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From: Sohaib Afzal on 2 Jan 2010 02:07
I am probably doing everything wrong:

The frequency i am searching for is stored in K. this code runs for K=
120, 260, ...12000
NN is my bin width, x is the signal.

for N=NN:NN:size of x
for each K
find coeff, put Q1 and Q2 = 0
for n=NN consecutive integers, determined using N
Q0(K) = coeff*Q1(K) - Q2(K) + x(n);
Q2(K) = Q1(K);
Q1(K) = Q0(K);
end;
pow(K) = Q1(K)*Q1(K) + Q2(K)*Q2(K) - coeff*Q1(K)*Q2(K);

i plot pow. Different plots for different values of N.
Ten lines of code :)

When i did fft, i got large peaks at 2000, 4500, 6000 as well as at
some smaller frequencies. But my code gives only tiny or no peaks
above 1200.

My implementation is probably/definitely wrong, but please also tell
me if it is recommended to use goertzel algo to view the audio
spectrum in real time, or would i be better-off using fft? I think
differentiation etc would be very difficult in the PIC controller.

By "sweeping it across the frequency range" do you mean i need to
apply goertzel to all values of K between 120 and 12000, i.e. also to
121, 122, 123... etc?

Thanks for helping!
From: Jerry Avins on 2 Jan 2010 11:10
Sohaib Afzal wrote:
> I am probably doing everything wrong:
>
> The frequency i am searching for is stored in K. this code runs for K=
> 120, 260, ...12000
> NN is my bin width, x is the signal.
>
> for N=NN:NN:size of x
> for each K
> find coeff, put Q1 and Q2 = 0
> for n=NN consecutive integers, determined using N
> Q0(K) = coeff*Q1(K) - Q2(K) + x(n);
> Q2(K) = Q1(K);
> Q1(K) = Q0(K);
> end;
> pow(K) = Q1(K)*Q1(K) + Q2(K)*Q2(K) - coeff*Q1(K)*Q2(K);
>
> i plot pow. Different plots for different values of N.
> Ten lines of code :)
>
> When i did fft, i got large peaks at 2000, 4500, 6000 as well as at
> some smaller frequencies. But my code gives only tiny or no peaks
> above 1200.
>
> My implementation is probably/definitely wrong, but please also tell
> me if it is recommended to use goertzel algo to view the audio
> spectrum in real time, or would i be better-off using fft? I think
> differentiation etc would be very difficult in the PIC controller.
>
> By "sweeping it across the frequency range" do you mean i need to
> apply goertzel to all values of K between 120 and 12000, i.e. also to
> 121, 122, 123... etc?

What do you expect from your code? If you think of an FT as a banl of
filters, each tuned to the center frequency of a "bin"m then a Goertzel
is a single filter tuned to a single bin. You may be enlightened by
http://www.mstarlabs.com/dsp/goertzel/goertzel.html

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: Jerry Avins on 2 Jan 2010 11:17
Jerry Avins wrote a jumble.

What do you expect from your code? If you think of an FT as a bank of
filters, each tuned to the center frequency of a "bin", then a Goertzel
is a single filter tuned to a single bin. You may be enlightened by
http://www.mstarlabs.com/dsp/goertzel/goertzel.html (Particularly by the
figure with the green border that shows the response to a wide spectrum.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: maury on 4 Jan 2010 17:21
On Jan 2, 1:07 am, Sohaib Afzal <504...(a)gmail.com> wrote:
> I am probably doing everything wrong:
>
> The frequency i am searching for is stored in K. this code runs for K=
> 120, 260, ...12000
> NN is my bin width, x is the signal.
>
> for N=NN:NN:size of x
>     for each K
>        find coeff, put Q1 and Q2 = 0
>        for n=NN consecutive integers, determined using N
>             Q0(K) = coeff*Q1(K) - Q2(K) + x(n);
>             Q2(K) = Q1(K);
>             Q1(K) = Q0(K);
>        end;
>        pow(K) = Q1(K)*Q1(K) + Q2(K)*Q2(K) - coeff*Q1(K)*Q2(K);
>
> i plot pow. Different plots for different values of N.
> Ten lines of code :)
>
> When i did fft, i got large peaks at 2000, 4500, 6000 as well as at
> some smaller frequencies. But my code gives only tiny or no peaks
> above 1200.
>
> My implementation is probably/definitely wrong, but please also tell
> me if it is recommended to use goertzel algo to view the audio
> spectrum in real time, or would i be better-off using fft? I think
> differentiation etc would be very difficult in the PIC controller.
>
> By "sweeping it across the frequency range" do you mean i need to
> apply goertzel to all values of K between 120 and 12000, i.e. also to
> 121, 122, 123... etc?
>
> Thanks for helping!

Sohaib,
I am assuming that your are running the Goertzel aganist K for each
tone you need, and NN is the number of samples taken from K in
consecutive order in NN steps. What I use to give a fairly accurate
amplitude measure is (using your notation)

y(N:N+NN-1) = sqrt(Q1^2 + Q2^2 - (Q1 * Q2 * coeff))*2/NN

For an approximate of power square y, pow(N:N+NN-1) = (Q1^2 + Q2^2 -
(Q1 * Q2 * coeff))*4/NN^2. This might work.

Also, there's a lot going on where you say
for each K
find coeff

in Matlab lingo, you should have something like

k = fix(0.5 + NN*f/Fs);
w = (2*pi/NN)*k;
cosine = cos(w);
coeff = 2 * cosine;

CAUTION: in Matlab the use of fix( ) could be important.

Maurice Givens

From: Sohaib Afzal on 5 Jan 2010 14:17
Thanks for your interest.
This is what i am trying to do:
K is an array of the frequencies i am looking for (sorry about the
confusing naming).
K = [120, 260, 660, 990, 1200, 2400, 6000, 10000]; (in Hertz)
I take NN samples from my input signal x, and then for each value of
K, i apply the code i gave above. I use the formula you have given for
magnitude calculation (although i didnt scale with 2/NN)
I do find the coefficients exactly as you have described, (although i
hav named f as K...)

After i get the values for magnitude, y, for NN consecutive samples of
signal x, i plot all the magnitudes y (corresponding to each frequency
K) on the same plot.

Ascii art:
|
|
|
|
| o
|o |
|| |
|| |
|| |
|| |
|| |
|| | o
|| | | o
|| | | | o
||_|_|_|_________|
_____________________________o_______________________________o_______
0 1000 2000 3000 4000 5000 6000 7000 8000
9000 10000

The problem is that for low frequencies, y has a very large value, and
for high frequencies, a very low value. I plot this graph for each NN
samples of x, and all the plots have this same problem.

What i expect from my code: plots for each NN consecutive values. The
x axis of the plots has values of frequency, K, and the y axis has
amplitude. The amplitudes should be the same order of magnitude, but
aren't.

When i apply the goertzel function in matlab:
y = goertzel(x, K);
plot(K, abs(y));
then i get the kind of plot i am looking for.

If i succeed in making my own code work, i eventually aim to implement
it in the PIC microcontroller.

.....
The sampling frequency is 22050 Hz. I have tried taking various values
of NN. Larger NN, say 900, give an even greater difference between the
values of y corresponding to high and low values of frequency K.
My code works quite well if i generate a signal myself in Matlab (sum
of a few sinusoids of different frequencies). But the problem is
happening when i get the signal from the function wavread (which reads
a .wav file and generates an array containing samples of its
magnitude).

Two questions:
Why does the goertzel function of Matlab not need sampling frequency
as an input?
And why does it give an error when i give it NN samples of x, and a
frequency K greater than NN? Does Goertzel algorithm require the
sample window NN to be larger than the greatest frequency being
searched for?

Thank you all for helping!
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