% --- Glossary Definitions ---
% Note: Descriptions are based on the provided Indonesian text but translated to English
% for typical glossary conventions. You can adjust the language as needed.

\newglossaryentry{not:signal}{
    name={\ensuremath{S}},
    description={vektor sinyal akselerometer berdimensi 1$\times$262144},
    sort={s},
    type=notation,
}

\newglossaryentry{not:sampling_freq}{
    name={\ensuremath{f_s}},
    description={frekuensi dengan nilai \textit{sampling} ($s$) di mana sinyal kontinu didigitalkan},
    sort={fs},
    type=notation,
}

\newglossaryentry{not:time_length}{
    name={\ensuremath{t}},
    description={panjang waktu data dalam detik},
    sort={t},
    type=notation,
}

\newglossaryentry{not:dataset_A}{
    name={\ensuremath{\mathcal{A}}},
    description={matriks dataset A},
    sort={adataset},
    type=notation,
}

\newglossaryentry{not:dataset_B}{
    name={\ensuremath{\mathcal{B}}},
    description={matriks dataset B},
    sort={bdataset},
    type=notation,
}

\newglossaryentry{not:damage_file}{
    name={\ensuremath{\mathbf{D}}},
    description={matriks akselerometer untuk setiap berkas dengan bentuk $262144\times30$},
    sort={filedamage},
    type=notation,
}
\newglossaryentry{not:joint_index}{
    name={\ensuremath{n}},
    description={indeks atau nomor kerusakan \textit{joint}},
    sort={indexjoint},
    type=notation,
}
\newglossaryentry{not:damage_file_set_case}{
    name={\ensuremath{\mathbf{d}}},
    description={set matriks kerusakan},
    sort={damagefilesetcase},
    type=notation,
}

\newglossaryentry{not:k}{
  name={$k$},
  description={Index for measurement nodes, an integer ranging from 0 to 29.},
  sort={k},
  type=notation,
}

\newglossaryentry{not:Fk}{
  name={$F_{k}$},
  description={Filename string for the raw time-domain signal from node $k$. The specific format mentioned is \texttt{zzzAD}$k$\texttt{.TXT}.},
  sort={Fk},
  type=notation,
}

\newglossaryentry{not:nkFk}{
  name={$n_{k}^{F_{k}}$},
  description={Represents the measurement \textit{node} with index $k$. The raw time-domain signal data from this node, $x_k$, has a length of $L=262144$ samples.},
  sort={nkFk},
  type=notation,
}

\newglossaryentry{not:i}{
  name={$i$},
  description={Index for ``damage-case'' folders, an integer ranging from 0 to 5.},
  sort={i},
  type=notation,
}

\newglossaryentry{not:di}{
  name={\ensuremath{d_{i}}},
  description={Set representing the $i$-th damage scenario, containing data from five consecutive nodes: $\bigl\{\,n_{5i}^{F_{5i}},\;n_{5i+1}^{F_{5i+1}},\;\dots,\;n_{5i+4}^{F_{5i+4}}\bigr\}$. Cardinality: $|d_i|=5$ nodes.},
  sort={di},
  type=notation,
}

\newglossaryentry{not:diTD}{
  name={$d_{i}^{\mathrm{TD}}$},
  description={Time-domain subset of nodes from damage case $d_i$, containing only the first and last nodes: $\bigl\{\,n_{5i}^{F_{5i}},\;n_{5i+4}^{F_{5i+4}}\bigr\}$. Cardinality: $|d_{i}^{\mathrm{TD}}| = 2$ nodes.},
  sort={diTD},
  type=notation,
}

\newglossaryentry{not:calT}{
  name={$\mathcal{T}$},
  description={Short-Time Fourier Transform (STFT) operator. It maps a raw time-domain signal $n_k^{F_k}$ (or $x_k$) from $\mathbb{R}^{L}$ (with $L=262144$) to a magnitude spectrogram matrix $\widetilde{n}_k^{F_k}$ in $\mathbb{R}^{513 \times 513}$.},
  sort={Tcal},
  type=notation,
}

\newglossaryentry{not:L}{
  name={$L$},
  description={Length of the raw time-domain signal, $L=262144$ samples.},
  sort={L},
  type=notation,
}

\newglossaryentry{not:Nw}{
  name={$N_{w}$},
  description={Length of the Hanning window used in the STFT, $N_{w}=1024$ samples.},
  sort={Nw},
  type=notation,
}

\newglossaryentry{not:Nh}{
  name={$N_{h}$},
  description={Hop size (or step size) used in the STFT, $N_{h}=512$ samples.},
  sort={Nh},
  type=notation,
}

\newglossaryentry{not:wn}{
  name={$w[n]$},
  description={Value of the Hanning window function at sample index $n$. The window spans $N_w$ samples.},
  sort={wn},
  type=notation,
}

\newglossaryentry{not:n_summation}{
  name={$n$},
  description={Sample index within the Hanning window and for the STFT summation, an integer ranging from $0$ to $N_w-1$.},
  sort={n_summation},
  type=notation,
}

\newglossaryentry{not:xkm}{
  name={$x_k[m]$}, % Or x_k if it's treated as the whole signal vector
  description={Represents the raw time-domain signal for node $k$. As a discrete signal, it consists of $L=262144$ samples. $x_k[m]$ would be the $m$-th sample.},
  sort={xkm},
  type=notation,
}

\newglossaryentry{not:Skpt}{
  name={$S_k(p,t)$},
  description={Complex-valued result of the STFT for node $k$ at frequency bin $p$ and time frame $t$. This is a scalar value for each $(p,t)$ pair.},
  sort={Skpt},
  type=notation,
}

\newglossaryentry{not:p}{
  name={$p$},
  description={Frequency bin index in the STFT or spectrogram, an integer ranging from $0$ to $512$.},
  sort={p},
  type=notation,
}

\newglossaryentry{not:t_stft}{ % Differentiating t for STFT time frame and t for feature vector time slice if necessary
  name={$t$},
  description={Time frame index in the STFT or spectrogram, an integer ranging from $0$ to $512$. Also used as the time slice index for extracting feature vectors $\mathbf{x}_{i,s,r,t}$ from spectrograms.},
  sort={t},
  type=notation,
}

\newglossaryentry{not:ntildekFk}{ % New entry for the matrix
  name={$\widetilde{n}_k^{F_k}$},
  description={The magnitude spectrogram matrix for node $k$, obtained by applying the STFT operator $\mathcal{T}$ to the time-domain signal $n_k^{F_k}$. This matrix is an element of $\mathbb{R}^{513 \times 513}$.},
  sort={ntildekFk},
  type=notation,
}

\newglossaryentry{not:ntildekFkpt}{ % Modified entry for the element
  name={$\widetilde{n}_k^{F_k}(p,t)$},
  description={Scalar value representing the magnitude of the STFT for node $k$ at frequency bin $p$ and time frame $t$; specifically, $\widetilde{n}_k^{F_k}(p,t) = |S_k(p,t)|$. This is an element of the spectrogram matrix $\widetilde{n}_k^{F_k}$.},
  sort={ntildekFkpt},
  type=notation,
}

\newglossaryentry{not:R}{
  name={\ensuremath{\mathbb{R}}},
  description={The set of real numbers. Used to denote vector spaces like $\mathbb{R}^{N}$ (N-dimensional real vectors) or $\mathbb{R}^{M \times N}$ (M-by-N real matrices).},
  sort={Rbb},
  type=notation,
}

\newglossaryentry{not:diFD}{
  name={$d_{i}^{\mathrm{FD}}$},
  description={Frequency-domain subset for damage case $i$. It contains two spectrogram matrices: $\bigl\{\,\widetilde{n}_{5i}^{F_{5i}},\; \widetilde{n}_{5i+4}^{F_{5i+4}}\,\bigr\}$, where each spectrogram $\widetilde{n}$ is in $\mathbb{R}^{513 \times 513}$. Cardinality: $|d_{i}^{\mathrm{FD}}| = 2$ spectrograms.},
  sort={diFD},
  type=notation,
}

\newglossaryentry{not:r_repetition}{
  name={$r$},
  description={Repetition index within a single damage case, an integer ranging from $0$ to $4$.},
  sort={r_repetition},
  type=notation,
}

\newglossaryentry{not:xboldisr}{
  name={$\mathbf{x}_{i,s,r,t}$},
  description={Feature vector (a row or column, often referred to as a time slice) taken from the $r$-th spectrogram repetition, for damage case $i$ and sensor side $s$, at time slice $t$. This vector is an element of $\mathbb{R}^{513}$.},
  sort={xisrt_bold},
  type=notation,
}

\newglossaryentry{not:s_sensor}{
  name={$s$},
  description={Index representing the sensor side (e.g., identifying Sensor A or Sensor B).},
  sort={s_sensor},
  type=notation,
}

\newglossaryentry{not:yi}{
  name={$y_{i}$},
  description={Scalar label for the damage case $i$, defined as $y_i = i$. This is an integer value from 0 to 5.},
  sort={yi},
  type=notation,
}

\newglossaryentry{not:Lambda}{
  name={$\Lambda(i,s,r,t)$},
  description={Slicing function that concatenates a feature vector $\mathbf{x}_{i,s,r,t} \in \mathbb{R}^{513}$ with its corresponding damage case label $y_i \in \mathbb{R}$, resulting in a combined vector $\bigl[\,\mathbf{x}_{i,s,r,t}, \;y_{i}\bigr] \in \mathbb{R}^{514}$.},
  sort={Lambda},
  type=notation,
}

\newglossaryentry{not:calDs}{
  name={$\mathcal{D}^{(s)}$},
  description={The complete dataset for sensor side $s$. It is a collection of $15390$ data points, where each point is a vector in $\mathbb{R}^{514}$ (513 features + 1 label). Thus, the dataset can be viewed as a matrix of size $15390 \times 514$.},
  sort={Dcal_s},
  type=notation,
}

% --- End Glossary Definitions ---

% --- Added Missing Notations ---
\newglossaryentry{not:U}{
    name={\ensuremath{\mathbf{U}}},
    description={Matrix representing undamaged data, $\mathbf{U} \in \mathbb{R}^{262144 \times 30}$},
    sort={U},
    type=notation,
}

\newglossaryentry{not:Dn}{
    name={\ensuremath{\mathbf{D}^{(n)}}},
    description={Matrix representing damaged data for joint $n$, $\mathbf{D}^{(n)} \in \mathbb{R}^{262144 \times 30}$},
    sort={Dn},
    type=notation,
}

\newglossaryentry{not:aj}{
    name={\ensuremath{\mathbf{a}_{j}^{(n)}}},
    description={Acceleration vector for joint $j$ in case $n$, $\mathbf{a}_{j}^{(n)} \in \mathbb{R}^{262144}$},
    sort={aj},
    type=notation,
}

\newglossaryentry{not:Cn}{
    name={\ensuremath{\mathcal{C}(n)}},
    description={Set of healthy complementary pairs for file $n$},
    sort={Cn},
    type=notation,
}

\newglossaryentry{not:CU}{
    name={\ensuremath{\mathcal{C}_{\mathbf{U}}}},
    description={Set of pairs from undamaged data $\mathbf{U}$},
    sort={CU},
    type=notation,
}

\newglossaryentry{not:DA}{
    name={\ensuremath{\mathcal{D}_A}},
    description={Dataset for the upper sensor channel},
    sort={DA},
    type=notation,
}

\newglossaryentry{not:DB}{
    name={\ensuremath{\mathcal{D}_B}},
    description={Dataset for the lower sensor channel},
    sort={DB},
    type=notation,
}

\newglossaryentry{not:D}{
    name={\ensuremath{\mathcal{D}}},
    description={Labeled dataset containing features and labels},
    sort={D},
    type=notation,
}

\newglossaryentry{not:concat_time}{
    name={\ensuremath{\operatorname{concat}_{\text{time}}}},
    description={Concatenation operator over time},
    sort={concat_time},
    type=notation,
}
% --- End Added Missing Notations ---