I have been working on a (potentially super simple) assignment in which one of the steps is to get a Fourrier transform. I have followed a guide from my university to transform a wave-sound which can be found here (channels: 2, samples: 17600, sample frequency: 16KHz).
Looking at the graph, it seems to work:
[y,fs,wmode,fidx]=readwav('piano.wav','r',-1,0);
left=y(:,1);
amountOfSlices = 6;
samplesPerSlice = fix(length(left) / 6);
frames=enframe(left, samplesPerSlice);
frames=transpose(frames);
fftdata=rfft(frames);
fftdata=fftdata.*conj(fftdata);
plot(fftdata);
Next, I created a code file with the tutorial code as a basis with the addition of accepting parameters (which are needed for the assignment, but have been left out for brevity).
samplerate = 512;
% Read the file with raw unscaled audio data from begin to end
[multiData,fs,wmode,fidx]=readwav(filename,'r',-1,0);
disp(sprintf('Number of channels: %d', fidx(5)))
disp(sprintf('Number of samples: %d', fidx(4)))
disp(sprintf('Sample frequency: %d Hz', fs))
% Extract the left channel of the data
leftData = multiData(:, 1);
% Slice the left channel into pieces of the size of 'samplerate'
samplesPerSlice = samplerate
% Splits the leftData vector up into frames of length equal to sample rate
slicedLeftData = enframe(leftData, samplerate)';
% Apply the real data fast fourrier transformation on each data slice
fftdata=rfft(slicedLeftData);
fftdata=fftdata.*conj(fftdata);
plot(fftdata);
Do you guys have any idea what I'm doing wrong here?
What my actual question is: Why isn't the second data in the frequency domain of 0 to 16.000 Hz? What am I doing wrong?
I guess by "whats wrong here" you mean the multiple colors? If so, looks like the fftdata plottet in both images are matrices (you want an array, correct?). Doesn't the .* perform the operation on each and every element? Check the dimensions for your ingoing arguments.
Furthermore, remember Nyquist theorem: You can never resolve any frequencies greater than half your sample frequency. In the case of having a sample frequency of 16KHz, you may have datapoints beyong 8kHz but it will not contain any information, so no need to include that in the frequency domain plot.
Related
we have measured data that we managed to determine the distribution type that it follows (Gamma) and its parameters (A,B)
And we generated n samples (10000) from the same distribution with the same parameters and in the same range (between 18.5 and 59) using for loop
for i=1:1:10000
tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);
W(i,:) =random(tot,1,1);
end
Then we tried to fit the generated data using:
h1=histfit(W);
After this we tried to plot the Gamma curve to compare the two curves on the same figure uing:
hold on
h2=histfit(W,[],'Gamma');
h2(1).Visible='off';
The problem s the two curves are shifted as in the following figure "Figure 1 is the generated data from the previous code and Figure 2 is without truncating the generated data"
enter image description here
Any one knows why??
Thanks in advance
By default histfit fits a normal probability density function (PDF) on the histogram. I'm not sure what you were actually trying to do, but what you did is:
% fit a normal PDF
h1=histfit(W); % this is equal to h1 = histfit(W,[],'normal');
% fit a gamma PDF
h2=histfit(W,[],'Gamma');
Obviously that will result in different fits because a normal PDF != a gamma PDF. The only thing you see is that for the gamma PDF fits the curve better because you sampled the data from that distribution.
If you want to check whether the data follows a certain distribution you can also use a KS-test. In your case
% check if the data follows the distribution speccified in tot
[h p] = kstest(W,'CDF',tot)
If the data follows a gamma dist. then h = 0 and p > 0.05, else h = 1 and p < 0.05.
Now some general comments on your code:
Please look up preallocation of memory, it will speed up loops greatly. E.g.
W = zeros(10000,1);
for i=1:1:10000
tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);
W(i,:) =random(tot,1,1);
end
Also,
tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);
is not depending in the loop index and can therefore be moved in front of the loop to speed things up further. It is also good practice to avoid using i as loop variable.
But you can actually skip the whole loop because random() allows to return multiple samples at once:
tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);
W =random(tot,10000,1);
I have a oscillator bank made in SuperCollider which receives phases and amplitudes from python via OSC. However the results don't sound correct at all. At first I thought the problem is in my SuperCollider code, but now I'm beginning to doubt my FFT function and normalization, here's my code:
def readNormalize(length, location,sample):
samplerate, data = wavfile.read(location)
a = data.T[0] # first track of audio
c = fft(a[sample:], length)
ownSum = 0;
length = int(length/2)
for i in range(0, length):
ownSum += abs(c[i])
normalizer = 1/ownSum
phases = []
amplitudes = []
for i in range(0,length):
amplitudes.append(abs(c[i])*normalizer)
phases.append(np.angle(c[i]))
return amplitudes, phases
So the function receives location from where to read, length of the FFT to be calculated and from which sample of the wav file to read. My normalization is done by taking the sum of the vectors of the complex numbers, dividing 1 by the sum and then multiplying the vectors with the normalizing value. I'm not sure if it is done correctly, is this the correct way to do it? Only thing I hear in the SuperCollider is this kick drum sound which is not how it should sound at all. Am I missing something important here?
We were recently taught the concepts of error control coding - basic codes such as Hamming code, repeatition code etc.
I thought of trying out these concepts in MATLAB. My goal was to compare how an audio file plays when corrupted by noise and in the case when the file is protected by basic codes and then corrupted by noise.
So I opened a small audio clip of 20-30 seconds in MATLAB using audioread function. I used 16 bit encoded PCM wave file.
If opened in 'native' format it is in int16 format . If not it opens in a double format.
I then added two types of noises to it : - AWGN noise (using double format) and Binary Symmetric Channel noise (by converting the int16 to uint16 and then by converting that to binary using dec2bin function). Reconverting back to the original int16 format does add a lot of noise to it.
Now my goal is to try out a basic repeatition code. So what I did was to convert the 2-d audio file matrix which consists of binary data into a 3-d matrix by adding redundancy. I used the following command : -
cat(3,x,x,x,x,x) ;
It created a 3-D matrix such that it had 5 versions of x along the 3rd dimension.
Now I wish to add noise to it using bsc function.
Then I wish to do the decoding of the redundant data by removing the repetition bits using a mode() function on the vector which contains the redundant bits.
My whole problem in this task is that MATLAB is taking too long to do the computation. I guess a 30 second file creates quite a big matrix so maybe its taking time. Moreover I suspect what I am doing is not the most efficient way to do it with regards to the various data types.
Can you suggest a way in which I may improve on the computation times. Are there some functions which can help do this basic task in a better way.
Thanks.
(first post on this site with respect to MATLAB so bear with me if the posting format is not upto the mark.)
Edit - posting the code here :-
[x,Fs] = audioread('sample.wav','native'); % native loads it in int16 format , Fs of sample is 44 khz , size of x is 1796365x1
x1 = x - min(x); % to make all values non negative
s = dec2bin(x); % this makes s as a 1796365x15 matrix the binary stream stored as character string of length 15. BSC channel needs double as the data type
s1 = double(s) - 48; % to get 0s and 1s in double format
%% Now I wish to compare how noise affects s1 itself or to a matrix which is error control coded.
s2 = bsc(s,0.15); % this adds errors with probability of 0.15
s3 = cat(3,s,s,s,s,s) ; % the goal here is to add repetition redundancy. I will try out other efficient codes such as Hamming Code later.
s4 = bsc(s3,0.15);% this step is taking forever and my PC is unresponsive because of this one.
s5 = mode(s4(,,:)) ; % i wish to know if this is a proper syntax, what I want to do is calculate mode along the 3rd dimension just to remove redundancy and thereby reduce error.
%% i will show what I did after s was corrupted by bsc errors in s2,
d = char(s2 + 48);
d1 = bin2dec(d) + min(x);
sound(d1,Fs); % this plays the noisy file. I wish to do the same with error control coded matrix but as I said in a previous step it is highly unresponsive.
I suppose what is mostly wrong with my task is that I took a large sampling rate and hence the vector was very big.
Here's my goal:
I'm trying to find a way to search through a data signal and find (index) locations where a known, repeating binary data sequence is located. Then, because the spreading code and demodulation is known, pull out the corresponding chip of data and read it. Currently, I believe xcorr will do the trick.
Here's my problem:
I can't seem to interpret my result from xcorr or xcorr2 to give me what I'm looking for. I'm either having a problem cross-referencing from the vector location of my xcorr function to my time vector, or a problem properly identifying my data sequence with xcorr, or both. Other possibilities may exist.
Where I am at/What I have:
I have created a random BPSK signal that consists of the data sequence of interest and garbage data over a repeating period. I have tried processing it using xcorr, which is where I am stuck.
Here's my code:
%% Clear Variables
clc;
clear all, close all;
%% Create random data
nbits = 2^10;
ngarbage = 3*nbits;
data = randi([0,1],1,nbits);
garbage = randi([0,1],1,ngarbage);
stream = horzcat(data,garbage);
%% Convert from Unipolar to Bipolar Encoding
stream_b = 2*stream - 1;
%% Define Parameters
%%% Variable Parameters
nsamples = 20*nbits;
nseq = 5 %# Iterate stream nseq times
T = 10; %# Number of periods
Ts = 1; %# Symbol Duration
Es = Ts/2; %# Energy per Symbol
fc = 1e9; %# Carrier frequency
%%% Dependent Parameters
A = sqrt(2*Es/Ts); %# Amplitude of Carrier
omega = 2*pi*fc %# Frequency in radians
t = linspace(0,T,nsamples) %# Discrete time from 0 to T periods with nsamples samples
nspb = nsamples/length(stream) %# Number of samples per bit
%% Creating the BPSK Modulation
%# First we have to stretch the stream to fit the time vector. We can quickly do this using _
%# simple matrix manipulation.
% Replicate each bit nspb/nseq times
repStream_b = repmat(stream_b',1,nspb/nseq);
% Tranpose and replicate nseq times to be able to fill to t
modSig_proto = repmat(repStream_b',1,nseq);
% Tranpose column by column, then rearrange into a row vector
modSig = modSig_proto(:)';
%% The Carrier Wave
carrier = A*cos(omega*t);
%% Modulated Signal
sig = modSig.*carrier;
Using XCORR
I use xcorr2() to eliminate the zero padding effect of xcorr on unequal vectors. See comments below for clarification.
corr = abs(xcorr2(data,sig); %# pull the absolute correlation between data and sig
[val,ind] = sort(corr(:),'descend') %# sort the correlation data and assign values and indices
ind_max = ind(1:nseq); %# pull the nseq highest valued indices and send to ind_max
Now, I think this should pull the five highest correlations between data and sig. These should correspond to the end bit of data in the stream for every iteration of stream, because I would think that is where the data would most strongly cross-correlate with sig, but they do not. Sometimes the maxes are not even one stream length apart. So I'm confused here.
Question
In a three part question:
Am I missing a certain step? How do I use xcorr in this case to find where data and sig are most strongly correlated?
Is my entire method wrong? Should I not be looking for the max correlations?
Or should I be attacking this problem from another angle, id est, not use xcorr and maybe use filter or another function?
Your overall method is great and makes a lot of sense. The problem you're having is that you're getting some actual correlation with your garbage data. I noticed that you shifted all of your sream to be zero-centered, but didn't do the same to your data. If you zero-center the data, your correlation peaks will be better defined (at least that worked when I tried it).
data = 2*data -1;
Also, I don't recommend using a simple sort to find your peaks. If you have a wide peak, which is especially possible with a noisy signal, you could have two high points right next to each other. Find a single maximum, and then zero that point and a few neighbors. Then just repeat however many times you like. Alternatively, if you know how long your epoch is, only do a correlation with one epoch's worth of data, and iterate through the signal as it arrives.
With #David K 's and #Patrick Mineault's help I manage to track down where I went wrong. First #Patrick Mineault suggested I flip the signals. The best way to see what you would expect from the result is to slide the small vector along the larger, searched vector. So
corr = xcorr2(sig,data);
Then I like to chop off the end there because it's just extra. I did this with a trim function I made that simply takes the signal you're sliding and trims it's irrelevant pieces off the end of the xcorr result.
trim = #(x,s2) x(1:end - (length(s2) - 1));
trim(corr,data);
Then, as #David K suggests, you need to have the data stream you're looking for encoded the same as your searched signal. So in this case
data = 2*data-1;
Second, if you just have your data at it's original bit length, and not at it's stretched, iterated length, it can be found in the signal but it will be VERY noisy. To reduce the noise, simply stretch the data to match it's stretched length in the iterated signal. So
rdata = repmat(data',1,nspb/nseq);
rdata = repmat(rdata',1,nseq);
data = rdata(:)';
Now finally, we should have crystal clear correlations for this case. And to pull out the maxes that should correspond to those correlations I wrote
[sortedValues sortIndex] = sort(corr(:),'descend');
c = 0 ;
for r = 1 : length(sortedValues)
if sortedValues(r,:) == max(corr)
c = c + 1;
maxIndex(1,c) = sortIndex(r,:);
else break % If you don't do this, you get loop lock
end
end
Now c should end up being nseq for this case and you should have 5 index times where the corrs should be! You can easily pull out the bits with another loop and c or length(maxIndex). I've also made this into a more "real world" toy script, where there is a data stream, doppler, fading, and it's over a time vector in seconds instead of samples.
Thanks for the help!
Try flipping the signal, i.e.:
corr = abs(xcorr2(data,sig(end:-1:1));
Is that any better?
FFT and changing frequency and vectorizing for loop
Greetings All
I can increase and decrease the frequency of a
signal using the combination of fft and a Fourier series expansion FOR loop in
the code below
but if the signal/array is to large it becomes extremely
slow (an array that's 1x44100 takes about 2 mins to complete) I'm sure
it has to do with the for loop but
I'm not exactly sure how to vectorize it to improve performance. Please note that this will be used with audio signals that are 3 to 6 mins long. The 1x44100 array is only a second and it takes about 2 mins to complete
Any recommendations
%create signal
clear all, clc,clf,tic
x= linspace(0,2*pi,44100)';
%Used in exporting to ycalc audio file make sure in sync with above
freq_orig=1;
freq_new=4
vertoff=0;
vertoffConj=0;
vertoffInv=0;
vertoffInvConj=0;
phaseshift=(0)*pi/180 ; %can use mod to limit to 180 degrees
y=sin(freq_orig*(x));
[size_r,size_c]=size(y);
N=size_r; %to test make 50
T=2*pi;
dt=T/N;
t=linspace(0,T-dt,N)';
phase = 0;
f0 = 1/T; % Exactly, one period
y=(y/max(abs(y))*.8)/2; %make the max amplitude here
C = fft(y)/N; % No semicolon to display output
A = real(C);
B = imag(C)*-1; %I needed to multiply by -1 to get the correct sign
% Single-Sided (f >= 0)
An = [A(1); 2*A(2:round(N/2)); A(round(N/2)+1)];
Bn = [B(1); 2*B(2:round(N/2)); B(round(N/2)+1)];
pmax=N/2;
ycalc=zeros(N,1); %preallocating space for ycalc
w=0;
for p=2:pmax
%
%%1 step) re-create signal using equation
ycalc=ycalc+An(p)*cos(freq_new*(p-1).*t-phaseshift)
+Bn(p)*sin(freq_new*(p-1).*t-phaseshift)+(vertoff/pmax);
w=w+(360/(pmax-1)); %used to create phaseshift
phaseshift=w;
end;
fprintf('\n- Completed in %4.4fsec or %4.4fmins\n',toc,toc/60);
subplot(2,1,1), plot(y),title('Orginal Signal');
subplot(2,1,2),plot(ycalc),title('FFT new signal');
Here's a pic of the plot if some one wants to see the output, which is correct the FOR loop is just really really slow
It appears as though you are basically shifting the signal upwards in the frequency domain, and then your "series expansion" is simply implementing the inverse DFT on the shifted version. As you have seen, the naive iDFT is going to be exceedingly slow. Try changing that entire loop into a call to ifft, and you should be able to get a tremendous speedup.