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I've only used MATLAB as a calculator, so I'm not as well versed in the program. I hope a kind person may be able to guide me on the way since Google currently is not my friend.
I have a wav file in the link below, where there is a human voice and some noise in the background. I want the noise removed. Is there anyone who can tell me how to do it in MATLAB?
https://www.dropbox.com/s/3vtd5ehjt2zfuj7/Hold.wav
This is a pretty imperfect solution, especially since some of the noise is embedded in the same frequency range as the voice you hear on the file, but here goes nothing. What I was talking about with regards to the frequency spectrum is that if you hear the sound, the background noise has a very low hum. This resides in the low frequency range of the spectrum, whereas the voice has a more higher frequency. As such, we can apply a bandpass filter to get rid of the low noise, capture most of the voice, and any noisy frequencies on the higher side will get cancelled as well.
Here are the steps that I did:
Read in the audio file using audioread.
Play the original sound so I can hear what it sounds like using. Do this by creating an audioplayer object.
Plotted both the left and right channels to take a look at the sound signal in time domain... if it gives any clues. Looking at the channels, they both seem to be the same, so it looks like it was just a single microphone being mapped to both channels.
I took the Fourier Transform and saw the frequency distribution.
Using (4) I figured out the rough approximation of where I should cut off the frequencies.
Designed a bandpass filter that cuts off these frequencies.
Filtered the signal then played it by constructing another audioplayer object.
Let's go then!
Step #1
%% Read in the file
clearvars;
close all;
[f,fs] = audioread('Hold.wav');
audioread will read in an audio file for you. Just specify what file you want within the ''. Also, make sure you set your working directory to be where this file is being stored. clearvars, close all just do clean up for us. It closes all of our windows (if any are open), and clears all of our variables in the MATLAB workspace. f would be the signal read into MATLAB while fs is the sampling frequency of your signal. f here is a 2D matrix. The first column is the left channel while the second is the right channel. In general, the total number of channels in your audio file is denoted by the total number of columns in this matrix read in through audioread.
Step #2
%% Play original file
pOrig = audioplayer(f,fs);
pOrig.play;
This step will allow you to create an audioplayer object that takes the signal you read in (f), with the sampling frequency fs and outputs an object stored in pOrig. You then use pOrig.play to play the file in MATLAB so you can hear it.
Step #3
%% Plot both audio channels
N = size(f,1); % Determine total number of samples in audio file
figure;
subplot(2,1,1);
stem(1:N, f(:,1));
title('Left Channel');
subplot(2,1,2);
stem(1:N, f(:,2));
title('Right Channel');
stem is a way to plot discrete points in MATLAB. Each point in time has a circle drawn at the point with a vertical line drawn from the horizontal axis to that point in time. subplot is a way to place multiple figures in the same window. I won't get into it here, but you can read about how subplot works in detail by referencing this StackOverflow post I wrote here. The above code produces the plot shown below:
The above code is quite straight forward. I'm just plotting each channel individually in each subplot.
Step #4
%% Plot the spectrum
df = fs / N;
w = (-(N/2):(N/2)-1)*df;
y = fft(f(:,1), N) / N; % For normalizing, but not needed for our analysis
y2 = fftshift(y);
figure;
plot(w,abs(y2));
The code that will look the most frightening is the code above. If you recall from signals and systems, the maximum frequency that is represented in our signal is the sampling frequency divided by 2. This is called the Nyquist frequency. The sampling frequency of your audio file is 48000 Hz, which means that the maximum frequency represented in your audio file is 24000 Hz. fft stands for Fast Fourier Transform. Think of it as a very efficient way of computing the Fourier Transform. The traditional formula requires that you perform multiple summations for each element in your output. The FFT will compute this efficiently by requiring far less operations and still give you the same result.
We are using fft to take a look at the frequency spectrum of our signal. You call fft by specifying the input signal you want as the first parameter, followed by how many points you want to evaluate at with the second parameter. It is customary that you specify the number of points in your FFT to be the length of the signal. I do this by checking to see how many rows we have in our sound matrix. When you plot the frequency spectrum, I just took one channel to make things simple as the other channel is the same. This serves as the first input into fft. Also, bear in mind that I divided by N as it is the proper way of normalizing the signal. However, because we just want to take a snapshot of what the frequency domain looks like, you don't really need to do this. However, if you're planning on using it to compute something later, then you definitely need to.
I wrote some additional code as the spectrum by default is uncentered. I used fftshift so that the centre maps to 0 Hz, while the left spans from 0 to -24000Hz while the right spans from 0 to 24000 Hz. This is intuitively how I see the frequency spectrum. You can think of negative frequencies as frequencies that propagate in the opposite direction. Ideally, the frequency distribution for a negative frequency should equal the positive frequency. When you plot the frequency spectrum, it tells you how much contribution that frequency has to the output. That is defined by the magnitude of the signal. You find this by taking the abs function. The output that you get is shown below.
If you look at the plot, there are a lot of spikes around the low frequency range. This corresponds to your humming whereas the voice probably maps to the higher frequency range and there isn't that much of it as there isn't that much of a voice heard.
Step #5
By trial and error and looking at Step #5, I figured everything from 700 Hz and down corresponds to the humming noise while the higher noise contributions go from 12000 Hz and higher.
Step #6
You can use the butter function from the Signal Processing Toolbox to help you design a bandpass filter. However, if you don't have this toolbox, refer to this StackOverflow post on how user-made function that achieves the same thing. However, the order for that filter is only 2. Assuming you have the butter function available, you need to figure out what order you want your filter. The higher the order, the more work it'll do. I choose n = 7 to start off. You also need to normalize your frequencies so that the Nyquist frequency maps to 1, while everything else maps between 0 and 1. Once you do that, you can call butter like so:
[b,a] = butter(n, [beginFreq, endFreq], 'bandpass');
The bandpass flag means you want to design a bandpass filter, beginFreq and endFreq map to the normalized beginning and ending frequency you want to for the bandpass filter. In our case, that's beginFreq = 700 / Nyquist and endFreq = 12000 / Nyquist. b,a are the coefficients used for a filter that will help you perform this task. You'll need these for the next step.
%% Design a bandpass filter that filters out between 700 to 12000 Hz
n = 7;
beginFreq = 700 / (fs/2);
endFreq = 12000 / (fs/2);
[b,a] = butter(n, [beginFreq, endFreq], 'bandpass');
Step #7
%% Filter the signal
fOut = filter(b, a, f);
%% Construct audioplayer object and play
p = audioplayer(fOut, fs);
p.play;
You use filter to filter your signal using what you got from Step #6. fOut will be your filtered signal. If you want to hear it played, you can construct and audioplayer based on this output signal at the same sampling frequency as the input. You then use p.play to hear it in MATLAB.
Give this all a try and see how it all works. You'll probably need to play around the most in Step #6 and #7. This isn't a perfect solution, but enough to get you started I hope.
Good luck!
I've a set of data from an EEG device from which I want to find the strength of different brain waves in Matlab. I tried to use EEGLAB but I wasn't really sure how, so at this point I'm simply using the dsp toolbox in Matlab.
For background: I've 15 epochs, 4 seconds in length. The device sampled at 256 Hz, and there are 264 sensors, so there are 1024 data points for each sensor for each epoch, i.e. my raw data is 264 x 1024 x 15. The baseline is removed. The data in each epoch is going to be used to train a classifier eventually, so I'm dealing with each epoch individually. I'll come up with more data samples later.
Anyways, what I've done so far is apply a Hann filter to the data and then run fft on the filtered data. So now I have the information in frequency domain. However, I'm not quite sure how to go from the power of the fft buckets to the power of certain frequency bands (e.g. alpha 8-13), to get the values I seek.
I know the answer should be straightforward but I can't seem to get find the answer I want online, and then there's further confusion by certain sources recommending using a wavelet transform? Here's the little bit of code I have so far, the input "data" is one epoch, i.e. 264 x 1024.
% apply a hann window
siz = size(data);
hann_window = hann(siz(2));
hann_window = repmat(hann_window.', siz(1), 1);
hann_data = data.' * hann_window;
% run fft
X = fft(hann_data, [], 2);
X_mag = abs(X);
X_mag = X_mag.';
Thanks for the assistance!
If I'm understanding your question correctly, you are wanting to scale the FFT output to get the correct power. To do this you need to divide by the number of samples used for the FFT.
X_mag = abs(X)/length(hann_data); % This gives the correct power.
See this question for more info.
Once the content is scaled correctly, you can find the power in a band (e.g. 8 - 13 Hz) by integrating the content from the start to the stop of the band. Since you are dealing with discrete values it is a discrete integration. For perspective, this is equivalent to changing the resolution bandwidth of a spectrum analyzer.
I've only used MATLAB as a calculator, so I'm not as well versed in the program. I hope a kind person may be able to guide me on the way since Google currently is not my friend.
I have a wav file in the link below, where there is a human voice and some noise in the background. I want the noise removed. Is there anyone who can tell me how to do it in MATLAB?
https://www.dropbox.com/s/3vtd5ehjt2zfuj7/Hold.wav
This is a pretty imperfect solution, especially since some of the noise is embedded in the same frequency range as the voice you hear on the file, but here goes nothing. What I was talking about with regards to the frequency spectrum is that if you hear the sound, the background noise has a very low hum. This resides in the low frequency range of the spectrum, whereas the voice has a more higher frequency. As such, we can apply a bandpass filter to get rid of the low noise, capture most of the voice, and any noisy frequencies on the higher side will get cancelled as well.
Here are the steps that I did:
Read in the audio file using audioread.
Play the original sound so I can hear what it sounds like using. Do this by creating an audioplayer object.
Plotted both the left and right channels to take a look at the sound signal in time domain... if it gives any clues. Looking at the channels, they both seem to be the same, so it looks like it was just a single microphone being mapped to both channels.
I took the Fourier Transform and saw the frequency distribution.
Using (4) I figured out the rough approximation of where I should cut off the frequencies.
Designed a bandpass filter that cuts off these frequencies.
Filtered the signal then played it by constructing another audioplayer object.
Let's go then!
Step #1
%% Read in the file
clearvars;
close all;
[f,fs] = audioread('Hold.wav');
audioread will read in an audio file for you. Just specify what file you want within the ''. Also, make sure you set your working directory to be where this file is being stored. clearvars, close all just do clean up for us. It closes all of our windows (if any are open), and clears all of our variables in the MATLAB workspace. f would be the signal read into MATLAB while fs is the sampling frequency of your signal. f here is a 2D matrix. The first column is the left channel while the second is the right channel. In general, the total number of channels in your audio file is denoted by the total number of columns in this matrix read in through audioread.
Step #2
%% Play original file
pOrig = audioplayer(f,fs);
pOrig.play;
This step will allow you to create an audioplayer object that takes the signal you read in (f), with the sampling frequency fs and outputs an object stored in pOrig. You then use pOrig.play to play the file in MATLAB so you can hear it.
Step #3
%% Plot both audio channels
N = size(f,1); % Determine total number of samples in audio file
figure;
subplot(2,1,1);
stem(1:N, f(:,1));
title('Left Channel');
subplot(2,1,2);
stem(1:N, f(:,2));
title('Right Channel');
stem is a way to plot discrete points in MATLAB. Each point in time has a circle drawn at the point with a vertical line drawn from the horizontal axis to that point in time. subplot is a way to place multiple figures in the same window. I won't get into it here, but you can read about how subplot works in detail by referencing this StackOverflow post I wrote here. The above code produces the plot shown below:
The above code is quite straight forward. I'm just plotting each channel individually in each subplot.
Step #4
%% Plot the spectrum
df = fs / N;
w = (-(N/2):(N/2)-1)*df;
y = fft(f(:,1), N) / N; % For normalizing, but not needed for our analysis
y2 = fftshift(y);
figure;
plot(w,abs(y2));
The code that will look the most frightening is the code above. If you recall from signals and systems, the maximum frequency that is represented in our signal is the sampling frequency divided by 2. This is called the Nyquist frequency. The sampling frequency of your audio file is 48000 Hz, which means that the maximum frequency represented in your audio file is 24000 Hz. fft stands for Fast Fourier Transform. Think of it as a very efficient way of computing the Fourier Transform. The traditional formula requires that you perform multiple summations for each element in your output. The FFT will compute this efficiently by requiring far less operations and still give you the same result.
We are using fft to take a look at the frequency spectrum of our signal. You call fft by specifying the input signal you want as the first parameter, followed by how many points you want to evaluate at with the second parameter. It is customary that you specify the number of points in your FFT to be the length of the signal. I do this by checking to see how many rows we have in our sound matrix. When you plot the frequency spectrum, I just took one channel to make things simple as the other channel is the same. This serves as the first input into fft. Also, bear in mind that I divided by N as it is the proper way of normalizing the signal. However, because we just want to take a snapshot of what the frequency domain looks like, you don't really need to do this. However, if you're planning on using it to compute something later, then you definitely need to.
I wrote some additional code as the spectrum by default is uncentered. I used fftshift so that the centre maps to 0 Hz, while the left spans from 0 to -24000Hz while the right spans from 0 to 24000 Hz. This is intuitively how I see the frequency spectrum. You can think of negative frequencies as frequencies that propagate in the opposite direction. Ideally, the frequency distribution for a negative frequency should equal the positive frequency. When you plot the frequency spectrum, it tells you how much contribution that frequency has to the output. That is defined by the magnitude of the signal. You find this by taking the abs function. The output that you get is shown below.
If you look at the plot, there are a lot of spikes around the low frequency range. This corresponds to your humming whereas the voice probably maps to the higher frequency range and there isn't that much of it as there isn't that much of a voice heard.
Step #5
By trial and error and looking at Step #5, I figured everything from 700 Hz and down corresponds to the humming noise while the higher noise contributions go from 12000 Hz and higher.
Step #6
You can use the butter function from the Signal Processing Toolbox to help you design a bandpass filter. However, if you don't have this toolbox, refer to this StackOverflow post on how user-made function that achieves the same thing. However, the order for that filter is only 2. Assuming you have the butter function available, you need to figure out what order you want your filter. The higher the order, the more work it'll do. I choose n = 7 to start off. You also need to normalize your frequencies so that the Nyquist frequency maps to 1, while everything else maps between 0 and 1. Once you do that, you can call butter like so:
[b,a] = butter(n, [beginFreq, endFreq], 'bandpass');
The bandpass flag means you want to design a bandpass filter, beginFreq and endFreq map to the normalized beginning and ending frequency you want to for the bandpass filter. In our case, that's beginFreq = 700 / Nyquist and endFreq = 12000 / Nyquist. b,a are the coefficients used for a filter that will help you perform this task. You'll need these for the next step.
%% Design a bandpass filter that filters out between 700 to 12000 Hz
n = 7;
beginFreq = 700 / (fs/2);
endFreq = 12000 / (fs/2);
[b,a] = butter(n, [beginFreq, endFreq], 'bandpass');
Step #7
%% Filter the signal
fOut = filter(b, a, f);
%% Construct audioplayer object and play
p = audioplayer(fOut, fs);
p.play;
You use filter to filter your signal using what you got from Step #6. fOut will be your filtered signal. If you want to hear it played, you can construct and audioplayer based on this output signal at the same sampling frequency as the input. You then use p.play to hear it in MATLAB.
Give this all a try and see how it all works. You'll probably need to play around the most in Step #6 and #7. This isn't a perfect solution, but enough to get you started I hope.
Good luck!
I am pretty new to Matlab and I am trying to write a simple frequency based speech detection algorithm. The end goal is to run the script on a wav file, and have it output start/end times for each speech segment. If use the code:
fr = 128;
[ audio, fs, nbits ] = wavread(audioPath);
spectrogram(audio,fr,120,fr,fs,'yaxis')
I get a useful frequency intensity vs. time graph like this:
By looking at it, it is very easy to see when speech occurs. I could write an algorithm to automate the detection process by looking at each x-axis frame, figuring out which frequencies are dominant (have the highest intensity), testing the dominant frequencies to see if enough of them are above a certain intensity threshold (the difference between yellow and red on the graph), and then labeling that frame as either speech or non-speech. Once the frames are labeled, it would be simple to get start/end times for each speech segment.
My problem is that I don't know how to access that data. I can use the code:
[S,F,T,P] = spectrogram(audio,fr,120,fr,fs);
to get all the features of the spectrogram, but the results of that code don't make any sense to me. The bounds of the S,F,T,P arrays and matrices don't correlate to anything I see on the graph. I've looked through the help files and the API, but I get confused when they start throwing around algorithm names and acronyms - my DSP background is pretty limited.
How could I get an array of the frequency intensity values for each frame of this spectrogram analysis? I can figure the rest out from there, I just need to know how to get the appropriate data.
What you are trying to do is called speech activity detection. There are many approaches to this, the simplest might be a simple band pass filter, that passes frequencies where speech is strongest, this is between 1kHz and 8kHz. You could then compare total signal energy with bandpass limited and if majority of energy is in the speech band, classify frame as speech. That's one option, but there are others too.
To get frequencies at peaks you could use FFT to get spectrum and then use peakdetect.m. But this is a very naïve approach, as you will get a lot of peaks, belonging to harmonic frequencies of a base sine.
Theoretically you should use some sort of cepstrum (also known as spectrum of spectrum), which reduces harmonics' periodicity in spectrum to base frequency and then use that with peakdetect. Or, you could use existing tools, that do that, such as praat.
Be aware, that speech analysis is usually done on a frames of around 30ms, stepping in 10ms. You could further filter out false detection by ensuring formant is detected in N sequential frames.
Why don't you use fft with `fftshift:
%% Time specifications:
Fs = 100; % samples per second
dt = 1/Fs; % seconds per sample
StopTime = 1; % seconds
t = (0:dt:StopTime-dt)';
N = size(t,1);
%% Sine wave:
Fc = 12; % hertz
x = cos(2*pi*Fc*t);
%% Fourier Transform:
X = fftshift(fft(x));
%% Frequency specifications:
dF = Fs/N; % hertz
f = -Fs/2:dF:Fs/2-dF; % hertz
%% Plot the spectrum:
figure;
plot(f,abs(X)/N);
xlabel('Frequency (in hertz)');
title('Magnitude Response');
Why do you want to use complex stuff?
a nice and full solution may found in https://dsp.stackexchange.com/questions/1522/simplest-way-of-detecting-where-audio-envelopes-start-and-stop
Have a look at the STFT (short-time fourier transform) or (even better) the DWT (discrete wavelet transform) which both will estimate the frequency content in blocks (windows) of data, which is what you need if you want to detect sudden changes in amplitude of certain ("speech") frequencies.
Don't use a FFT since it calculates the relative frequency content over the entire duration of the signal, making it impossible to determine when a certain frequency occured in the signal.
If you still use inbuilt STFT function, then to plot the maximum you can use following command
plot(T,(floor(abs(max(S,[],1)))))
We're trying to analyse flow around circular cylinder and we have a set of Cp values that we got from wind tunnel experiment. Initially, we started off with a sample frequency of 20 Hz and tried to find the frequency of vortex shedding using FFT in matlab. We got a frequency of around 7 Hz. Next, we did the same experiment, but the only thing we changed was the sampling frequency- from 20 Hz to 200 Hz. We got the frequency of the vortex shedding to be around 70 Hz (this is where the peak is located in the graph). The graph doesn't change regardless of the Cp data that we enter. The only time the peak differs is when we change the sample frequency. It seems like the increase in the frequency of vortex shedding is proportional to the sample frequency and this doesn't seem to make sense at all. Any help regarding establishing a relation between sample frequency and vortex shedding frequency would be greatly appreaciated.
The problem you are seeing is related to "data aliasing" due to limitations of the FFT being able to detect frequencies higher than the Nyquist Frequency (half-the sampling frequency).
With data aliasing, a peak in real frequency will be centered around (real frequency modulo Nyquist frequency). In your 20 Hz sampling (assuming 70 Hz is the true frequency, that results in zero frequency which means you're not seeing the real information. One thing that can help you with this is to use FFT "windowing".
Another problem that you may be experiencing is related to noisy data generation via single-FFT measurement. It's better to take lots of data, use windowing with overlap, and make sure you have at least 5 FFTs which you average to find your result. As Steven Lowe mentioned, you should also sample at faster rates if possible. I would recommend sampling at the fastest rate your instruments can sample.
Lastly, I would recommend that you read some excerpts from Numerical Recipes in C (<-- link):
Section 12.0 -- Introduction to FFT
Section 12.1 (Discusses data aliasing)
Section 13.4 (Discusses FFT windowing)
You don't need to read the C source code -- just the explanations. Numerical Recipes for C has excellent condensed information on the subject.
If you have any more questions, leave them in the comments. I'll try to do my best in answering them.
Good luck!
this is probably not a programming problem, it sounds like an experiment-measurement problem
i think the sampling frequency has to be at least twice the rate of the oscillation frequency, otherwise you get artifacts; this might explain the difference. Note that the ratio of the FFT frequency to the sampling frequency is 0.35 in both cases. Can you repeat the experiment with higher sampling rates? I'm thinking that if this is a narrow cylinder in a strong wind, it may be vibrating/oscillating faster than the sampling rate can detect..
i hope this helps - there's a 97.6% probability that i don't know what i'm talking about ;-)
If it's not an aliasing problem, it sounds like you could be plotting the frequency response on a normalised frequency scale, which will change with sample frequency. Here's an example of a reasonably good way to plot a frequency response of a signal in Matlab:
Fs = 100;
Tmax = 10;
time = 0:1/Fs:Tmax;
omega = 2*pi*10; % 10 Hz
signal = 10*sin(omega*time) + rand(1,Tmax*Fs+1);
Nfft = 2^8;
[Pxx,freq] = pwelch(signal,Nfft,[],[],Fs)
plot(freq,Pxx)
Note that the sample frequency must be explicitly passed to the pwelch command in order to output the “real” frequency data. Otherwise, when you change the sample frequency the bin where the resonance occurs will seem to shift, which is similar to the problem you describe.
Methinks you need to do some serious reading on digital signal processing before you can even begin to understand all the nuances of the DFT (FFT). If I was you, I'd get grounded in it first with this great book:
Discrete-Time Signal Processing
If you want more of a mathematical treatment that will really expand your abilities,
Fourier Analysis by Körner
Take a look at this related question. While it was originally asked about asked about VB the responses are generically about FFTs
I tried using the frequency response code as above but it seems that I dont have the appropriate toolbox in Matlab. Is there any way to do the same thing without using fft command? So far, this is what I have:
% FFT Algorithm
Fs = 200; % Sampling frequency
T = 1/Fs; % Sample time
L = 65536; % Length of signal
t = (0:L-1)*T; % Time vector
y = data1; % Your CP values go in this vector
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2);
% Plot single-sided amplitude spectrum.
loglog(f,2*abs(Y(1:NFFT/2)))
title(' y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')
I think there might be something wrong with the code I am using. I'm not sure what though.
A colleague of mine has written some nice GPL-licenced functions for spectral analysis:
http://www.mecheng.adelaide.edu.au/~pvl/octave/
(Update: this code is now part of one of the Octave modules:
http://octave.svn.sourceforge.net/viewvc/octave/trunk/octave-forge/main/signal/inst/.
But it might be tricky to extract just the pieces you need from there.)
They're written for both Matlab and Octave and serve mostly as a drop-in replacement for the analogous functions in the Signal Processing Toolbox. (So the code above should still work fine.)
It may help with your data analysis; better than rolling your own with fft and the like.