# Thesis of Kim Øyhus

In 1993, I finished my study at NTH, the Norwegian institute of
technology, later changed to NTNU, at the Department
of Physics. This thesis is my final work, which is the complete
development of a cheap spectrum analyzer, mainly intended for sound.
As the hacker-physicist I am, I chose a task where could
combine my abilities. Considering that I made a Commodore Amiga
computer from 1984-93 do spectrum analyzis of comparable quality to a $50
000 instrument of the same era, I really did deserve
the grade of 1.5.

In order to make such a slow machine do such a demanding task, i had
to make everything efficient. The fourier part was
constructed with the aid of number theoretic analyzes of matrixes and
fields, giving a
next to ultimately fast program for fourier transform on a 68000
Motorola processor. The sampling and drawing of the spectrum is also
done with efficient interleaved methods, too complex to describe
here. I also designed and built the sampler itself, which is of a
clean simple design, with low distortion, noise comparable to the
quantization noise, and good immunity to radio noise, a necessity,
since the lab was next to a radio station.

I have since translated the fourier routine to C for use in
other processors. The processors of today, 1997, are very different
beasts compared to the M68000. Their caches, pipelines, and
multiplicators make other implementations of the fourier transform
more efficient.
However, microcontrollers of today have similar architecture to the
Motorola 68000, and will therefore be excellent candidates for my
program. Email me if you are interested.

(PS: My English has improved since I wrote the thesis.)

## Cheap Realtime Spectral-Analyzer

### Contents

1 Abstract

Index

### I. Description

2 What can the spectral analyzer be used
for?

3 Apparatus

4 Ear and sound

5 The Fourier Transform

6 The Large Winograd FFT

7 Processor specifics

8 The Program

9 Examples

10 Conclusion

### II. Appendixes

A. Programs and makefiles

K. Spectral analyzer main program

L. Interrupt sampler and drawer of spectrum

M. Debugged small Winograd FFT of length
9

N. Sampler board

Bibliography

Last modified: Mon Oct 14 14:51:39 CEST 2002