# User's manual for the FERDO and FERD unfolding codes

## Abstract

FERDO and FERD are unfolding codes which can be used to correct observed pulse-height distributions for the nonideal response of a pulse-height spectrometer or to solve poorly conditioned linear equations. It is assumed that the response of the spectrometer is given by Ax = b, where A is the spectrometer response function matrix, x is the unknown spectrum, and b is the pulse-height distribution. FERDO does not solve directly for x, but instead solves for p = Wx, where W is a window function matrix. Typically, W is the resolution function of an ideal spectrometer which has a single Gaussian response. The effective resolution of the unfolding solution may be varied by choice of W. Confidence intervals (p/sup 10/, p/sup up/) are found for each element of the solution p. FERDO and FERD are written in IBM 360/370 Fortran (Level H). This manual describes and derives the mathematical procedures used by the codes, tells how to write input data for them, and gives solutions to some sample problems to illustrate the output.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab., TN (USA)

- OSTI Identifier:
- 5664784

- Report Number(s):
- ORNL/TM-8720

ON: DE84000294

- DOE Contract Number:
- W-7405-ENG-26

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Portions are illegible in microfiche products. Original copy available until stock is exhausted

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COMPUTER CODES; F CODES; SPECTRA UNFOLDING; GAMMA SPECTRA; MANUALS; NEUTRON SPECTRA; DATA PROCESSING; DOCUMENT TYPES; PROCESSING; SPECTRA; 440103* - Radiation Instrumentation- Nuclear Spectroscopic Instrumentation; 990200 - Mathematics & Computers

### Citation Formats

```
Rust, B. W., Ingersoll, D. T., and Burrus, W. R.
```*User's manual for the FERDO and FERD unfolding codes*. United States: N. p., 1983.
Web. doi:10.2172/5664784.

```
Rust, B. W., Ingersoll, D. T., & Burrus, W. R.
```*User's manual for the FERDO and FERD unfolding codes*. United States. https://doi.org/10.2172/5664784

```
Rust, B. W., Ingersoll, D. T., and Burrus, W. R. Thu .
"User's manual for the FERDO and FERD unfolding codes". United States. https://doi.org/10.2172/5664784. https://www.osti.gov/servlets/purl/5664784.
```

```
@article{osti_5664784,
```

title = {User's manual for the FERDO and FERD unfolding codes},

author = {Rust, B. W. and Ingersoll, D. T. and Burrus, W. R.},

abstractNote = {FERDO and FERD are unfolding codes which can be used to correct observed pulse-height distributions for the nonideal response of a pulse-height spectrometer or to solve poorly conditioned linear equations. It is assumed that the response of the spectrometer is given by Ax = b, where A is the spectrometer response function matrix, x is the unknown spectrum, and b is the pulse-height distribution. FERDO does not solve directly for x, but instead solves for p = Wx, where W is a window function matrix. Typically, W is the resolution function of an ideal spectrometer which has a single Gaussian response. The effective resolution of the unfolding solution may be varied by choice of W. Confidence intervals (p/sup 10/, p/sup up/) are found for each element of the solution p. FERDO and FERD are written in IBM 360/370 Fortran (Level H). This manual describes and derives the mathematical procedures used by the codes, tells how to write input data for them, and gives solutions to some sample problems to illustrate the output.},

doi = {10.2172/5664784},

url = {https://www.osti.gov/biblio/5664784},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1983},

month = {9}

}