-1
$\begingroup$

what is the reason for that? The gain should increase ideally I guess.

This is the code I tried. As I increase the length of F by zero padding,the gain of PSD reduces.

A=["48","03","0C","F6","00","F5","40","02","04","02","94","F4","D0","F5","2C","03","50","01","38","F4","24","F7","14","04","80","00","F4","F3","5C","F8","C4","04","28","FF","84","F3","08","F9","6C","04","EC","FD","CC","F2","2C","FA","E4","04","44","FC","C4","F2","1C","FC","6C","05","E4","FB","08","F3","40","FD","60","05","5C","FA","20","F3","70","FE","C8","04","A4","F8","04","F3","1C","FF","F0","03","84","F7","D4","F3","84","00","DC","03","2C","F7","00","F5","18","02","24","03","BC","F5","88","F5","08","03","78","02","20","F5","40","F6","34","03","D0","00","08","F4","5C","F7","0C","04","DC","FF","98","F3","7C","F8","C8","04","F8","FE","48","F3","F0","F9","34","05","70","FD","C8","F2","40","FB","40","05","24","FC","C0","F2","DC","FB","F4","04","18","FB","E4","F2","70","FD","D4","04","A8","F9","54","F3","F4","FE","FC","04","68","F8","50","F3","0C","00","34","04","50","F7","80","F3","BC","00","54","03","00","F6","8C","F4","48","02","60","03","CC","F5","A0","F5","14","03","D8","01","44","F4","28","F7","D0","03","70","00","44","F4","E0","F7","70","04","D4","FF","6C","F3","A8","F8","E8","04","9C","FE","3C","F3","38","FA","2C","05","FC","FC","EC","F2","38","FB","0C","05","20","FC","C4","F2","80","FC","24","05","40","FA","BC","F2","14","FE","1C","05","38","F9","10","F3","F8","FE","94","04","38","F8","D0","F3","80","00","0C","04","70","F7","68","F4","24","01","F0","02","CC","F5","BC","F4","CC","01","FC","01","18","F5","14","F6","70","03","6C","01","68","F4","60","F7","24","04","BC","00","0C","F4","3C","F8","A8","04","80","FF","9C","F3","50","F9","C4","04","98","FD","8C","F2","78","FA","0C","05","98","FC","E8","F2","E8","FB","20","05","80","FB","2C","F3","B4","FD","B0","05","80","FA","F4","F2","58","FE","D8","04","C0","F8","24","F3","4C","FF","CC","03","78","F7","1C","F4","B4","00","DC","03","14","F7","A0","F4","E8","01","1C","03","D8","F5","6C","F5","30","03","A0","01","0C","F4","FC","F5","5C","03","F0","00","14","F4","50","F7","E0","03","C8","FF","DC","F3","C8","F8","AC","04","AC","FE","60","F3","0C","FA","A8","05","F0","FD","44","F3","40","FB","54","05","88","FC","04","F3","04","FC","2C","05","CC","FA","80","F2","3C","FD","00","05","CC","F9","5C","F3","D8","FE","6C","04","5C","F8","B4","F3","44","00","6C","04","AC","F7","3C","F4","00","01","90","03","5C","F6","CC","F4","FC","01","7C","02","50","F5","C4","F5","E8","02","74","01","94","F4","B0","F6","C4","03","AC","00","E0","F3","FC","F7","38","04","70","FF","64","F3","E4","F8","E4","04","90","FE","1C","F3","1C","FA","08","05","FC","FC","EC","F2","4C","FB","F0","04","F0","FB","3C","F3","F4","FC","9C","05","C0","FA","04","F3","40","FE","E8","04","48","F9","54","F3","44","FF","80","04","BC","F7","6C","F3","5C","00","EC","03","0C","F7","30","F4","1C","01","04","03","30","F6","60","F5","C8","02","C4","02","EC","F4","04","F6","5C","03","60","01","4C","F4","E8","F6","DC","03","D8","FF","98","F3","3C","F8","54","04","18","FF","74","F3","4C","F9","E4","04","28","FE","38","F3","74","FA","0C","05","E0","FC","28","F3","30","FC","7C","05","58","FB","6C","F2","0C","FD","98","05","4C","FA","18","F3","50","FE","64","04","BC","F8","68","F3","8C","FF","9C","04","20","F8","40","F4","CC","00","98","03","E0","F6","EC","F4","DC","01","D4","02","B0","F5","50","F5","E8","02","2C","02","AC","F4","08","F6","28","03","0C","01","28","F4","A0","F7","20","04","E4","FF","94","F3","8C","F8","6C","04","78","FE","78","F3","14","FA","E0","04","74","FD","60","F2","9C","FA","3C","05","30","FC","9C","F2","40","FC","E0","04","48","FB","28","F3","90","FD","0C","05","BC","F9","1C","F3","FC","FE","DC","04","A0","F8","D8","F3","3C","00","18","04","54","F7","58","F4","2C","01","80","03","2C","F6","80","F4","0C","02","C0","02","88","F5","A0","F5","E8","02","68","01","94","F4","EC","F6","1C","04","E8","00","FC","F3","E0","F7","8C","04","9C","FF","7C","F3","FC","F8","BC","04","0C","FE","E4","F2","D8","F9","0C","05","70","FD","C8","F2","EC","FA","20","05","CC","FB","98","F2","B8","FC","68","05","A0","FA","D0","F2","E8","FD","F4","04","24","F9","3C","F3","7C","FF","A4","04","18","F8","AC","F3","1C","00","A4","03","2C","F7","7C","F4","5C","01","84","03","78","F6","78","F5","54","02","6C","02","58","F5","EC","F5","3C","03","78","01","04","F4","FC","F6","10","04","24","00","94","F3","CC","F7","34","04","0C","FF","64","F3","84","F9","0C","05","0C","FE","10","F3","BC","FA","34","05","B4","FC","44","F3","F8","FB","04","05","EC","FA","88","F2","18","FD","34","05","00","FA","C4","F2","50","FE","D8","04","F0","F8","8C","F3","9C","FF","50","04","F8","F7","44","F4","1C","01","C4","03","7C","F6","94","F4","B8","01","84","02","6C","F5","8C","F5","CC","02","28","02","BC","F4","54","F6","D4","03","5C","01","68","F4","8C","F7","04","04","D0","FF","D8","F3","B8","F8","A4","04","74","FE","EC","F2","B8","F9","1C","05","70","FD","AC","F2","D8","FA","2C","05","1C","FC","A4","F2","AC","FC","9C","05","2C","FB","D8","F2","7C","FD","20","05","A0","F9","38","F3","08","FF","5C","04","F0","F7","64","F3","3C","00","E0","03","54","F7","40","F4","B8","00","40","03","B0","F6","40","F5","08","02","B0","02","3C","F5","70","F5","0C","03","F8","01","24","F5","F8","F6"];
B=A';
C1 = reshape(A,2,[])';
C=[C1(:,2) C1(:,1)];
D=join(C);   %512*1
E=regexprep(D,'[^\w'']','');  %remove spaces
F=hex2dec(E);   %hex2dec

N = length(F);
xdft = fft(F);
xdft = xdft(1:N/2+1);
psdx = (1/(Fs*N)) * abs(xdft).^2;
psdx(2:end-1) = 2*psdx(2:end-1);
freq = 0:Fs/length(F):Fs/2;
figure
plot(freq,20*log10(psdx))
grid on
title('Periodogram Using FFT')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')
$\endgroup$
  • $\begingroup$ Possible duplicate of MATLAB: $\tt fft$ and $\tt ifft$ scaling $\endgroup$ – Marcus Müller Jul 18 '17 at 9:07
  • $\begingroup$ i read the info from the link,i am unable to link to my question,when i double the no of points in fft there shud be a 3db gain in psd,but in matlab it shows an exact 3db loss $\endgroup$ – Akshay Rathod Jul 18 '17 at 10:37
  • $\begingroup$ Can you please show us how you are forming F ? $\endgroup$ – Peter K. Jul 18 '17 at 11:17
  • $\begingroup$ @AkshayRathod no, there's nothing that says you should have a "gain". Mathematically justify that claim, and then check against the documentation of the fft function you're using. $\endgroup$ – Marcus Müller Jul 18 '17 at 16:00
  • $\begingroup$ @MarcusMüller the formula for fft gain is 10log(M/2)..where M is the no of points..for details pls visit this page,it has somewhat given the answer. designnews.com/aerospace/where-does-fft-process-gain-come/… $\endgroup$ – Akshay Rathod Jul 19 '17 at 5:44
2
$\begingroup$

There is gain, and there is level, assuming you are asking about the bin levels, consider Parseval's theorem,

https://en.wikipedia.org/wiki/Parseval%27s_theorem

for the DFT,

$$ \sum_{n=0}^{N-1} | x[n] |^2 = \frac{1}{N} \sum_{k=0}^{N-1} | X[k] |^2 $$

when you increase $N$ by zero padding, you increase the denominator on the right, which reduces the levels.

$\endgroup$
  • $\begingroup$ this is very nice info..thanx $\endgroup$ – Akshay Rathod Jul 19 '17 at 5:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.