Reply by Vladimir Vassilevsky●January 5, 201020100105
Hello all,
Could you suggest a reading about the effects of clock jitter in
deltasigma ADCs ? How does it affect SNR, THD, IMD, SFDR ? For some
reason, this practical aspect is not mentioned in the ADC datasheets and
manuals; the typical phrase is "good quality low jitter clock should be
provided", whatever it means.
It shouldn't be too difficult to figure out the numbers by hand; however
I am pretty sure there must be a closed form solution already.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Reply by Sohaib Afzal●January 5, 201020100105
oops. the ascii art width was too large. umm.
This is like what i am getting:
(y)




 o
o





 o
  o
   o
_____________________________o_______________________o_
0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k
(K)
This is what the goertzel function is showing:
(and Windows Media Player etc too)
(y)



 o
 o 
o o o 
  o   o
     
     
     
     
     
     
     
_____________________________________________________
0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k
(K)
Reply by Sohaib Afzal●January 5, 201020100105
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!
Reply by maury●January 4, 201020100104
On Jan 2, 1:07�am, Sohaib Afzal <504...@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 betteroff 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+NN1) = sqrt(Q1^2 + Q2^2  (Q1 * Q2 * coeff))*2/NN
For an approximate of power square y, pow(N:N+NN1) = (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
Reply by Jerry Avins●January 2, 201020100102
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.
�����������������������������������������������������������������������
Reply by Jerry Avins●January 2, 201020100102
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 betteroff 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.
�����������������������������������������������������������������������
Reply by Sohaib Afzal●January 2, 201020100102
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 betteroff 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!
Reply by Tim Wescott●December 31, 200920091231
On Thu, 31 Dec 2009 14:41:14 0500, Jerry Avins wrote:
> Sohaib Afzal wrote:
>> Hi
>>
>> I am trying to use the goertzel algo to make a real time audio spectrum
>> analyzer using a PIC controller. I have started out by trying it on
>> Matlab, but i am getting this problem:
>>
>> The high frequency peaks in the power graph are much smaller than the
>> low frequency peaks. For example, the peak at 60Hz is, say 50 units on
>> the plot, then the peak at 8000Hz is only 0.023 units or so. Windows
>> Media Player and other players show the peaks are approximately the
>> same size throughout the sound file (.wav) that i am testing.
>>
>> Please tell me if this algorithm is appropriate for what i am doing,
>> and if this difference in the magnitudes of peaks for power is usual or
>> due to some error in coding.
>
> The Goertzel algorithm is effectively a stripped Fourier transform that
> looks at only a few frequencies. It is useful, for example, for
> detecting DTMF tones. If there is a good way to use it for displaying a
> broad spectrum, I don't know of it.
If you were willing to sweep it across the frequency range it could be
made to work  but that's not what the OP says he's doing.
Hmm. Need more detail...

www.wescottdesign.com
Reply by Jerry Avins●December 31, 200920091231
Sohaib Afzal wrote:
> Hi
>
> I am trying to use the goertzel algo to make a real time audio
> spectrum analyzer using a PIC controller. I have started out by trying
> it on Matlab, but i am getting this problem:
>
> The high frequency peaks in the power graph are much smaller than the
> low frequency peaks. For example, the peak at 60Hz is, say 50 units on
> the plot, then the peak at 8000Hz is only 0.023 units or so. Windows
> Media Player and other players show the peaks are approximately the
> same size throughout the sound file (.wav) that i am testing.
>
> Please tell me if this algorithm is appropriate for what i am doing,
> and if this difference in the magnitudes of peaks for power is usual
> or due to some error in coding.
The Goertzel algorithm is effectively a stripped Fourier transform that
looks at only a few frequencies. It is useful, for example, for
detecting DTMF tones. If there is a good way to use it for displaying a
broad spectrum, I don't know of it.
Jerry

Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Vladimir Vassilevsky●December 31, 200920091231
What you are doing is wrong in so many ways.
If your goal is nice looking visualization, just differentiate a signal,
measure distance between zero crossings and display the periodogram.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Sohaib Afzal wrote:
> Hi
>
> I am trying to use the goertzel algo to make a real time audio
> spectrum analyzer using a PIC controller. I have started out by trying
> it on Matlab, but i am getting this problem:
>
> The high frequency peaks in the power graph are much smaller than the
> low frequency peaks. For example, the peak at 60Hz is, say 50 units on
> the plot, then the peak at 8000Hz is only 0.023 units or so. Windows
> Media Player and other players show the peaks are approximately the
> same size throughout the sound file (.wav) that i am testing.
>
> Please tell me if this algorithm is appropriate for what i am doing,
> and if this difference in the magnitudes of peaks for power is usual
> or due to some error in coding.
>
> Thank you for your time.