Sine generation by an IIR filter approach on low-cost 8 bit MCU's

This project describes the generation of sine waves by a simple recursive digital filter in a way that only 8 bit shift/add/subtraction operations, two permanently occupied 8 bit registers and no data tables are required, therefore permitting the usage of low-cost micro-controllers without multiplication units and little storage capacity. It contains the complete theory of this approach, the finding of suitable parameters under the constraint of 8 bit operations plus substitution of multiplications by shift operations and an example implementation on an ATtiny45 MCU.

Project Elements

ATtiny.zip (ZIP)

Source code

IIRSinus.pdf_.zip (ZIP)

Publication (german)

IIRSinus_en.pdf_.zip (ZIP)

Publication (english)

Discussion (6 comments)

Lukas Bartels 6 years ago

Nice artical and thanks a lot for the attached theory. In the Articel Magazin Jan/Feb 2015 (German language) at the last sentance the autor discribes a primitive low pass filter for smoothing out the PWM Singnal. There cutoff frequency 1kHz is calculated by 1/(RC). Shouldn't bee 1/(2PI RC)!?

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JLM7174 6 years ago

Another method was readily described by N.Darwood in the june 1981 edition of Wireless World, available here: www.americanradiohistory.com/Archive-Wireless-World/80s/Wireless-World-1981-06.pdf

DAVID COMER 6 years ago

Thanks for the reference and the site. I sure miss Wireless Electronics Magazine!

1 Comment(s)

Walter Mayer 6 years ago

I like the idea to calcultate the sine wave insead of using tables.

I have calcualted the resulting sine wave with an spread sheet and could see some jitter in the amplitude. With a small change in the calculation, the results become much better.

See the attached file.

Descrition of an other method of sine wave calculation and comparison of the output data of the sine wave generators. (90kb)

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Laurens Philippo 6 years ago

I was wondering if this sine wave can be amplified to deliver 230V 50Hz and let’s say several amps?

purple-bobby 6 years ago

Although it would be possible, the analog amplifier would be inefficient.

The y[n] number could be used as duty input to PWM, and the output of the PWM used to drive a class D amp or H bridge. Perhaps, the output low pass filter could use the inductance of a transformer and you could have low voltage high current primary and high voltage low current secondary. A 500W transformer will be expensive, this could be elminated with a 326V DC supply and a suitable H bridge and drive circuit, 2A inductors and 350V capacitors are still quite expensive.

1 Comment(s)

DAVID COMER 6 years ago

Wunderbar! Not since I read Bar-Giora, "Digital Techniques in Frequency Synthesis", have I seen such a clear concise article with a great practicle example. I really appreciate the work.

0 Comment(s)

lux36 11 years ago

Nice implementation, I also used ATTiny45 to run an IIR digital filter loop (it was peaking bandpass filter, 2nd order, with automatic gain control) for my Nixie-VFD guitar tuner. I programmed mine in assembly code. It works fine to extract basic harmonic sine from a guitar signal.

lux36 11 years ago

If you want to take a look, my nixie-VFD guitar tuner is here: http://www.elektor-projects.com/project/nixie-vfd-guitar-tuner.13169.html It uses a peaking bandpass IIR filter implemented with two ATTiny45s, you might find it interesting. My other project, a random numbers generator, is here: http://www.elektor-projects.com/project/random-numbers-generator.13168.html

DrKnoerig77 11 years ago

Thank you very much! IMHO the main problem is to master the numeric problems resulting from the limited precision of 8 bit integer operations. But after all, even an ATtiny is a system which would have been the dream of a programmer in the early 80ies....