I want to make a program that would record audio data using PortAudio (I have this part done) and then display the frequency information of that recorded audio (for now, I'd like to display the average frequency of each of the group of samples as they come in).
From some research I've done, I know that I need to do an FFT. So I googled for a library to do that, in C, and found FFTW.
However, now I am a little lost. What exactly am I supposed to do with the samples I recorded to extract some frequency information from them? What kind of FFT should I use (I assume I'd need a real data 1D?)?
And once I'd do the FFT, how do I get the frequency information from the data it gives me?
EDIT : I now found also the autocorrelation algorithm. Is it better? Simpler?
Thanks a lot in advance, and sorry, I have absolutely no experience if this. I hope it makes at least a little sense.
To convert your audio samples to a power spectrum:
if your audio data is integer data then convert it to floating point
pick an FFT size (e.g. N=1024)
apply a window function to N samples of your data (e.g. Hanning)
use a real-to-complex FFT of size N to generate frequency domain data
calculate the magnitude of your complex frequency domain data (magnitude = sqrt(re^2 + im^2))
optionally convert magnitude to a log scale (dB) (magnitude_dB = 20*log10(magnitude))
Related
I have a 2 column vector with times and speeds of a subset of data, like so:
5 40
10 37
15 34
20 39
And so on. I want to get the fourier transform of speeds to get a frequency. How would I go about doing this with a fast fourier transform (fft)?
If my vector name is sampleData, I have tried
fft(sampleData);
but that gives me a vector of real and imaginary numbers. To be able to get sensible data to plot, how would I go about doing this?
Fourier Transform will yield a complex vector, when you fft you get a vector of frequencies, each has a spectral phase. These phases can be extremely important! (they contain most of the information of the time-domain signal, you won't see interference effects without them etc...). If you want to plot the power spectrum, you can
plot(abs(fft(sampleData)));
To complete the story, you'll probably need to fftshift, and also produce a frequency vector. Here's a more elaborate code:
% Assuming 'time' is the 1st col, and 'sampleData' is the 2nd col:
N=length(sampleData);
f=window(#hamming,N)';
dt=mean(diff(time));
df=1/(N*dt); % the frequency resolution (df=1/max_T)
if mod(N,2)==0
f_vec= df*((1:N)-1-N/2); % frequency vector for EVEN length vector
else
f_vec= df*((1:N)-0.5-N/2);
end
fft_data= fftshift(fft(fftshift(sampleData.*f))) ;
plot(f_vec,abs(fft_data))
I would recommend that you back up and think about what you are trying to accomplish, and whether an FFT is an appropriate tool for your situation. You say that you "want to ... get a frequency", but what exactly do you mean by that? Do you know that this data has exactly one frequency component, and want to know what the frequency is? Do you want to know both the frequency and phase of the component? Do you just want to get a rough idea of how many discrete frequency components are present? Are you interested in the spectrum of the noise in your measurement? There are many questions you can ask about "frequencies" in a data set, and whether or not an FFT and/or power spectrum is the best approach to getting an answer depends on the question.
In a comment above you asked "Is there some way to correlate the power spectrum to the time values?" This strikes me as a confused question, but also makes me think that maybe the question you are really trying to answer is "I have a signal whose frequency varies with time, and I want to get an estimate of the frequency vs time". I'm sure I've seen a question along those lines within the past few months here on SO, so I would search for that.
I would like to know how noise can be removed from data (say, radio data that is an array of rows and columns with each data point representing intensity of the radiation in the given frequency and time).The array can contain radio bursts. But many fixed frequency radio noise also exists(RFI=radio frequency intereference).How to remove such noise and bring out only the burst.
I don't mean to be rude, but this question isn't clear at all. Please sharpen it up.
The normal way to remove noise is first to define it exactly and then filter it out. Usually this is done in the frequency domain. For example, if you know the normalized power spectrum P(f) of the noise, build a filter with response
e/(e + P(f))
where e<1 is an attenuation factor.
You can implement the filter digitally using FFT or a convolution kernel.
When you don't know the spectrum of the noise or when it's white, then just use the inverse of the signal band.
I am making a finger plethysmograph(FP) using an LED and a receiver. The sensor produces an analog pulse waveform that is filtered, amplified and fed into a microcontroller input with a range of 3.3-0V. This signal is converted into its digital form.
Smapling rate is 8MHz, Processor frequency is 26MHz, Precision is 10 or 8 bit.
I am having problems coming up with a robust method for peak detection. I want to be able to detect heart pulses from the finger plethysmograph. I have managed to produce an accurate measurement of heart rate using a threshold method. However, the FP is extremely sensitive to movement and the offset of the signal can change based on movement. However, the peaks of the signal will still show up but with varying voltage offset.
Therefore, I am proposing a peak detection method that uses the slope to detect peaks. In example, if a peak is produced, the slope before and after the maximum point will be positive and negative respectively.
How feasible do you think this method is? Is there an easier way to perform peak detection using a microcontroller?
You can still introduce detection of false peaks when the device is moved. This will be present whether you are timing average peak duration or applying an FFT (fast Fourier Transform).
With an FFT you should be able to ignore peaks outside the range of frequencies you are considering (ie those < 30 bpm and > 300 bpm, say).
As Kenny suggests, 8MHz might overwhelm a 26MHz chip. Any particular reason for such a high sampling rate?
Like some of the comments, I would also recommend lowering your sample rate since you only care about pulse (i.e. heart rate) for now. So, assuming you're going to be looking at resting heart rate, you'll be in the sub-1Hz to 2Hz range (60 BPM = 1Hz), depending on subject health, age, etc.
In order to isolate the frequency range of interest, I would also recommend a simple, low-order digital filter. If you have access to Matlab, you can play around with Digital Filter Design using its Filter Design and Analysis Tool (Introduction to the FDATool). As you'll find out, Digital Filtering (wiki) is not computationally expensive since it is a matter of multiplication and addition.
To answer the detection part of your question, YES, it is certainly feasible to implement peak detection on the plethysmograph waveform within a microcontroller. Taking your example, a slope-based peak detection algorithm would operate on your waveform data, searching for changes in slope, essentially where the slope waveform crosses zero.
Here are a few other things to consider about your application:
Calculating slope can have a "spread" (i.e. do you find the slope between adjacent samples, or samples which are a few samples apart?)
What if your peak detection algorithm locates peaks that are too close together, or too far apart, in a physiological sense?
A Pulse Oximeter (wiki) often utilizes LEDs which emit Red and Infrared light. How does the frequency of the LED affect the plethysmograph? (HINT: It may not be significant, but I believe you'll find one wavelength to yield greater amplitudes in your frequency range of interest.)
Of course you'll find a variety of potential algorithms if you do a literature search but I think slope-based detection is great for its simplicity. Hope it helps.
If you can detect the period using zero crossing, even at 10x oversampling of 10 Hz, you can use a line fit of the quick-n-dirty-edge to find the exact period, and then subtract the new wave's samples in that period with the previous, and get a DC offset. The period measurement will have the precision of your sample rate. Doing operations on the time and amplitude-normalized data will be much easier.
This idea is computationally light compared to FFT, which still needs additional data processing.
What is a simple way to see if my low-pass filter is working? I'm in the process of designing a low-pass filter and would like to run tests on it in a relatively straight forward manner.
Presently I open up a WAV file and stick all the samples in a array of ints. I then run the array through the low-pass filter to create a new array. What would an easy way to check if the low-pass filter worked?
All of this is done in C.
You can use a broadband signal such as white noise to measure the frequency response:
generate white noise input signal
pass white noise signal through filter
take FFT of output from filter
compute log magnitude of FFT
plot log magnitude
Rather than coding this all up you can just dump the output from the filter to a text file and then do the analysis in e.g. MATLAB or Octave (hint: use periodogram).
Depends on what you want to test. I'm not a DSP expert, but I know there are different things one could measure about your filter (if that's what you mean by testing).
If the filter is linear then all information of the filter can be found in the impulse response. Read about it here: http://en.wikipedia.org/wiki/Linear_filter
E.g. if you take the Fourier transform of the impulse response, you'll get the frequency response. The frequency response easily tells you if the low-pass filter is worth it's name.
Maybe I underestimate your knowledge about DSP, but I recommend you to read the book on this website: http://www.dspguide.com. It's a very accessible book without difficult math. It's available as a real book, but you can also read it online for free.
EDIT: After reading it I'm convinced that every programmer that ever touches an ADC should definitely have read this book first. I discovered that I did a lot of things the difficult way in past projects that I could have done a thousand times better when I had a little bit more knowledge about DSP. Most of the times an unexperienced programmer is doing DSP without knowing it.
Create two monotone signals, one of a low frequency and one of a high frequency. Then run your filter on the two. If it works, then the low frequency signal should be unmodified whereas the high frequency signal will be filtered out.
Like Bart above mentioned.
If it's LTI system, I would insert impulse and record the samples and perform FFT using matlab and plot magnitude.
You ask why?
In time domain, you have to convolute the input x(t) with the impulse response d(t) to get the transfer function which is tedious.
y(t) = x(t) * d(t)
In frequency domain, convolution becomes simple multiplication.
y(s) = x(s) x d(s)
So, transfer function is y(s)/x(s) = d(s).
That's the reason you take FFT of impulse response to see the behavior of the filter.
You should be able to programmatically generate tones (sine waves) of various frequencies, stuff them into the input array, and then compare the signal energy by summing the squared values of the arrays (and dividing by the length, though that's mathematically not necessary here because the signals should be the same length). The ratio of the output energy to the input energy gives you the filter gain. If your LPF is working correctly, the gain should be close to 1 for low frequencies, close to 0.5 at the bandwidth frequency, and close to zero for high frequencies.
A note: There are various (but essentially the same in spirit) definitions of "bandwidth" and "gain". The method I've suggested should be relatively insensitive to the transient response of the filter because it's essentially averaging the intensity of the signal, though you could improve it by ignoring the first T samples of the input, where T is related to the filter bandwidth. Either way, make sure that the signals are long compared to the inverse of the filter bandwidth.
When I check a digital filter, I compute the magnitude response graph for the filter and plot it. I then generate a linear sweeping sine wave in code or using Audacity, and pass the sweeping sine wave through the filter (taking into account that things might get louder, so the sine wave is quiet enough not to clip) . A visual check is usually enough to assert that the filter is doing what I think it should. If you don't know how to compute the magnitude response I suspect there are tools out there that will compute it for you.
Depending on how certain you want to be, you don't even have to do that. You can just process the linear sweep and see that it attenuated the higher frequencies.
Given two recorded voices in digital format, is there an algorithm to compare the two and return a coefficient of similarity?
I recommend to take a look into the HTK toolkit for speech recognition http://htk.eng.cam.ac.uk/, especially the part on feature extraction.
Features that I would assume to be good indicators:
Mel-Cepstrum coefficients (general timbre)
LPC (for the harmonics)
Given your clarification I think what you are looking for falls under speech recognition algorithms.
Even though you are only looking for the measure of similarity and not trying to turn speech into text, still the concepts are the same and I would not be surprised if a large part of the algorithms would be quite useful.
However, you will have to define this coefficient of similarity more formally and precisely to get anywhere.
EDIT:
I believe speech recognition algorithms would be useful because they do abstraction of the sound and comparison to some known forms. Conceptually this might not be that different from taking two recordings, abstracting them and comparing them.
From wikipedia article on HMM
"In speech recognition, the hidden
Markov model would output a sequence
of n-dimensional real-valued vectors
(with n being a small integer, such as
10), outputting one of these every 10
milliseconds. The vectors would
consist of cepstral coefficients,
which are obtained by taking a Fourier
transform of a short time window of
speech and decorrelating the spectrum
using a cosine transform, then taking
the first (most significant)
coefficients."
So if you run such an algorithm on both recordings you would end up with coefficients that represent the recordings and it might be far easier to measure and establish similarities between the two.
But again now you come to the question of defining the 'similarity coefficient' and introducing dogs and horses did not really help.
(Well it does a bit, but in terms of evaluating algorithms and choosing one over another, you will have to do better).
There are many different algorithms - the general name for this task is Speaker Identification - start with this Wikipedia page and work from there: http://en.wikipedia.org/wiki/Speaker_recognition
I'm not sure this will work for soundfiles, but it gives you an idea how to proceed i hope. That is a basic way how to find a pattern (image) in another image.
You first have to calculate the fft of both the soundfiles and then do a correlation. In formular it would look like (pseudocode):
fftSoundFile1 = fft(soundFile1);
fftConjSoundFile2 = conj(fft(soundFile2));
result_corr = real(ifft(soundFile1.*soundFile2));
Where fft= fast Fourier transform, ifft = inverse, conj = conjugate complex.
The fft is performed on the sample values of the soundfiles.
The peaks in the result_corr vector will then give you the positions of high correlation.
Note that both soundfiles must in this case be of the same size-otherwise you have to place the shorter one into a file of max(soundFileLength) vector.
Regards
Edit: .* means (in matlab style) a component wise mult, you must not do a vector mult!
Next Edit: Note that you have to operate with complex numbers - but there are several Complex classes out there so I think you don't have to bother about this.