Audio Signal Processing and Coding

PROBLEMS

9.1. Modify the DFT such that the frequency components are computed from . Why is this approach useful in sinusoidal analysis-synthesis?

9.2. In sinusoidal analysis-synthesis, we require the analysis window to be normalized, i.e., . Explain with mathematical arguments the reason for the use of this normalization.

9.3. Explain with diagrams, text, and equations how the sinusoidal birth-death frequency tracker works.

9.4. Let s(n) be the input audio frame of size N samples. Let S(k) be the N-point DFT.

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

9.5. Write an algorithm that selects the K peaks from an N-point DFT magnitude spectrum (K < N). Assume that the K spectral peaks are associated with pure tones in the input signal, s(n). Design a sinusoidal analysis-synthesis model that minimizes the MSE, ε,

where s(n) is the input speech, A_k represents the amplitude, ω_k represents the frequency, and ϕ_k denotes the phase of the k-th sinusoid. Hint: Refer to [McAu86].

9.6. In this problem, we ...