According to Wikipedia, The Itakura–Saito distance (or Itakura–Saito divergence) (IS-distance) is a measure of the difference between an original spectrum and an approximation of that spectrum. It was proposed by Fumitada Itakura and Shuzo Saito in the 1960s while they were with NTT.[1] This is the distance used in several spectral estimation methods. Especially in speech … Continue reading Probabilistic interpretation of Itakura Saito distance

The spectrum of the square wave contains just the nonzero values only at the odd multiple of its frequency(0 ,f0 ,3*f0 ).The intuition behind it is the spectrum value/Fourier series coefficient at given frequency is the measure of correlation(multiply and add) between the signal and sinusoidal signal of given frequency.Consider and square wave(anti-symmetric around zeros) of some … Continue reading What is the intuition behind the square wave spectrum(Fourier series)

The definition of the positive definite(PD) of the matrix(H) is v’*H*v>0 for all non zero vector. The inner product between the vector is proportional to cosine of the angle between the vectors. If we consider v’*(H*v)>0 means the angle between the vector v and H*v(transformed vector) is acute.So positive definite matrix is not going to transforms … Continue reading What is the geometric meaning behind the positive definite matrix ?