Human hearing beats FFT 
Human hearing beats FFT 
Feb 9 2013, 15:20
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#1


Group: Members Posts: 37 Joined: 5October 08 Member No.: 59436 



Apr 11 2013, 19:33
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#2


Group: Members Posts: 8 Joined: 1April 13 Member No.: 107483 
The paper described the mathematical basis of EST, which uses the ideal case of perfect increasing/decreasing sinusoids.
For realistic data, EST uses different processes, that expect noise. For audio, the EST process is as follows. 1. Find linear prediction coefficients, preferably using the covariance method and not the autocorrelation method. 2. Create the linear prediction polynomial. 3. Find the roots of the linear prediction polynomial to establish the basis set of an exponential sum function, as described in the paper. 4. Use the samples and the basis set to find the coefficients of the function. The key point is that linear prediction coefficients and an exponential sum function, are equivalent, with the exponential sum function having the distinct advantage of being an analytic function with a useful structure. The mathematical basis proves this equivalence. Due to the equivalence, an exponential sum function models an audio signal with the same quality as linear prediction. You may note that the best lossless audio compressors, like OptimFROG, use linear prediction. This is a strong indication of the power of linear prediction to model audio. Since EST generates an analytic function, it is suitable for lossy audio compression, as well as other audio applications. Once EST generated an exponential sum function, you can do the following: Identify noise elements, using frequency and/or amplitude, and remove them. Identify inaudible elements, and remove them. Quantize the coefficients. Resample the audio signal, both sample rate and sample depth. And various other things. Unlike Fourier related methods, which use a predefined basis, EST uses a basis derived from the data. In short, EST for audio combines the flexibility and usefulness of an analytic function with the modeling power of linear prediction. 


Apr 11 2013, 20:36
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#3


Group: Members Posts: 1425 Joined: 9January 05 From: In the kitchen Member No.: 18957 
Unlike Fourier related methods, which use a predefined basis, EST uses a basis derived from the data. In short, EST for audio combines the flexibility and usefulness of an analytic function with the modeling power of linear prediction. Try applying EST to the first 30 seconds of the track "We Shall Be Happy" by Ry Cooder off the album titled "Jazz". Let me know how big your covariance matrix is, too, ok?  
J. D. (jj) Johnston 


Apr 11 2013, 21:32
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#4


Group: Members Posts: 8 Joined: 1April 13 Member No.: 107483 
Unlike Fourier related methods, which use a predefined basis, EST uses a basis derived from the data. In short, EST for audio combines the flexibility and usefulness of an analytic function with the modeling power of linear prediction. Try applying EST to the first 30 seconds of the track "We Shall Be Happy" by Ry Cooder off the album titled "Jazz". Let me know how big your covariance matrix is, too, ok? In a practical implementation the samples will be broken into blocks and there will be a chosen matrix size for that block size. The size of the matrix and the block size will determine accuracy and an accuracyspeed tradeoff. This is also the way it is done when using linear prediction for lossless audio compression or for speech compression. The difference is that EST returns an analytic function. 30 senconds of audio will therefore be broken into many smaller blocks, and not treated as a single block. 


LoFi Version  Time is now: 28th August 2015  21:01 