# Error analysis of the chirp-z transform when implemented using waveform synthesizers and FFTs

## Abstract

This report analyzes the effects of finite-precision arithmetic on discrete Fourier transforms (DFTs) calculated using the chirp-z transform algorithm. An introduction to the chirp-z transform is given together with a description of how the chirp-z transform is implemented in hardware. Equations for the effects of chirp rate errors, starting frequency errors, and starting phase errors on the frequency spectrum of the chirp-z transform are derived. Finally, the maximum possible errors in the chirp rate, the starting frequencies, and starting phases are calculated and used to compute the worst case effects on the amplitude and phase spectrums of the chirp-z transform. 1 ref., 6 figs.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (USA)

- Sponsoring Org.:
- DOE/AD

- OSTI Identifier:
- 6297820

- Report Number(s):
- SAND-90-1965

ON: DE91004939

- DOE Contract Number:
- AC04-76DP00789

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; FOURIER TRANSFORMATION; ALGORITHMS; ERRORS; WAVE FORMS; INTEGRAL TRANSFORMATIONS; MATHEMATICAL LOGIC; TRANSFORMATIONS; 990200* - Mathematics & Computers

### Citation Formats

```
Bielek, T.P.
```*Error analysis of the chirp-z transform when implemented using waveform synthesizers and FFTs*. United States: N. p., 1990.
Web. doi:10.2172/6297820.

```
Bielek, T.P.
```*Error analysis of the chirp-z transform when implemented using waveform synthesizers and FFTs*. United States. doi:10.2172/6297820.

```
Bielek, T.P. Thu .
"Error analysis of the chirp-z transform when implemented using waveform synthesizers and FFTs". United States.
doi:10.2172/6297820. https://www.osti.gov/servlets/purl/6297820.
```

```
@article{osti_6297820,
```

title = {Error analysis of the chirp-z transform when implemented using waveform synthesizers and FFTs},

author = {Bielek, T.P.},

abstractNote = {This report analyzes the effects of finite-precision arithmetic on discrete Fourier transforms (DFTs) calculated using the chirp-z transform algorithm. An introduction to the chirp-z transform is given together with a description of how the chirp-z transform is implemented in hardware. Equations for the effects of chirp rate errors, starting frequency errors, and starting phase errors on the frequency spectrum of the chirp-z transform are derived. Finally, the maximum possible errors in the chirp rate, the starting frequencies, and starting phases are calculated and used to compute the worst case effects on the amplitude and phase spectrums of the chirp-z transform. 1 ref., 6 figs.},

doi = {10.2172/6297820},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Nov 01 00:00:00 EST 1990},

month = {Thu Nov 01 00:00:00 EST 1990}

}

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