I have to extract the fundamental frequency from a .wav file of 1 second long.
I have looked over several options like finding the peaks or doing a complex cepstrum but no luck so far. I have read over the last couple of weeks a lot about it but still i cannot find a viable and optimal way of doing it. I am new to Matlab and Signal Processing.
filedir = dir('*.wav');
[y, Fs] = audioread(filedir.name);
x = y(y ~= 0) % removing the zeroes from the array
psdest = psd(spectrum.periodogram,x,'Fs',Fs,'NFFT',length(x));
[~,I] = max(psdest.Data);
fprintf('Maximum occurs at %d Hz.\n',psdest.Frequencies(I));
The output is for example: Maximum occurs at 5.758645e+02 Hz
I will probably need to actually transform that number into Hz.
For the complex cepstrum:
load mtlb
dt = 1/Fs;
I0 = round(0.1/dt);
Iend = round(1/dt);
x = mtlb(I0:Iend);
c = cceps(x);
t = 0:dt:length(x)*dt-dt;
trng = t(t>=2e-3 & t<=10e-3);
crng = c(t>=2e-3 & t<=10e-3);
[~,I] = max(crng);
fprintf('Complex cepstrum F0 estimate is %3.2f Hz.\n',1/trng(I))
clearvars
The output values is the same for all the files I load so clearly something is wrong.
I have been struggling for a while and I really need to figure this out. To extract that fundamental frequency. I use Matlab 2016b.
Thanks a lot!
Related
I have a 10000x1 matrix. I need to find the percentage of information contained in each case. The method of doing so is to make another matrix that contains the sum of remaining cells.
Example:
% info is a 10000x1
% info_n contains percentages of information.
info_n = zeros([10000 1]);
info_n(1)= info(1) /sum(info);
info_n(2)=(info(1)+info(2)) /sum(info);
info_n(3)=(info(1)+info(2)+info(3))/sum(info);
I need to do this but all the way to info_n(10000).
So far, I tried this:
for i = 1:10000
info_n(i)=(info(i))/sum(info);
end
but I can't think of a way to add previous information. Thank you for the help!
You can use cumsum ("cumulative sum") for this task:
info_n = cumsum(info)/sum(info);
EDIT: #LuisMendo's comment sparked my curiosity. It seems that you actually gain something by using his method if the length N of the vector is below about 2^15 but the advantage after that drops. This is because cumsum probably needs O(N^2) but sum only needs O(N) time.
On the left you see the times as well as the ratio of the times of the two methods plotted against the logarithm of the size. On the right you see the actual absolute time differences, which varies a lot depending on what else is currently running:
Testing script:
N = 2.^(1:28);
y1 = zeros(size(N));
y2 = zeros(size(N));
vec = 1:numel(N);
for k=vec;
disp(k)
info = zeros(N(k),1);
% flawr's suggestion
tic
info_n = cumsum(info);
info_n = info_n / info_n(end);
y1(k) = toc;
% LuisMendo's suggestion
tic
info_m = cumsum(info)/sum(info);
y2(k) = toc;
end
subplot(1,2,1)
semilogy(vec,y1,vec,y2,vec,y1./y2,vec,vec.^0);
legend('LuisMendo','flawr','LM/f','Location','SouthEast');
subplot(1,2,2)
plot(vec,y1-y2)
I'm trying to estimate the (unknown) original datapoints that went into calculating a (known) moving average. However, I do know some of the original datapoints, and I'm not sure how to use that information.
I am using the method given in the answers here: https://stats.stackexchange.com/questions/67907/extract-data-points-from-moving-average, but in MATLAB (my code below). This method works quite well for large numbers of data points (>1000), but less well with fewer data points, as you'd expect.
window = 3;
datapoints = 150;
data = 3*rand(1,datapoints)+50;
moving_averages = [];
for i = window:size(data,2)
moving_averages(i) = mean(data(i+1-window:i));
end
length = size(moving_averages,2)+(window-1);
a = (tril(ones(length,length),window-1) - tril(ones(length,length),-1))/window;
a = a(1:length-(window-1),:);
ai = pinv(a);
daily = mtimes(ai,moving_averages');
x = 1:size(data,2);
figure(1)
hold on
plot(x,data,'Color','b');
plot(x(window:end),moving_averages(window:end),'Linewidth',2,'Color','r');
plot(x,daily(window:end),'Color','g');
hold off
axis([0 size(x,2) min(daily(window:end))-1 max(daily(window:end))+1])
legend('original data','moving average','back-calculated')
Now, say I know a smattering of the original data points. I'm having trouble figuring how might I use that information to more accurately calculate the rest. Thank you for any assistance.
You should be able to calculate the original data exactly if you at any time can exactly determine one window's worth of data, i.e. in this case n-1 samples in a window of length n. (In your case) if you know A,B and (A+B+C)/3, you can solve now and know C. Now when you have (B+C+D)/3 (your moving average) you can exactly solve for D. Rinse and repeat. This logic works going backwards too.
Here is an example with the same idea:
% the actual vector of values
a = cumsum(rand(150,1) - 0.5);
% compute moving average
win = 3; % sliding window length
idx = hankel(1:win, win:numel(a));
m = mean(a(idx));
% coefficient matrix: m(i) = sum(a(i:i+win-1))/win
A = repmat([ones(1,win) zeros(1,numel(a)-win)], numel(a)-win+1, 1);
for i=2:size(A,1)
A(i,:) = circshift(A(i-1,:), [0 1]);
end
A = A / win;
% solve linear system
%x = A \ m(:);
x = pinv(A) * m(:);
% plot and compare
subplot(211), plot(1:numel(a),a, 1:numel(m),m)
legend({'original','moving average'})
title(sprintf('length = %d, window = %d',numel(a),win))
subplot(212), plot(1:numel(a),a, 1:numel(a),x)
legend({'original','reconstructed'})
title(sprintf('error = %f',norm(x(:)-a(:))))
You can see the reconstruction error is very small, even using the data sizes in your example (150 samples with a 3-samples moving average).
I have a question if that's ok. I was recently looking for algorithm to calculate MFCCs. I found a good tutorial rather than code so I tried to code it by myself. I still feel like I am missing one thing. In the code below I took FFT of a signal, calculated normalized power, filter a signal using triangular shapes and eventually sum energies corresponding to each bank to obtain MFCCs.
function output = mfcc(x,M,fbegin,fs)
MF = #(f) 2595.*log10(1 + f./700);
invMF = #(m) 700.*(10.^(m/2595)-1);
M = M+2; % number of triangular filers
mm = linspace(MF(fbegin),MF(fs/2),M); % equal space in mel-frequency
ff = invMF(mm); % convert mel-frequencies into frequency
X = fft(x);
N = length(X); % length of a short time window
N2 = max([floor(N+1)/2 floor(N/2)+1]); %
P = abs(X(1:N2,:)).^2./N; % NoFr no. of periodograms
mfccShapes = triangularFilterShape(ff,N,fs); %
output = log(mfccShapes'*P);
end
function [out,k] = triangularFilterShape(f,N,fs)
N2 = max([floor(N+1)/2 floor(N/2)+1]);
M = length(f);
k = linspace(0,fs/2,N2);
out = zeros(N2,M-2);
for m=2:M-1
I = k >= f(m-1) & k <= f(m);
J = k >= f(m) & k <= f(m+1);
out(I,m-1) = (k(I) - f(m-1))./(f(m) - f(m-1));
out(J,m-1) = (f(m+1) - k(J))./(f(m+1) - f(m));
end
end
Could someone please confirm that this is all right or direct me if I made mistake> I tested it on a simple pure tone and it gives me, in my opinion, reasonable answers.
Any help greatly appreciated :)
PS. I am working on how to apply vectorized Cosinus Transform. It looks like I would need a matrix of MxM of transform coefficients but I did not find any source that would explain how to do it.
You can test it yourself by comparing your results against other implementations like this one here
you will find a fully configurable matlab toolbox incl. MFCCs and even a function to reverse MFCC back to a time signal, which is quite handy for testing purposes:
melfcc.m - main function for calculating PLP and MFCCs from sound waveforms, supports many options.
invmelfcc.m - main function for inverting back from cepstral coefficients to spectrograms and (noise-excited) waveforms, options exactly match melfcc (to invert that processing).
the page itself has a lot of information on the usage of the package.
Hey guys I am trying to find the Power Spectral Density of a .wav signal i recorded which is essentially a sine immersed in noise. The function that i have written is supposed to take records all of 1024 points in length and use it to find the Gxx of the signal by finding Gxx per record and then adding them and dividing them by the number of records better explained in the algorithm below:
a. Step through the wav file and extract the first record length (e.g. 1 to 1024 points). (Note that the record length is your new “N”, hence the frequency spacing changes in accordance with this, NOT the total length of the wav file).
b. Perform the normal PSD function on this record.
c. Store this vector.
d. Extract the next 1024 points in the wav file (e.g. 1025:2048) and perform PSD on this record.
e. Add this to the previously stored record and continue through steps c to e until you reach the end of your wav file or the total number of records you want. (Remember that total records*record length must be less than the total length of the wavfile!)
f. Divide the PSD by the number of averages (or number of records).
This is your averaged PSD
The function I created is as follows:
%Function to plot PSD
function[f1, GxxAv] = HW3_A_Fn_811003472_RCT(x,fs,NumRec)
Gxx = 0;
GxxAv = 0;
N = 1024;
df = fs/N;
f1 = 0:df:fs/2;
dt = 1/fs;
T = N*dt;
q = 0;
e = 1;
for i = 1:NumRec;
for r = (1+q):(N*e);
L = x(1+q:N*e);
M = length(L);
Xm = fft(L).*dt;
aXm = abs(Xm);
Gxx(1)=(1/T).*(aXm(1).*aXm(1));
for k = 2:(M/2);
Gxx(k) = (2/T) *(aXm(k).*(aXm(k)));
%Gxx = Gxx + Gxx1(k);
end
Gxx((M/2)+1)= (1/T)*(aXm((M/2)+1)).*(aXm((M/2)+1));
q = q+1024;
e = e+1;
%Gxx = Gxx + Gxx1((M/2)+1);
end
GxxAv = GxxAv + Gxx;
%Gxx = Gxx + Gxx1;
end
GxxAv = GxxAv/NumRec;
And the code I used to call this function is as follows:
[x,fs] = wavread('F:\Final\sem1Y3\Acoustics\sinenoise5s.wav');
[f1,GxxAv] = HW3_A_Fn_811003472_RCT(x,fs,100); %where 100 is the number of records to generated
plot(f1,GxxAv)
xlabel ('Frequency / Hz', 'fontsize', 18)
ylabel ('Amplitude Squared per Frequency / WU^2/Hz', 'fontsize', 18)
title ('Plot of the single sided PSD, using Averaging', 'fontsize', 18)
grid on
When Trying to plot this graph the following error was observed:
??? Index exceeds matrix dimensions.
Error in ==> HW3_A_Fn_811003472_RCT at 19
L = x(1+q:N*e);
Error in ==> HW3_A_3_811003472_RCT at 3
[f1,GxxAv] = HW3_A_Fn_811003472_RCT(x,fs,100); %where 100 is the number of records to generated
I am not sure how to fix it and i have tried many different methods but still i get this error. I am not too familiar with Matlab but all I really want to do for line 19 is to go like:
x(1:1024), x(1025:2048), x(2049:3072), x(3072:4096)...etc to 100 records
Any ideas??? Thanks
This is obviously homework, so I am not gonna do your work for you. But there quite some things wrong with your code. Start by fixing all of those first:
Use more appropriate function names, homework123 is not a good name to describe what the function does.
Use more appropriate variable names. More standard in this context would be nfft instead of N and n_average instead of NumRec. I don't care about the exact thing you use, but it should describe exactly what the variable does.
Your error message clearly hints that you are trying to index x in some illegal way. Start with making a loop that just prints the right indices (1..1024, 1025..2048, ...) and make sure it follows your instruction E. Only when this works as expected add the rest of the code.
you use a triple-nested for-loop. You only need a single for-loop or while-loop to solve this problem.
Say I have performed FFT on a set of data and i have the frequency and amplitude values.
I want to find the highest amplitude in each FFT block. The I need to find the frequency and amplitude of the points that are atleast greater than 0.4 times the max amplitude and save them in an array.. How can i do this??
I tried the following method by I keep getting an empty matrix....
% the code after FFT
peak_points = [];
fmin = 60;
fmax = 1000;
region_of_interest = fmax>f & f>fmin;
froi = f(region_of_interest);
[p_max,loc] = max(seg_fft2(region_of_interest));
p_max;
fpeaks = froi(loc);
[points, locatn] = findpeaks(seg_fft2(region_of_interest));
if points > 0.4*p_max
peak_points = [peak_points ; points locatn]
end
Im bad with arrays.. So I cant seem to figure this out. Would appreciate someone's help in this... Thanks in advance...
Are you intending to do the seg_ffr2 on the region of interest logical array or on froi?
or maybe points is vector and you should have:
aboveMax = points > 0.4*p_max;
if any(aboveMax)
peak_points = [peak_points ; points(aboveMax) locatn(aboveMax)]
end