| Original time series: | \(T = [t_0, t_1, \ldots , t_N] \in \mathbb {R}^{N+1}\) |
| After compression: | \([(\texttt {len}_1, \texttt {inc}_1), (\texttt {len}_2, \texttt {inc}_2), \ldots , (\texttt {len}_n, \texttt {inc}_n)] \in \mathbb {R}^{2 \times n}\) |
| After digitization: | \(S=[s_1, s_2, \ldots , s_n] \in \mathbb {A}^n\) with \(\mathbb {A} = \{ a_1, a_2, \ldots , a_k \}\) |
| After inverse-digitization: | \([(\widetilde{\texttt {len}}_1, \widetilde{\texttt {inc}}_1), (\widetilde{\texttt {len}}_2, \widetilde{\texttt {inc}}_2), \ldots , (\widetilde{\texttt {len}}_n, \widetilde{\texttt {inc}}_n)] \in \mathbb {R}^{2 \times n}\) |
| After quantization: | \([(\widehat{\texttt {len}}_1, \widehat{\texttt {inc}}_1), (\widehat{\texttt {len}}_2, \widehat{\texttt {inc}}_2), \ldots , (\widehat{\texttt {len}}_n, \widehat{\texttt {inc}}_n)] \in \mathbb {R}^{2 \times n}\) |
| After inverse-compression: | \(\widehat{T} = [\widehat{t}_0, \widehat{t}_1, \ldots , \widehat{t}_N] \in \mathbb {R}^{N+1}\) |