Quardrature Direct Fourier Transform

Luhan Monat · May 31, 2004

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

--
Luhan Monat: Luhan Knows at Yahoo dot Com
http://members.cox.net/berniekm
"The Future is not what it used to be."

Jim Thompson · May 31, 2004

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
<fakemeout@nowhere.xyz> wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

480)460-2350 | |
| E-mail Address at Website Fax

Activ8 · May 31, 2004

On Mon, 31 May 2004 08:05:56 -0700, Jim Thompson wrote:

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
fakemeout@nowhere.xyz> wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

Very interesting! Care to elaborate on your circuitry?

...Jim Thompson

it's a PIC12F675. an 8 pin job. I guess you have to sample the hell
out of the tones to find the peaks. First you'd have to filter out
the high and low tones though.
--
Best Regards,
Mike

Allan Herriman · May 31, 2004

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
<fakemeout@nowhere.xyz> wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

Your website says:
" The resultant sums are then 'vector added' by taking the 'square
root of the sum of the squares'."

The DFT is defined with a complex output, which means that the real
and imaginary parts are left as is; there is no square root operation
in a DFT per se.

You might want to use a sqrt to find the magnitude. However, if
converting to dB, it's better to just sum the squares of the two parts
then take 10.log(), rather than 20.log(sqrt()).

As for your invention: this technique is well known. I posted a
tutorial [about something that was essentially equivalent] to comp.dsp
a few years ago.
http://www.dspguru.com/comp.dsp/tricks/alg/cpxdown.htm

Don't be discouraged though; this is an excellent idea, and you did
well to think of it by yourself.

Regards,
Allan.

Allan Herriman · May 31, 2004

On Tue, 01 Jun 2004 01:48:16 +1000, Allan Herriman
<allan.herriman.hates.spam@ctam.com.au.invalid> wrote:

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
fakemeout@nowhere.xyz> wrote:

You might want to use a sqrt to find the magnitude. However, if
converting to dB, it's better to just sum the squares of the two parts
then take 10.log(), rather than 20.log(sqrt()).

Also, if comparing the magnitude against a threshold, it is much
cheaper to compare the square of the magnitude against the square of
the threshold, as this avoids a sqrt operation needed to find the
magnitude.

Also look at this family of cheap rectangular to magnitude
approximations:
http://www.dspguru.com/comp.dsp/tricks/alg/mag_est.htm

Regards,
Allan.

Tim Wescott · May 31, 2004

Luhan Monat wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

I designed a radio for my Master's thesis in 1990 that used this sort of
gimmick to decode 400 baud MSK on a Motorola 6811 -- it worked very
well, being only a dB or two below theoretically optimal performance.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Luhan Monat · May 31, 2004

Jim Thompson wrote:

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
fakemeout@nowhere.xyz> wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

Very interesting! Care to elaborate on your circuitry?

...Jim Thompson

Hi Jim,

Circuitry - two 22k resistors from the A/D input to + and ground
respectively, and a 0.1 uf cap from the source to the A/D input.

--
Luhan Monat: Luhan Knows at Yahoo dot Com
http://members.cox.net/berniekm
"The Future is not what it used to be."

Luhan Monat · May 31, 2004

Activ8 wrote:

On Mon, 31 May 2004 08:05:56 -0700, Jim Thompson wrote:

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
fakemeout@nowhere.xyz> wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

Very interesting! Care to elaborate on your circuitry?

...Jim Thompson

it's a PIC12F675. an 8 pin job. I guess you have to sample the hell
out of the tones to find the peaks. First you'd have to filter out
the high and low tones though.

No, I just time the samples for the tartget frequency. You dont
actually have to find the peak since the computations use both sine and
cosine - just like regular old FFT.

--
Luhan Monat: Luhan Knows at Yahoo dot Com
http://members.cox.net/berniekm
"The Future is not what it used to be."

Luhan Monat · May 31, 2004

Allan Herriman wrote:

On Tue, 01 Jun 2004 01:48:16 +1000, Allan Herriman
allan.herriman.hates.spam@ctam.com.au.invalid> wrote:

On Mon, 31 May 2004 07:49:07 -0700, Luhan Monat
fakemeout@nowhere.xyz> wrote:

You might want to use a sqrt to find the magnitude. However, if
converting to dB, it's better to just sum the squares of the two parts
then take 10.log(), rather than 20.log(sqrt()).

Also, if comparing the magnitude against a threshold, it is much
cheaper to compare the square of the magnitude against the square of
the threshold, as this avoids a sqrt operation needed to find the
magnitude.

Also look at this family of cheap rectangular to magnitude
approximations:
http://www.dspguru.com/comp.dsp/tricks/alg/mag_est.htm

Regards,
Allan.

Thanks, that answers my question.

--
Luhan Monat: Luhan Knows at Yahoo dot Com
http://members.cox.net/berniekm
"The Future is not what it used to be."

Joel Kolstad · May 31, 2004

Luhan Monat <fakemeout@nowhere.xyz> wrote:

I've been using this method for tone decoding on several projects so
far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

I can't say I've seen it used before, but I think it's a clever idea --
taking the usual 'correlation' approach and breaking it down to just 4
samples per period! Have you compared the performance against other, say,
DTMF decoders? I would suspect it's not quite as good, but given how
parsimonious its CPU requirements are, I'd say it's still a big 'win!'

I'd be particularly interested in comparing the performance to a straight
'bandpass filter using coefficients of 0/+/-1' approach. This doesn't
require the computation of I^2+Q^2 (which seems like it would be adequate
for your needs, right? The square root, as others have pointed out, is
rather slow to perform and is usually approximated anyway.), but needs
(noticeably) more than 2 additions or subtractions per period.

---Joel Kolstad

Fred Bloggs · May 31, 2004

Luhan Monat wrote:

Hi,

I've been using this method for tone decoding on several projects so far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have no
idea if this idea is original. Anybody know anything about this?

Yes- you are about 22 years behind the curve- this type of processing is
known as quadrature sampling with digital mixing:

Considine,V. "Digital Complex Sampling" Electronics Letters, 19, 4 Aug 1983
Rader, C.M., "A Simple Method for Sampling In-Phase and Quadrature
Components", IEEE Transactions Aerospace and Electronics Systems, Vol.
AES-20, No.6, November 1984
Rice,D. and Wu, K.,"Quadrature Sampling with High Dynamic Range", IEEE
Transactions Aerospace and Electronic Systems, Vol. AES-18, No.4, Nov 1982
Pellon,L.E.,"A Double Nyquist Digital Product detector for Quadrature
Sampling", IEEE Trans. Signal Processing, Vol.40,N0.7, July 1992

Luhan Monat · May 31, 2004

Fred Bloggs wrote:

Luhan Monat wrote:

Hi,

I've been using this method for tone decoding on several projects so
far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have
no idea if this idea is original. Anybody know anything about this?

Yes- you are about 22 years behind the curve- this type of processing is
known as quadrature sampling with digital mixing:

Considine,V. "Digital Complex Sampling" Electronics Letters, 19, 4 Aug 1983
Rader, C.M., "A Simple Method for Sampling In-Phase and Quadrature
Components", IEEE Transactions Aerospace and Electronics Systems, Vol.
AES-20, No.6, November 1984
Rice,D. and Wu, K.,"Quadrature Sampling with High Dynamic Range", IEEE
Transactions Aerospace and Electronic Systems, Vol. AES-18, No.4, Nov 1982
Pellon,L.E.,"A Double Nyquist Digital Product detector for Quadrature
Sampling", IEEE Trans. Signal Processing, Vol.40,N0.7, July 1992

Wow, only 22 years! Looks like I'm catching up.

--
Luhan Monat: Luhan Knows at Yahoo dot Com
http://members.cox.net/berniekm
"The Future is not what it used to be."

maxfoo · May 31, 2004

On Mon, 31 May 2004 15:32:09 -0700, Luhan Monat <fakemeout@nowhere.xyz> wrote:

Wow, only 22 years! Looks like I'm catching up.

That should get you an honorary doctorate degree from the prestigious 'S.E.D.'

Remove "HeadFromButt", before replying by email.

Bill Sloman · Jun 1, 2004

"Luhan Monat" <fakemeout@nowhere.xyz> wrote in message
news:4nOuc.8898$aM1.3033@fed1read02...

Fred Bloggs wrote:

Luhan Monat wrote:

Hi,

I've been using this method for tone decoding on several projects so
far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have
no idea if this idea is original. Anybody know anything about this?

Yes- you are about 22 years behind the curve- this type of processing is
known as quadrature sampling with digital mixing:

Considine,V. "Digital Complex Sampling" Electronics Letters, 19, 4 Aug
1983
Rader, C.M., "A Simple Method for Sampling In-Phase and Quadrature
Components", IEEE Transactions Aerospace and Electronics Systems, Vol.
AES-20, No.6, November 1984
Rice,D. and Wu, K.,"Quadrature Sampling with High Dynamic Range", IEEE
Transactions Aerospace and Electronic Systems, Vol. AES-18, No.4, Nov
1982
Pellon,L.E.,"A Double Nyquist Digital Product detector for Quadrature
Sampling", IEEE Trans. Signal Processing, Vol.40,N0.7, July 1992

Wow, only 22 years! Looks like I'm catching up.

The basic idea is definitely older - colour TV encodes the colour
information as sine and cosine components of the colour carrier (which is
something like 5MHz). The original systems used analog decoding in
quadrature to demodulate two separate colour signals from the 5MHz carrier.
IIRR RCA (America) and EMI (UK) patented identical systems at much the same
time, one describing it as "sine and cosine" as the other as "quadrature".

When the matter came to court, the lawyers couldn't be persuaded that the
systems were identical .....

--------
Bill Sloman, Nijmegen

Fred Bloggs · Jun 1, 2004

Bill Sloman wrote:

"Luhan Monat" <fakemeout@nowhere.xyz> wrote in message
news:4nOuc.8898$aM1.3033@fed1read02...

Fred Bloggs wrote:

Luhan Monat wrote:

Hi,

I've been using this method for tone decoding on several projects so
far...

http://members.cox.net/berniekm/qdft.html

Since I am nearly 100% self educated in electronics and such, I have
no idea if this idea is original. Anybody know anything about this?

Yes- you are about 22 years behind the curve- this type of processing is
known as quadrature sampling with digital mixing:

Considine,V. "Digital Complex Sampling" Electronics Letters, 19, 4 Aug

1983

Rader, C.M., "A Simple Method for Sampling In-Phase and Quadrature
Components", IEEE Transactions Aerospace and Electronics Systems, Vol.
AES-20, No.6, November 1984
Rice,D. and Wu, K.,"Quadrature Sampling with High Dynamic Range", IEEE
Transactions Aerospace and Electronic Systems, Vol. AES-18, No.4, Nov

1982

Pellon,L.E.,"A Double Nyquist Digital Product detector for Quadrature
Sampling", IEEE Trans. Signal Processing, Vol.40,N0.7, July 1992

Wow, only 22 years! Looks like I'm catching up.

The basic idea is definitely older - colour TV encodes the colour
information as sine and cosine components of the colour carrier (which is
something like 5MHz). The original systems used analog decoding in
quadrature to demodulate two separate colour signals from the 5MHz carrier.
IIRR RCA (America) and EMI (UK) patented identical systems at much the same
time, one describing it as "sine and cosine" as the other as "quadrature".

When the matter came to court, the lawyers couldn't be persuaded that the
systems were identical .....

--------
Bill Sloman, Nijmegen

The idea here is not quadrature decoding per se but digital quadrature
decoding using a single sampling channel. The impetus for this
development was the shortfall in the analog circuitry available at the
time for maintaining the quadrature in phase and amplitude across the
requisite bandwidth at the required precision.

Quardrature Direct Fourier Transform

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