Audio Signal Processing and Coding

COMPUTER EXERCISES

7.3. In this problem, we will study the energy compaction of the DFT and the DCT. Use x(n) = e^−0.5n sin(0.4πn), n = 0, 1, … , 15. Plot the 16-point DFT and 16-point DCT of the input signal, x(n). See how the energy of the sequence is concentrated. Now pick two peaks of the DFT vector and the DCT vector and synthesize the input signal, x(n). Let the synthesized signals be, and . Compute the MSE values between the input signal and the two reconstructed signals. Repeat this for four peaks, six peaks, and eight peaks. Plot the estimated MSE values across the number of peaks selected and comment on your result.

7.4. This computer exercise is a combination of Problems 2.24 and 2.25 in Chapter 2. In particular, the FFT analysis/synthesis module, in Problem 2.25, will be used within the two bands of the QMF bank. The configuration is shown in Figure 7.5.

1. Given, H₀(z) = 1 − z⁻¹, H₁(z) = 1 + z⁻¹. Choose F₀(z) and F₁(z) such that the aliasing term can be cancelled. Use L = 32 and the peak-picking method for component selection. Perform speech synthesis and give time-domain plots of both input and output speech records.
2. Use the same voiced frame selected in Problem 2.24. Give time-domain and frequency-domain plots of and in Figure 7.5.
3. Compute the overall SNR (between