I have experimentally recorded the Sound Pressure Levels of a horn. The SPLs have been obtained through simulation from LMS. But the output of LMS is in the form of spectrum in excel. I want to conver this excel into an audible sound to make psychoacoustic characterisation. How can I do it in MATLAB or any other available resource?
Just import the excel file in Matlab and use "sound(y,Fs)" command, where y is your sample data and Fs is the sample rate.
if it is in form of spectrum and you only have the final spectrum, you probably can't (unless u have the spectrum with the number of samples of the recording, that is usualy not the case).
If it is the case that you have an spectrum with all the samples (remember that humans hear between 20 and 20.000 Hz, so if you need quality audio you need at least 30.000 samples per second), you can obtain the original audio data using the ifft (Inverse discrete Fourier transform ) , but if you only have the spectrum divided in frecuency bands, you can't do it
From what you are saying I can see that what you got is the spectrum by means of the impulse response technique. An LMS signal is known for being very similar to what can be obtained with random noise. This means that your input is very similar to broad band noise, therefore your output is also noise, but it also contains the response of the studied system, in your case, the horn itself. If you try to go back to the sound produced you will end up with noise, which will not be very useful in the case of psychoacoustics evaluation analysis.
Also you have a mistake in your statement. You do not record the sound pressure levels, you do record the sound as it comes in acoustic instantaneous pressure, and then, the SPL can be computed, either in bands on for the whole spectrum, but once this is preformed it is not possible with this data alone to recreate the original signal.
Regards
Your SPL levels will be given for frequency bands, and therefore your information, as all colleagues above pointed out is a spectrum rather than an "audio file". If you want the equivalent magnitude in the time domain (the information that characterises a linear system in the time domain) you are looking to obtain the Impulse response. This can be obtained by using your spectrum (don't expect good resolution though as frequency bands are VERY rough frequency measurements), reconstructing its conjugate symmetric, and then applying the inverse fft. You can´t use excel for this, but maybe you can use audacity or other acoustic software. Ideally, though, you´d program this in python or matlab. If you already have a code for this I suggest you upload it so that we can help you further, or try stackoverflow.com
I have to disagree with Hector, in that it might be possible to obtain the original recorded signal, as you know what the input (excitation) signal was: LMS. This is not a random input so your recorded signal will be y(t)=x(t)*h(t); where x(t)is the LMS signal, * is convolution and h(t) is the impulse response. All of this of course, assuming there are NO non-linear components in your system.
For further characterisation of, almost any, acoustical system I recommend using a slowly swept sine, as described by Farina in the publication below.
Cheers.
Article Simultaneous Measurement of Impulse Response and Distortion ...
Sorry if I wasn't clear enough. On one hand, what I was saying (which is pretty much what Amaya said again at the beginning of her answer), is that using only sound pressure level data, it is not possible to reconstruct the original sound signal.
On the other hand, if you extract the h(t) (impulse response) using the LMS technique, what you get is the response of the system in the frequency domain, there is no original audio per se, you would have to create a signal based on the response of the system, frequency components, relative amplitude, and what is also important, phase information that is not present in the frequency domain. The result would be very similar to the sound produced by the horn, differences will be observed accordingly to the excitation used in order to produce sound with it.
Regards
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