peterj@fmrib.ox.ac.uk

Home Page: http://www.fmrib.ox.ac.uk

Other information:
FMRIB Centre, University of Oxford, John Radcliffe Hospital, Headington, Oxford, OX3 9DU, ENGLAND