1 INTRODUCTION
2 THE FAST FOLDING ALGORITHM
2.1 The folding transform
2.2 A depth-first traversal, arbitrary length FFA
2.3 Spacing of trial periods
3 OPTIMALLY SEARCHING FOR PERIODIC SIGNALS AND SENSITIVITY OF THE FFA
3.1 Problem formulation
3.2 Evaluating a test statistic
3.3 Constructing the most powerful test: the Z-statistic
3.4 Case of periodic signals
3.5 Searching for periodic signals with unknown parameters
4 SENSITIVITY ANALYSIS OF THE STANDARD FFT PROCEDURE
4.1 The incoherent detection statistic
4.2 Distribution of the incoherent detection statistic
4.3 Statistical power analysis
4.4 Summary
5 AN IMPLEMENTATION OF THE FFA TO PROCESS LARGE SCALE PULSAR SURVEYS
5.1 Overview of the implementation
5.2 Data whitening and normalisation
5.3 Searching a period range
5.4 Matched Filtering
5.5 Identifying statistically significant candidate signals
5.6 Improving performance with dynamic duty cycle resolution
5.7 Full pipeline overview
5.8 Benchmarks
6 DISCUSSION
6.1 A more realistic radiometer equation to determine detectable flux densities
6.2 Improving FFT searches with coherent harmonic summing
6.3 Efficacy of the FFA in a real search
7 CONCLUSION