Goertzl Algorithm
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From: Vladimir Vassilevsky on 30 Mar 2010 19:01 Ron N. wrote: > On Mar 28, 5:14 am, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote: > >>Rick Lyons wrote: >> >>>On Fri, 26 Mar 2010 19:46:26 -0700 (PDT), "Ron N." >>><rhnlo...(a)yahoo.com> wrote: >>> >>>>Somewhere on my website is an explanation of >>>>this 1-bin DFT/Goertzel "leakage": >>>>http://www.nicholson.com/rhn/dsp.html >> >>>It's the "Frequency Response of Zero-padded FFT/DFT" >>>section of your web page. By the way, I thnk your >>>"Common FFT Usage Misconceptions" material is interesting. >> >>The most common FFT misconception is the one with is scaling of the FFT >>results. It had been 1000 times when I had to explain them that they >>can't compare 512pt FFT to 4096pt FFT directly; people just don't seem >>to understand that. > > > I would believe there could be confusion about that. What do you find > to be the most common area of misconception? The frequency > represented by a particular bin number? The bin "width"? Something > about the time/resolution trade-off when changing the number of > points? > > I'll add that to my list. Let's say there is a mix of a sine wave and a white noise. They take a 512-pt FFT of this mix, measure the amplitude of the FFT peak and the noise floor level, then calculate peak to noise floor difference in dB. They are absolutely sure this number === actual SNR. Then they take another measurement, using FFT with 4096 points at this time. They calculate SNR in the same way, and compare it to the first result. -Aha! We got an improvement! Not very many people actually understand what is the meaning of the FFT result, and what is the relation between dB, V and V/root(Hz). VLV
From: Eric Jacobsen on 30 Mar 2010 19:15 On 3/30/2010 4:01 PM, Vladimir Vassilevsky wrote: > > > Ron N. wrote: > >> On Mar 28, 5:14 am, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote: >> >>> Rick Lyons wrote: >>> >>>> On Fri, 26 Mar 2010 19:46:26 -0700 (PDT), "Ron N." >>>> <rhnlo...(a)yahoo.com> wrote: >>>> >>>>> Somewhere on my website is an explanation of >>>>> this 1-bin DFT/Goertzel "leakage": >>>>> http://www.nicholson.com/rhn/dsp.html >>> >>>> It's the "Frequency Response of Zero-padded FFT/DFT" >>>> section of your web page. By the way, I thnk your >>>> "Common FFT Usage Misconceptions" material is interesting. >>> >>> The most common FFT misconception is the one with is scaling of the FFT >>> results. It had been 1000 times when I had to explain them that they >>> can't compare 512pt FFT to 4096pt FFT directly; people just don't seem >>> to understand that. >> >> >> I would believe there could be confusion about that. What do you find >> to be the most common area of misconception? The frequency >> represented by a particular bin number? The bin "width"? Something >> about the time/resolution trade-off when changing the number of >> points? >> >> I'll add that to my list. > > > Let's say there is a mix of a sine wave and a white noise. They take a > 512-pt FFT of this mix, measure the amplitude of the FFT peak and the > noise floor level, then calculate peak to noise floor difference in dB. > They are absolutely sure this number === actual SNR. > > Then they take another measurement, using FFT with 4096 points at this > time. They calculate SNR in the same way, and compare it to the first > result. -Aha! We got an improvement! > > Not very many people actually understand what is the meaning of the FFT > result, and what is the relation between dB, V and V/root(Hz). > > > VLV "Processing gain" seems counter-intuitive to some people. Sometimes you can get the idea across to people with an rf background by explaining it's no different than SNR improvement via BW reduction. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: Vladimir Vassilevsky on 31 Mar 2010 11:27 Eric Jacobsen wrote: > On 3/30/2010 4:01 PM, Vladimir Vassilevsky wrote: > >>>> The most common FFT misconception is the one with is scaling of the FFT >>>> results. > "Processing gain" seems counter-intuitive to some people. Sometimes you > can get the idea across to people with an rf background by explaining > it's no different than SNR improvement via BW reduction. Let's put it simpler. It is very common that FFT plots are in dB wrt full scale. What I really want to see is the spectral density plot (W/Hz). Most people just can't understand the difference. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
From: Thad Smith on 2 Apr 2010 11:53 Mark wrote: > Thad Smith wrote: >>>> ... >>>> It worked after adding the following line: >>>> #define PI 3.14159265358979 >>>> >>>> PI is not defined by the either of the standard headers. >>>> >>> >>> Did you try M_PI? >> >> That's not defined by a Standard C header, either. Either one of >> those might be defined in a non-conforming compiler, but not Standard >> C. > So the C standard leaves PI defintion, as well as other constants (for > example, log2e, log10e) to implementation? No. It is left to the careful programmer. It could have been defined in Standard C, but wasn't (there may be a need to define separate values for double and long double, possibly float). Since there is no definition of pi in Standard C, the careful programmer provides his own, giving a portable program. If compiler XYZ defines PI or M_PI, and you use it, the program works for that compiler, but not another. There are probably portable add-on libraries that add those constants and other useful constants and functions. For publishing code though, it makes more sense to me to add one additional line to make it not compiler-dependent. -- Thad
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