On Wed, 23 Oct 2013 14:48:38 -0700 (PDT), maury <maury001@core.com>
wrote:

>On Friday, October 18, 2013 3:43:25 PM UTC-5, Eric Jacobsen wrote:
>> On Fri, 18 Oct 2013 12:54:51 -0700 (PDT), makolber@yahoo.com wrote:
>>
>>
>>
>> >I thought the Goertzel was used to reduce computation when only a few frequency bin outputs are needed, not to reduce the number of input time samples.
>>
>> >
>>
>> >Mark
>>
>>
>>
>> Pretty much. One of the driving applications was DTMF detection for
>>
>> telephone key presses. In that case there are only a few known tones
>>
>> to detect and it must be done quickly and cheaply.
>>
>>
>>
>>
>>
>>
>>
>> Eric Jacobsen
>>
>> Anchor Hill Communications
>>
>> http://www.anchorhill.com
>
>AND, using slow, fixed-point, inefficient processors.

Exactly. So having a really simple algorithm with low computational
complexity was necessary for the job. Not having many multiplies
helped, since on many of the candidate processors multiplies tended
to take way longer than adds/subtracts.
Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

Reply by maury●October 23, 20132013-10-23

On Friday, October 18, 2013 3:43:25 PM UTC-5, Eric Jacobsen wrote:

> On Fri, 18 Oct 2013 12:54:51 -0700 (PDT), makolber@yahoo.com wrote:
>
>
>
> >I thought the Goertzel was used to reduce computation when only a few frequency bin outputs are needed, not to reduce the number of input time samples.
>
> >
>
> >Mark
>
>
>
> Pretty much. One of the driving applications was DTMF detection for
>
> telephone key presses. In that case there are only a few known tones
>
> to detect and it must be done quickly and cheaply.
>
>
>
>
>
>
>
> Eric Jacobsen
>
> Anchor Hill Communications
>
> http://www.anchorhill.com

AND, using slow, fixed-point, inefficient processors.

Reply by Rick Lyons●October 19, 20132013-10-19

>On Fri, 18 Oct 2013 09:00:34 -0700, techsavyjoe wrote:
>

[Snipped by Lyons]

>
>Even assuming that you've got an environment where the Goertzel is more
>efficient, the IDFT isn't useful to do one bin at a time -- one "bin" of
>the IDFT is just the signal value at one particular delay, and you're
>generally interested in enough of them that it's far more efficient to do

>the whole thing using the fast Fourier transform algorithm.

Hi Tim,
I agree with what you're saying here. I wonder if the
DSP beginners in this thread understand that
implementing the Goertzel algorithm, over N time-
domain samples, produces a *SINGLE* frequency-
domain sample. And when they write about performing
an IDFT using Goertzel, are they thinking about producing
a *SINGLE* time-domain sample?
If they *ARE* talking about producing a single time-domain
sample based on N freq-domain samples, it seems to me
that you could do this using the Goertzel algorithm.
I haven't tried this out, but I'm willing to bet one bottle of
beer that you could (1) conjugate all your freq-domain
samples, (2) perform a standard N-point Goertzel
process to produce a single complex-valued time-
domain sample, and (3) conjugate that single
time-domain sample to arrive at your final result.
Just a thought,
[-Rick-]
_____________________________
Posted through www.DSPRelated.com

Reply by Steve Underwood●October 18, 20132013-10-18

On 10/19/2013 04:43 AM, Eric Jacobsen wrote:

> On Fri, 18 Oct 2013 12:54:51 -0700 (PDT), makolber@yahoo.com wrote:
>
>> I thought the Goertzel was used to reduce computation when only a few frequency bin outputs are needed, not to reduce the number of input time samples.
>>
>> Mark
>
> Pretty much. One of the driving applications was DTMF detection for
> telephone key presses. In that case there are only a few known tones
> to detect and it must be done quickly and cheaply.

I think it only got associated with DTMF detection because of a few
application notes.
Goertzel has been widely used for tone detection, especially on the
PSTN, where the frequency of the expected tone is well known, but the
duration doesn't need to be detected precisely. Of course, tone
detection is trivial. Avoiding false detection is where things get
interesting, and a wide range of approaches have been combined with
Goertzel to deal with false detections.
For things like 2280Hz/2600Hz signalling, where the duration of the tone
needs to be passed on precisely, a purely time domain approach has
generally proved more suitable.
Steve

Reply by Eric Jacobsen●October 18, 20132013-10-18

On Fri, 18 Oct 2013 12:54:51 -0700 (PDT), makolber@yahoo.com wrote:

>I thought the Goertzel was used to reduce computation when only a few frequency bin outputs are needed, not to reduce the number of input time samples.
>
>Mark

Pretty much. One of the driving applications was DTMF detection for
telephone key presses. In that case there are only a few known tones
to detect and it must be done quickly and cheaply.
Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

Reply by ●October 18, 20132013-10-18

I thought the Goertzel was used to reduce computation when only a few frequency bin outputs are needed, not to reduce the number of input time samples.
Mark

Reply by ●October 18, 20132013-10-18

On Thursday, December 22, 2011 8:48:25 AM UTC-5, aredo3606gif wrote:

> Hello,
>
>
>
> I found various documents regarding the Goertzel Algorithm along with
>
> formulas, pseudocodes and Fortran implementations as a way for performing a
>
> faster and more accurate DFT in real-time on a small number of samples.
>
> However what I don't get is that I can't find any example for the IDFT of
>
> the Goertzel algorithm. What is the trick to get the inverse computation
>
> out of using Goertzel either 1st order or 2nd order?
>
> Is it as simple as with DFT where a sign inversion practically inverses the
>
> transform or is it more difficult to achieve?
>
> Otherwise while Goertzel is not limited to 2^N input number of samples the
>
> standard IDFT is so using IDFT on a Goertzel computed DFT would surely lead
>
> to errors,right?
>
> If anyone could explain to me more clearly and provide a way to do inverse
>
> Goertzel both 1st order and 2nd order..
>
> Thanks.

In theory you can do the inverse transform via a Goertzel process, but let's go over why that brings new problems to the table.
Standard Goertzel is a process whereby you recursively compute a single value of the DFT given a series of real valued data.
To go the other way will work the same if your DFT's frequency values are all real valued and you make the oscillator rotate the other way. However, having only real valued frequency data is unlikely to be the case. Now the Goerzel algo is one version of using a driven oscillator to find a single DFT value, so you can drive the oscillator with complex values to achieve the desired result, but the extra computational machinery is going to nullify the savings that standard Goertzel brings to the table.
The driven oscillator idea extends to doing cosine transforms as well, and you can find some .jpg engines using this algo.
Clay

Reply by Tim Wescott●October 18, 20132013-10-18

On Fri, 18 Oct 2013 09:00:34 -0700, techsavyjoe wrote:

> I too was searching for an answer to this problem,(I too am learning
> DSP).
> I think u can find the idft using goertzel algorithm with the fact that
> time is reciprocal to frequency.
>
> so dft{dft{x(n)}}=dft{X(k)}=N*x(-n)
> N is the length of the dft sequence.
>
> so u actually find the dft of X(k) which is nothing but N*x(-n).

The Goertzel algorithm is, in my opinion, a honey trap set out to entrap
beginners to DSP.
It is a supposedly-efficient way of finding just one bin of the DFT. As
such, it can come in handy when you need to separate out just one
frequency component from a signal.
If you need lots of frequency information then the fast Fourier transform
is more efficient.
If you want to trade off clarity in your software for storage space, then
doing a multiply and accumulate reads much easier and assuming a pre-
calculated sine table should actually take fewer clock ticks on modern
processors, and many fewer clock ticks on a DSP with dedicated MAC
hardware.
Even assuming that you've got an environment where the Goertzel is more
efficient, the IDFT isn't useful to do one bin at a time -- one "bin" of
the IDFT is just the signal value at one particular delay, and you're
generally interested in enough of them that it's far more efficient to do
the whole thing using the fast Fourier transform algorithm.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Reply by ●October 18, 20132013-10-18

I too was searching for an answer to this problem,(I too am learning DSP).
I think u can find the idft using goertzel algorithm with the fact that time is reciprocal to frequency.
so dft{dft{x(n)}}=dft{X(k)}=N*x(-n)
N is the length of the dft sequence.
so u actually find the dft of X(k) which is nothing but N*x(-n).

Reply by Rick Lyons●December 22, 20112011-12-22

>Hello,
>
>I found various documents regarding the Goertzel Algorithm along with
>formulas, pseudocodes and Fortran implementations as a way for performing

a

>faster and more accurate DFT in real-time on a small number of samples.
>However what I don't get is that I can't find any example for the IDFT of
>the Goertzel algorithm. What is the trick to get the inverse computation
>out of using Goertzel either 1st order or 2nd order?
>Is it as simple as with DFT where a sign inversion practically inverses

the

>transform or is it more difficult to achieve?
>Otherwise while Goertzel is not limited to 2^N input number of samples

the

>standard IDFT is so using IDFT on a Goertzel computed DFT would surely

lead

>to errors,right?
>If anyone could explain to me more clearly and provide a way to do

inverse

>Goertzel both 1st order and 2nd order..
>Thanks.

Hi.
Humm, what exactly is an 'inverse Geortzel'
process. The output of a Goertzel operation is a
single complex number, in the form of X = a+jb.
Now given that a+jb sample, what is it you're
trying to compute? I hope you're not trying to
compute the input time samples that were used
to compute the X = a+jb sample.
[-Rick-]