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Let $s(n)$ be the input audio frame of size $N$ samples. Let $S(k)$ be the $N$-point DFT. $$ S(k)=\frac{1}{N} \sum_{n=0}^{N-1} s(n) e^{-j 2 \pi k n / N}, \quad k=0,1,2, \ldots, N-1 $$ Obtain a $p$-th order frequency-domain AR model using least squares algorithm that fits the DFT spectral components. Assume that $p<N-1$.

   Let $s(n)$ be the input audio frame of size $N$ samples. Let $S(k)$ be the $N$-point DFT.
$$
S(k)=\frac{1}{N} \sum_{n=0}^{N-1} s(n) e^{-j 2 \pi k n / N}, \quad k=0,1,2, \ldots, N-1
$$

Obtain a $p$-th order frequency-domain AR model using least squares algorithm that fits the DFT spectral components. Assume that $p<N-1$.

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Audio Signal Processing and Coding

Audio Signal Processing and Coding

Andreas Spanias, Ted… 1st Edition

Chapter 9, Problem 4

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We are given an audio frame \( s(n) \) of size \( N \) and its \( N \)-point Discrete Fourier Transform (DFT) \( S(k) \). We need to fit a \( p \)-th order autoregressive (AR) model to the DFT spectral components using the least squares algorithm, where \( p < N-1 Show more…

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Let $s(n)$ be the input audio frame of size $N$ samples. Let $S(k)$ be the $N$-point DFT. $$ S(k)=\frac{1}{N} \sum_{n=0}^{N-1} s(n) e^{-j 2 \pi k n / N}, \quad k=0,1,2, \ldots, N-1 $$ Obtain a $p$-th order frequency-domain AR model using least squares algorithm that fits the DFT spectral components. Assume that $p<N-1$.

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