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{IDFT}; +\node [block, right of=idft,node distance=2.5cm,text width=1.5cm] (window) {Window $t(n)$}; +\node [circ, right of=window,node distance=3cm] (sum) {$+$}; +\node [block, below of=sum,text width=1.5cm] (delay) {1 frame delay}; +\node [output, right of=sum,node distance=1cm] (routput) {}; + +\draw [->] node[left of=rinput,node distance=0.5cm] {$\omega_0$\\$\{A_m\}$\\$\{\theta_m\}$} (rinput) -- (construct); +\draw [->] (construct) --(idft); +\draw [->] (idft) -- node[below] {$\hat{s}_l(n)$} (window); +\draw [->] (window) -- node[above of=window, node distance=1cm] + {$\begin{aligned} n =& 0,..,\\ & N-1 \end{aligned}$} (sum); +\draw [->] (window) |- (delay) node[left of=delay,below, node distance=2cm] + {$\begin{aligned} n =& N,...,\\ & 2N-1 \end{aligned}$}; +\draw [->] (delay) -- (sum); +\draw [->] (sum) -- (routput) node[right] {$\hat{s}(n+lN)$}; + +\end{tikzpicture} +\end{center} +\end{figure} + The synthetic speech spectrum is constructed using the sinusoidal model parameters by populating a DFT array $\hat{S}_w(k)$ with weighted impulses at the harmonic centres: \begin{equation} \begin{split} \hat{S}_w(k) &= \begin{cases} - A_m e^{\theta_m}, & m=1..L \\ + A_m e^{j\theta_m}, & m=1..L \\ 0, & otherwise \end{cases} \\ k &= \left \lfloor \frac{m \omega_0 N_{dft}}{2 \pi} + 0.5 \right \rfloor @@ -372,7 +400,7 @@ t(n) = \begin{cases} \end{equation} The frame size, $N=80$, is the same as the encoder. The shape and overlap of the synthesis window is not important, as long as sections separated by the frame size (frame to frame shift) sum to 1: \begin{equation} -t(n) + t(N-1) = 1 +t(n) + t(N-n) = 1 \end{equation} The continuous synthesised speech signal $\hat{s}(n)$ for the $l$-th frame is obtained using: \begin{equation}