Problem: stuck with simple spectral analysis

I am just beginning to conquer the FFT stuff and I already need some major
help.

I would like to draw a very rough estimate of signal spectrum using Don's
FFT.

I do the following after running a chunk of data:

//----------------------------

for(unsigned int n=0; n < N/2-1; n++)
{
 float power = 20*log10( re[n] * re[n] + im[n] * im[n] );
}

//----------------------------

As I understand, I only need the first half of data since real input
produces "mirrored" FFT.

The problem is that compared to commercial spectrum analyzers, my results
make no sense. Relatively, the lower frequencies should have much more
power, while any component above 18K should be very, very small. What I get
is almost flat. You would never tell what frequency range you are in by
looking at the numbers. A quick code that draws the spectrum also confirms
it. I cannot see any power reduction in the high frequency range, and I
should. Also, I do try windowing, but it does not help. By the way, is this
hamming code correct? I wrote it myself so I would need to check with the
pros :-)

//----------------------------

void WindowFFTData(float* pLeft, float* pRight)
{
     for(unsigned int n = 0; n < N; n++)
    {
     const float Coeff = 0.54 - 0.46 * cos( 2 * M_PI * n / (N-1)  );
     pLeft[n] *= Coeff;
     pRight[n] *= Coeff;
    }
}

//----------------------------

I will appreciate any help, guys. Thank you.

-- 
Andy

"Andy" <none@none.com> wrote in message
news:xJv_a.48578$Sr6.8389@fe08.atl2.webusenet.com...
> I am just beginning to conquer the FFT stuff and I already need some major
> help.
>
> I would like to draw a very rough estimate of signal spectrum using Don's
> FFT.
>
> I do the following after running a chunk of data:
>
> //----------------------------
>
> for(unsigned int n=0; n < N/2-1; n++)
> {
>  float power = 20*log10( re[n] * re[n] + im[n] * im[n] );
> }
>
> //----------------------------
>
> As I understand, I only need the first half of data since real input
> produces "mirrored" FFT.
>
> The problem is that compared to commercial spectrum analyzers, my results
> make no sense. Relatively, the lower frequencies should have much more
> power, while any component above 18K should be very, very small. What I
get
> is almost flat. You would never tell what frequency range you are in by
> looking at the numbers. A quick code that draws the spectrum also confirms
> it. I cannot see any power reduction in the high frequency range, and I
> should. Also, I do try windowing, but it does not help. By the way, is
this
> hamming code correct? I wrote it myself so I would need to check with the
> pros :-)
>
> //----------------------------
>
> void WindowFFTData(float* pLeft, float* pRight)
> {
>      for(unsigned int n = 0; n < N; n++)
>     {
>      const float Coeff = 0.54 - 0.46 * cos( 2 * M_PI * n / (N-1)  );
>      pLeft[n] *= Coeff;
>      pRight[n] *= Coeff;
>     }
> }
>
> //----------------------------
>
> I will appreciate any help, guys. Thank you.

Andy,

Many commercial analyzers use a log frequency scale.  This means that equal
divisions of the frequency scale have fewer or greater absolute bandwidths.
Example:  1 octave resolution has 50Hz from 50 to 100Hz, 100Hz from 100 to
200Hz, etc.

You didn't say what the spectral shape was in terms of frequency scale.  So,
if it has high per Hz energy at low frequencies on a linear scale and the
per Hz energy decreases with frequency, it will have a flatter curve if the
plot is converted to one with frequency resolution with a log basis.

Fred

On 13-Aug-2003, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:

> it will have a flatter curve if the
> plot is converted to one with frequency resolution with a log basis.

Thanks for the reply, Fred. I am actually using the one in Sound Forge and
you can switch between log an linear. In log, you are right, the curve is
quite flat at most of the range. So, checking again, I am looking at the
linear scale where, starting from 0 Hz to 22.05 Hz, power goes from about
-64 to -120 dB. I guess that's relative power, but no matter - that's not
the picture I get when trying to simulate it. The power does not reduce at
high frequencies, for some reason. I went back to basics and made sure I am
using the FFT right. I used an example from "Understanding DSP" by R. Lyons
- my output is dead on. It is really baffling :0

-- 
Andy

"Every nation has the government it deserves."

"Andy" <none@none.com> wrote in message
news:ruy_a.61272$Ll4.2775@fe14.atl2.webusenet.com...
>
> On 13-Aug-2003, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:
>
> > it will have a flatter curve if the
> > plot is converted to one with frequency resolution with a log basis.
>
> Thanks for the reply, Fred. I am actually using the one in Sound Forge and
> you can switch between log an linear. In log, you are right, the curve is
> quite flat at most of the range. So, checking again, I am looking at the
> linear scale where, starting from 0 Hz to 22.05 Hz, power goes from about
> -64 to -120 dB. I guess that's relative power, but no matter - that's not
> the picture I get when trying to simulate it. The power does not reduce at
> high frequencies, for some reason. I went back to basics and made sure I
am
> using the FFT right. I used an example from "Understanding DSP" by R.
Lyons
> - my output is dead on. It is really baffling :0

Andy,

Well, if your output is dead on, then what's the problem?  Let's see .......

Oh!  You said zero Hz!  Well, that probably could be zero if you were to
remove the average from the original data.  If there's a large average, then
that could "artificially" give a high value at zero Hz.  I say artificially
because there may simply be a large dc offset in the data that isn't
representative of anything you're interested in.

You've thrown in a bunch of things without explanation - so it's impossible
to go further.  18K???, absolute numbers like -64 and -120dB, etc.  What the
heck is the signal you're analyzing?

Fred

On 13-Aug-2003, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:

> absolute numbers like -64 and -120dB

Heh, I did say I thought this is relative - my test segment is just a piece
of music :) I try to keep away from the -92 dB mark unless I deal with noise
:)

I am mostly interested in getting a spectral signature that matches. I think
you have a great point about DC. I will have to look into that further
because that just might be it. Oh well, welcome to the world of DSP, where
everything is a bit more complicated than it should be :-)

-- 
Andy

"Every nation has the government it deserves."

"Andy" <none@none.com> wrote in message news:<ruy_a.61272$Ll4.2775@fe14.atl2.webusenet.com>...
> On 13-Aug-2003, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:
> 
> > it will have a flatter curve if the
> > plot is converted to one with frequency resolution with a log basis.
> 
> Thanks for the reply, Fred. I am actually using the one in Sound Forge and
> you can switch between log an linear. In log, you are right, the curve is
> quite flat at most of the range. So, checking again, I am looking at the
> linear scale where, starting from 0 Hz to 22.05 Hz, power goes from about
> -64 to -120 dB. I guess that's relative power, but no matter - that's not
> the picture I get when trying to simulate it. The power does not reduce at
> high frequencies, for some reason. I went back to basics and made sure I am
> using the FFT right. I used an example from "Understanding DSP" by R. Lyons
> - my output is dead on. It is really baffling :0

Given that you are using Sound Forge as a reference I am assuming that
you are attempting to make a real time analyzer that measures the
power on a octave or third octave basis. I'm pretty sure this is what
your reference would be doing.

The bins that contain the your power spectrum estimate are of fixed
bandwidth whereas you want to bin the energy in bands that have
increasing bandwidth with increasing frequency (constant Q). If your
using an FFT/periodogram to do this then you will need to combine
multiple bins to form each band and most likely interpolate between
bins at the low frequnecy end.

If you weren't attempting to make an RTA then you could try the AtSpec
demo version out as a reference to getting your code running the way
you expect it to.

Regards,


Paavo Jumppanen
Author of AtSpec : A 2 channel PC based FFT spectrum analyzer
http://www.taquis.com

"Andy" <none@none.com> wrote in message
news:eVC_a.44772$gL3.20347@fe07.atl2.webusenet.com...
>
> On 13-Aug-2003, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:
>
> > absolute numbers like -64 and -120dB
>
> Heh, I did say I thought this is relative - my test segment is just a
piece
> of music :) I try to keep away from the -92 dB mark unless I deal with
noise
> :)
>
> I am mostly interested in getting a spectral signature that matches. I
think
> you have a great point about DC. I will have to look into that further
> because that just might be it. Oh well, welcome to the world of DSP, where
> everything is a bit more complicated than it should be :-)

Andy,

Well everything should only be as complicated as it needs to be.  Albert
Einstein said: "everything should be as simple as it is, but not simpler."

"Making the simple complicated is commonplace; making the complicated
simple, awesomely simple, that's creativity." -- Charles Mingus

It's a quest to keep things simple / understandable to the least
sophisticated audience.  I get a great kick out of helping folks "get it".

Getting a spectral signature that "matches"??  That's a *very* tough problem
if you need it to work well.  Often there are too many matches compared to
what you'd like.  Depends on the situation a lot and on the expectations!!

Fred

On 14-Aug-2003, PaavoJumppanen@iname.com (Paavo Jumppanen) wrote:

> If you weren't attempting to make an RTA then you could try the AtSpec
> demo version out as a reference to getting your code running the way
> you expect it to.

No no, not RTA - in SF it's under "Tools", where it analyzes the current
selection. Ok, basic question: in theory, if I collect the average power of
all components in FFT and plot them - is that my basic spectrum? Are there
any catches to it? I mean, I went over the theory quite a few times, but I
think the practical side has more to it than that.

Sorry for not providing enough information in the beginning - I guess that
goes to show you that I have little idea about what I am doing :)
-- 
Andy

Andy wrote:
> 
  ...

> everything is a bit more complicated than it should be :-)
> 
In home repair, that's called "The Mushroom Effect". Under different
aliases, it's universal.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Andy wrote:

> The problem is that compared to commercial spectrum analyzers,
> my results make no sense. Relatively, the lower frequencies
> should have much more power, while any component above 18K
> should be very, very small. What I get is almost flat.

So your results still differ from Sound Forge's after checking your 
use of the routine. But have you checked if Don's FFT code itself is 
actually working properly? You might probe it with some simpler test 
signals than your music snippet (single sinusoids at various 
frequencies and amplitudes, for starters) and see if the results are 
sane.

> const float Coeff = 0.54 - 0.46 * cos( 2 * M_PI * n / (N-1) );

You should divide by N, not (N-1), as the latter duplicates the first 
window point which already belongs to the next cos period.


Martin