In Figure 2.36, $x(n)$ denotes speech frames of 256 samples and $x^{\prime}(n)$ denotes the synthesized speech frames. For $L=N(=256)$, the synthesized speech will be identical to the input speech. In this computer exercise, you need to perform speech synthesis on a frame-by-frame basis from a select number (subset) of FFT components, i.e., $L<N$. We will use two methods for the FFT component selection, (i) Method 1: selecting the first $L$ components including their conjugate-symmetric ones out of a total of $N$ components; and (ii) Method 2: the least-squares method (peak-picking method that selects the $L$ components that minimize the sum of squares error.)
a. Use $L=64$ and Method 1 for component selection. Perform speech synthesis and give time-domain plots of both input and output speech records.
b. Repeat the above step using the peak-picking Method 2 (choose $L$ peaks including symmetric components in the FFT magnitude spectrum). List the SNR values in both the cases. Listen to the output files corresponding to (a) and (b) and provide a subjective evaluation (on a MOS scale 1-5). To calibrate the process think of a wireline telephone quality (toll) as 4, cellphone quality around 3.7.
c. Perform speech synthesis for (i) $L=16$ and (ii) $L=128$. Use the peakpicking Method 2 for the FFT component selection. Compute the overall SNR values and provide a subjective evaluation of the output speech for both the cases. Tabulate your results in Table 2.2.