Fwd: Re: [sdiy] CORDIC

[Stephen Lenham]

> Hi James,
> 
> CORDIC is a very powerful and fascinating algorithm. The earliest use 
of 
> this algorithm was in air navigation computers. The algorithm was 
> developed by Jack Volder at Convair in the late 1950's. It got a lot 
of 
> exposure in 1972 through the HP-35 calculator, the first handheld 
> "electronic slide rule," as it was called in those days. At that time,

> AFAIK, the first description of the hyperbolic transcendental version 
of 
> the algorithm was introduced, though it's possible some other 
researcher 
> or group got to it before that time. Another application for CORDIC 
is in 
> sexigesimal number systems, for instance for MM:HH:SS conversion to 
> decimal minutes. Additionally, CORDIC can be performed in other 
number 
> bases, such as in Radix-4, or in decimal (powers-of-10).
> 
> CORDIC was also used in the 1980's for VLSI array processing 
computers
> which performed signal processing. Essentially, you can do fourier
> transforms and a wide variety of other systems operations, using 
batches
> of CORDIC processing blocks. I feel very lucky that I got a chance to 
meet
> Jack Volder over lunch in the 1980's to chat about CORDIC.
> 
> This link will bring up about 181 references you can follow:
> http://citeseer.nj.nec.com/cs?q=CORDIC&cs=1
> 
> You can probably find threads for CORDIC and FPGA on comp.arch.fpga 
by Ray 
> Andraka, who has done a lot of innovating in this area for signal 
> processing with FPGAs. He did a great demo of a FPGA-based digital 
radio 
> tuning in WWV on short-wave, last Spring at FCCM'03. There's more 
> information about FCCM at:
> http://www.fccm.org
> 
> If you can find them, these papers are IMHO the absolute best ones 
about
> CORDIC, though certainly a lot more modern stuff has come out (see
> citeseer, above):
> 
> J. E. Volder, "The CORDIC Trignometric Computing Technique," IRE 
Trasn. 
> Elec. Computers, vol. EC-S, no. 3, pp. 330-334 (Sep. 1959).
> 
> J. S. Walther, "A Unified Algorithm for Elementary Functions," Spring 

> Joint Computer Conference, 1971, pp. 379-385.
> 
> Alvin M. Despain, "Fourier Transform Computers Using CORDIC 
Iterations," 
> IEEE Trans. on Computers, vol. C-23, no. 10, pp. 993-1001 (Oct. 1974).

> 
> Additionally, in the June 1981 issue of Wireless World (which is from 

> the UK), there was an article about an iterative digital sine-wave 
> oscillator, and it's very CORDIC like, though no mention of CORDIC is 

> made. It's title, "Accurate sine-wave oscillator," by N. Darwood.
> 
> Some small number of months later, an analog version of this same 
idea was 
> written about in Wireless World in an article titled "Analogue Sine 
Waves 
> -- Analogue implementation of the Darwood accurate sine-wave 
oscillator 
> algorithm," by D. H. Follett. This analog circuit version was done 
with 
> LF353 dual opamps, CD4066 CMOS switches, and capacitors, offering a 
> quadrature output over a wide range of audio frequency. Sorry I don't 
have 
> the date reference for this one, but I'm guessing Summer or Fall 1981.

> 
> Kindly yours,
> Michael
> 
> On Mon, 10 Nov 2003, James Patchell wrote:
> 
> > Well, I am hoping somebody on this list can give me some help.  I 
am 
> > looking for information on the CORDIC algorithm.  That stands for 
> > Coordinate Rotation Digital Computer.  At first blush, this may 
seem to 
> > have very little to do with Synth-DIY, but this algorithm can be 
used to 
> > generate transcendental functions using only shifts and adds very 
quickly 
> > (sin, cos, atan, hyperbolic functions, square roots...etc), and can 
be 
> > easily implemented in FPGA's, as well as simple micros, such as the 
AVR.  I 
> > am looking into applications for digital synths, as well as other 
> > things...so, if anybody knows of any good links with information, 
please 
> > let me know...here are a couple of good ones I have found...
> > 
> > http://www.andraka.com/cordic.htm
> > http://www.dspguru.com/info/faqs/cordic.htm
> > 
> > 
> >          -Jim
> > ***************************************************
> > I'm a man
> > But I can change
> > If I have to
> > I guess.
> > 
> > Man's Prayer
> > Red Green
> > 
> > ***************************************************
> > http://www.oldcrows.net/~patchell
> > 
> > http://members.cox.net/patchell
> > 
> > ***************************************************
> > 
> > 
> > 
> > 
> 
>