\section{Experimental Results}
\label{sec:experiments}
This section discusses the experimental details, and the results obtained by comparing the proposed WaveDIF model with state-of-the-art deepfake detection techniques. 

% \begin{figure*}[!t]
%     \centering
%     \makebox[0.16\linewidth]{Original}
%     \makebox[0.16\linewidth]{\textsc{Deepfake}}
%     \makebox[0.16\linewidth]{\textsc{Face2Face}}
%     \makebox[0.16\linewidth]{\textsc{FaceShifter}}
%     \makebox[0.16\linewidth]{\textsc{FaceSwap}}
%     \makebox[0.16\linewidth]{\textsc{NeuralTextures}}
    
%     \textbf{\\}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LL_original.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LL_diff.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LL_diff_f2f.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LL_diff_fshft.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LL_diff_fs.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LL_diff_ntx.png}

%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LH_original.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LH_diff.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LH_diff_f2f.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LH_diff_fshft.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LH_diff_fs.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/LH_diff_ntx.png}

%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HL_original.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HL_diff.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HL_diff_f2f.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HL_diff_fshft.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HL_diff_fs.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HL_diff_ntx.png}

%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HH_original.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HH_diff.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HH_diff_f2f.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HH_diff_fshft.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HH_diff_fs.png}
%     \includegraphics[width=0.16\linewidth]{sec/band_plots_ff++/HH_diff_ntx.png}

%     \caption{\label{fig:band_plots_ff++} Three-dimensional visualization of DWT sub-bands. The first row of images depicts the DWT visualization corresponding to Low-Low (LL) sub-band. The following rows depicts visualization corresponding to Low-High (LH), High-Low (HL), and High-High (HH) sub-bands respectively. For the visualizations corresponding to different deepfake models, the wavelet coefficients with variations (from the original video) have been highlighted in with yellow dots.}
% \end{figure*}


\subsection{Dataset}
To evaluate the performance of WaveDIF, it was tested on the \texttt{FaceForensics++} \cite{rossler2019faceforensics++}, and \texttt{CelebDF (v2)} \cite{li2019celeb} dataset. \texttt{FaceForensics++} consists of 1000 real and corresponding 5000 synthetic videos (from five different deepfake generational models). The reason behind the choice of \texttt{FaceForensics++} is the presence of synthetic videos from multiple techniques such as \textsc{Face2Face} \cite{thies2019face2face}, \textsc{FaceSwap} \cite{nirkin2019fsgan}, \textsc{Neural Textures} \cite{thies2019deferred}, etc. \texttt{CelebDF (v2)} consists of 590 real and 5639 synthetic videos of celebrities in various lighting conditions, angles, and expressions. The reason behind the choice of \texttt{CelebDF (v2)} is the specific designing paradigm of the dataset, which reduce visual artifacts (in both spatial, and spectral domain) commonly found in synthetic videos, thus makes the deepfakes look much more realistic and therefore challenging to detect
\cite{li2019celeb}. Additionally, since the objective of this research is to detect deepfakes strictly from artifacts in frequency domain, videos (with no audio) were chosen as is the property of each video in \texttt{FaceForensics++}, and \texttt{CelebDF (v2)} dataset. 

Fig.~\ref{fig:tsne} shows \emph{t-distributed Stochastic Neighbor Embedding} (t-SNE) representation (as suggested by Naskar \emph{et al.} \cite{naskar2024deepfake}) of the four-dimensional feature vectors $\displaystyle{\mathbf{F}_v = [\mathcal{E}_{\text{LL}}, \mathcal{E}_{\text{LH}}, \mathcal{E}_{\text{HL}}, \mathcal{E}_{\text{HH}}]}$ for original and deepfake videos 
from \texttt{FaceForensics++}, and \texttt{CelebDF (v2)}. It can be interpreted from the visualization that \texttt{FaceForensics++} have well separated clusters, thus classification will be more accurate than \texttt{CelebDF (v2)} where there are few overlapping clusters. Note that, these features are log-transformed (refer to Subsection \ref{subsec:exp_setup} for the reason)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
    \centering
    \begin{subfigure}{0.49\linewidth}
        \centering
        \includegraphics[width=\linewidth]{sec/ff_intro/tsne_visualization_ff++.pdf}
        % \caption{t-SNE visualization for \texttt{FaceForensics++}}
    \end{subfigure}
    \begin{subfigure}{0.49\linewidth}
        \centering
        \includegraphics[width=\linewidth]{sec/ff_intro/tsne_visualization_celeb.pdf}
        % \caption{t-SNE visualization for \texttt{CelebDF (v2)}}
    \end{subfigure}
    \caption{\label{fig:tsne} t-SNE visualization (corresponding to wavelet sub-bands' energies, as features) for both the deepfake datasets - \texttt{FaceForensics++} (left sub-figure), and \texttt{CelebDF (v2)} (right sub-figure)}.
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}[htbp]
\caption{\label{compar_ff+} Comparison  of performance between different models operating in spatial and spectral domains for the \texttt{FaceForensics++} data.}
\renewcommand{\arraystretch}{1.2}
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|cccc|cccc|c|}
\hline
\multirow{2}{*}{\textbf{Basis}}                                                         & \multirow{2}{*}{\textbf{Metrics}} & \multicolumn{4}{c|}{\textbf{Classification on   Spatial Features}}                                                                                                                                                                                                                                                                                                                                                                    & \multicolumn{4}{c|}{\textbf{Classification on   Frequency Features}}                                                                                                                                                                                                                                                                                                                                                                        & \multirow{2}{*}{\textbf{Proposed}}           \\ \cline{3-10}
                                                                                        &                                   & \multicolumn{1}{c|}{\textbf{Naskar \emph{et al.}   \cite{naskar2024deepfake}}} & \multicolumn{1}{c|}{\textbf{Agarwal  \emph{et al.}   \cite{agarwal2021md}}} & \multicolumn{1}{c|}{\textbf{Das \emph{et al.} \cite{das2023unmasking}}} & \textbf{He \emph{et al.} \cite{he2024gazeforensics}} & \multicolumn{1}{c|}{\textbf{Tan  \emph{et al.}   \cite{tan2024frequency}}} & \multicolumn{1}{c|}{\textbf{Kohli  \emph{et al.}   \cite{kohli2021detecting}}} & \multicolumn{1}{c|}{\textbf{Jeong \emph{et al.} \cite{jeong2022frepgan}}} & \textbf{Hasanaath \emph{et al.} \cite{hasanaath2025fsbi}} &                                              \\ \hline \hline
\multirow{5}{*}{\begin{tabular}[c]{@{}c@{}}In-Dataset \\ Classification\end{tabular}}   & Accuracy                          & \multicolumn{1}{c|}{0.9701}                                                                                      & \multicolumn{1}{c|}{0.9762}                                                                                   & \multicolumn{1}{c|}{0.9905}                                                                               & 0.9850                                                                                 & \multicolumn{1}{c|}{0.9350}                                                                                  & \multicolumn{1}{c|}{0.9075}                                                                                      & \multicolumn{1}{c|}{0.9471}                                                                                 & 0.9434                                                                                      & 0.9493                                       \\ \cline{2-11} 
                                                                                        & Precision                         & \multicolumn{1}{c|}{0.9719}                                                                                      & \multicolumn{1}{c|}{0.9755}                                                                                   & \multicolumn{1}{c|}{0.9884}                                                                               & 0.9824                                                                                 & \multicolumn{1}{c|}{0.9280}                                                                                  & \multicolumn{1}{c|}{0.9048}                                                                                      & \multicolumn{1}{c|}{0.9447}                                                                                 & 0.9431                                                                                      & 0.9487                                       \\ \cline{2-11} 
                                                                                        & Recall                            & \multicolumn{1}{c|}{0.9702}                                                                                      & \multicolumn{1}{c|}{0.9760}                                                                                   & \multicolumn{1}{c|}{0.9891}                                                                               & 0.9831                                                                                 & \multicolumn{1}{c|}{0.9311}                                                                                  & \multicolumn{1}{c|}{0.9061}                                                                                      & \multicolumn{1}{c|}{0.9453}                                                                                 & 0.9515                                                                                      & 0.9502                                       \\ \cline{2-11} 
                                                                                        & F1-Score                          & \multicolumn{1}{c|}{0.9706}                                                                                      & \multicolumn{1}{c|}{0.9755}                                                                                   & \multicolumn{1}{c|}{0.9885}                                                                               & 0.9794                                                                                 & \multicolumn{1}{c|}{0.9295}                                                                                  & \multicolumn{1}{c|}{0.9055}                                                                                      & \multicolumn{1}{c|}{0.9440}                                                                                 & 0.9392                                                                                      & 0.9495                                       \\ \cline{2-11} 
                                                                                        & Complexity                        & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d^2 \cdot T\right)$}                                                & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot L^2  \cdot T\right)$}                                    & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot L \cdot h^2 + L\cdot a \cdot   h^2\right)$}                  & $\mathcal{O}\left(n\cdot d \cdot k^2 \cdot T\right)$                                   & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot f \cdot T\right)$}                                      & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot k^2 \cdot T\right)$}                                        & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot f^2 \cdot k^2 \cdot T\right)$}                         & $\mathcal{O}\left(n\cdot d \cdot f \cdot L \cdot T\right)$                                  & $\mathcal{O}\left(n \cdot d \log{d} \cdot f \right)$   \\ \hline 
\multirow{5}{*}{\begin{tabular}[c]{@{}c@{}}Cross-Dataset\\ Classification\end{tabular}} & Accuracy                          & \multicolumn{1}{c|}{0.9401}                                                                                      & \multicolumn{1}{c|}{0.9232}                                                                                   & \multicolumn{1}{c|}{0.9615}                                                                               & 0.9457                                                                                 & \multicolumn{1}{c|}{0.8816}                                                                                  & \multicolumn{1}{c|}{0.8640}                                                                                      & \multicolumn{1}{c|}{0.8745}                                                                                 & 0.8879                                                                                      & 0.8883                                       \\ \cline{2-11} 
                                                                                        & Precision                         & \multicolumn{1}{c|}{0.9354}                                                                                      & \multicolumn{1}{c|}{0.9206}                                                                                   & \multicolumn{1}{c|}{0.9579}                                                                               & 0.9418                                                                                 & \multicolumn{1}{c|}{0.8782}                                                                                  & \multicolumn{1}{c|}{0.8613}                                                                                      & \multicolumn{1}{c|}{0.8720}                                                                                 & 0.8848                                                                                      & 0.8876                                       \\ \cline{2-11} 
                                                                                        & Recall                            & \multicolumn{1}{c|}{0.9387}                                                                                      & \multicolumn{1}{c|}{0.9216}                                                                                   & \multicolumn{1}{c|}{0.9594}                                                                               & 0.9421                                                                                 & \multicolumn{1}{c|}{0.8758}                                                                                  & \multicolumn{1}{c|}{0.8589}                                                                                      & \multicolumn{1}{c|}{0.8689}                                                                                 & 0.8810                                                                                      & 0.8875                                       \\ \cline{2-11} 
                                                                                        & F1-Score                          & \multicolumn{1}{c|}{0.9365}                                                                                      & \multicolumn{1}{c|}{0.9208}                                                                                   & \multicolumn{1}{c|}{0.9585}                                                                               & 0.9414                                                                                 & \multicolumn{1}{c|}{0.8741}                                                                                  & \multicolumn{1}{c|}{0.8595}                                                                                      & \multicolumn{1}{c|}{0.8669}                                                                                 & 0.8826                                                                                      & 0.8876                                       \\ \cline{2-11} 
                                                                                        & Complexity                        & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d^2 \cdot T\right)$}                                              & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot L^2  \cdot T\right)$}                                  & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot L \cdot h^2 + L\cdot a \cdot   h^2\right)$}                & $\mathcal{O}\left(n^*\cdot d \cdot k^2 \cdot T\right)$                                 & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot f \cdot T\right)$}                                    & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot k^2 \cdot T\right)$}                                      & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot f^2 \cdot k^2 \cdot   T\right)$}                     & $\mathcal{O}\left(n^*\cdot d \cdot f \cdot L \cdot T\right)$                                & $\mathcal{O}\left(n^*\cdot d \log{d} \cdot f \right)$ \\ \hline
\end{tabular}
}
\end{table*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}[htbp]
\caption{\label{compar_celeb} Comparison  of performance between different models operating in spatial and spectral domains for the \texttt{CelebDF (v2)} data. }
\renewcommand{\arraystretch}{1.2}
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|cccc|cccc|c|}
\hline
\multirow{2}{*}{\textbf{Basis}}                                                         & \multirow{2}{*}{\textbf{Metrics}} & \multicolumn{4}{c|}{\textbf{Classification on   Spatial Features}}                                                                                                                                                                                                                                                                                                                                                                    & \multicolumn{4}{c|}{\textbf{Classification on   Frequency Features}}                                                                                                                                                                                                                                                                                                                                                                        & \multirow{2}{*}{\textbf{Proposed}}           \\ \cline{3-10}
                                                                                        &                                   & \multicolumn{1}{c|}{\textbf{Naskar \emph{et al.}   \cite{naskar2024deepfake}}} & \multicolumn{1}{c|}{\textbf{Agarwal  \emph{et al.}   \cite{agarwal2021md}}} & \multicolumn{1}{c|}{\textbf{Das \emph{et al.} \cite{das2023unmasking}}} & \textbf{He \emph{et al.} \cite{he2024gazeforensics}} & \multicolumn{1}{c|}{\textbf{Tan  \emph{et al.}   \cite{tan2024frequency}}} & \multicolumn{1}{c|}{\textbf{Kohli  \emph{et al.}   \cite{kohli2021detecting}}} & \multicolumn{1}{c|}{\textbf{Jeong \emph{et al.} \cite{jeong2022frepgan}}} & \textbf{Hasanaath \emph{et al.} \cite{hasanaath2025fsbi}} &                                              \\ \hline \hline
\multirow{5}{*}{\begin{tabular}[c]{@{}c@{}}In-Dataset \\ Classification\end{tabular}}   & Accuracy                          & \multicolumn{1}{c|}{0.9402}                                                                                      & \multicolumn{1}{c|}{0.9644}                                                                                   & \multicolumn{1}{c|}{0.9759}                                                                               & 0.9704                                                                                 & \multicolumn{1}{c|}{0.9017}                                                                                  & \multicolumn{1}{c|}{0.8808}                                                                                      & \multicolumn{1}{c|}{0.9089}                                                                                 & 0.8950                                                                                      & 0.9203                                       \\ \cline{2-11} 
                                                                                        & Precision                         & \multicolumn{1}{c|}{0.9364}                                                                                      & \multicolumn{1}{c|}{0.9598}                                                                                   & \multicolumn{1}{c|}{0.9722}                                                                               & 0.9683                                                                                 & \multicolumn{1}{c|}{0.8994}                                                                                  & \multicolumn{1}{c|}{0.8780}                                                                                      & \multicolumn{1}{c|}{0.9072}                                                                                 & 0.8916                                                                                      & 0.9196                                       \\ \cline{2-11} 
                                                                                        & Recall                            & \multicolumn{1}{c|}{0.9396}                                                                                      & \multicolumn{1}{c|}{0.9620}                                                                                   & \multicolumn{1}{c|}{0.9748}                                                                               & 0.9694                                                                                 & \multicolumn{1}{c|}{0.9009}                                                                                  & \multicolumn{1}{c|}{0.8788}                                                                                      & \multicolumn{1}{c|}{0.9101}                                                                                 & 0.8937                                                                                      & 0.9201                                       \\ \cline{2-11} 
                                                                                        & F1-Score                          & \multicolumn{1}{c|}{0.9564}                                                                                      & \multicolumn{1}{c|}{0.9609}                                                                                   & \multicolumn{1}{c|}{0.9737}                                                                               & 0.9685                                                                                 & \multicolumn{1}{c|}{0.8992}                                                                                  & \multicolumn{1}{c|}{0.8785}                                                                                      & \multicolumn{1}{c|}{0.9077}                                                                                 & 0.8925                                                                                      & 0.9193                                       \\ \cline{2-11} 
                                                                                        & Complexity                        & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d^2   \cdot T\right)$}                                              & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot L^2  \cdot T\right)$}                                    & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot L \cdot h^2 + L\cdot a \cdot   h^2\right)$}                  & $\mathcal{O}\left(n\cdot d \cdot k^2 \cdot T\right)$                                   & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot f \cdot T\right)$}                                      & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot k^2 \cdot T\right)$}                                        & \multicolumn{1}{c|}{$\mathcal{O}\left(n\cdot d \cdot f^2 \cdot k^2 \cdot T\right)$}                         & $\mathcal{O}\left(n\cdot d \cdot f \cdot L \cdot T\right)$                                  & $\mathcal{O}\left(n \cdot d \log{d} \cdot f \right)$   \\ \hline
\multirow{5}{*}{\begin{tabular}[c]{@{}c@{}}Cross-Dataset\\ Classification\end{tabular}} & Accuracy                          & \multicolumn{1}{c|}{0.9256}                                                                                      & \multicolumn{1}{c|}{0.9138}                                                                                   & \multicolumn{1}{c|}{0.9557}                                                                               & 0.9371                                                                                 & \multicolumn{1}{c|}{0.8412}                                                                                  & \multicolumn{1}{c|}{0.8174}                                                                                      & \multicolumn{1}{c|}{0.8505}                                                                                 & 0.8330                                                                                      & 0.8701                                       \\ \cline{2-11} 
                                                                                        & Precision                         & \multicolumn{1}{c|}{0.9182}                                                                                      & \multicolumn{1}{c|}{0.9100}                                                                                   & \multicolumn{1}{c|}{0.9500}                                                                               & 0.9314                                                                                 & \multicolumn{1}{c|}{0.8383}                                                                                  & \multicolumn{1}{c|}{0.8144}                                                                                      & \multicolumn{1}{c|}{0.8448}                                                                                 & 0.8294                                                                                      & 0.8692                                       \\ \cline{2-11} 
                                                                                        & Recall                            & \multicolumn{1}{c|}{0.9201}                                                                                      & \multicolumn{1}{c|}{0.9124}                                                                                   & \multicolumn{1}{c|}{0.9521}                                                                               & 0.9338                                                                                 & \multicolumn{1}{c|}{0.8350}                                                                                  & \multicolumn{1}{c|}{0.8126}                                                                                      & \multicolumn{1}{c|}{0.8435}                                                                                 & 0.8257                                                                                      & 0.8695                                       \\ \cline{2-11} 
                                                                                        & F1-Score                          & \multicolumn{1}{c|}{0.9194}                                                                                      & \multicolumn{1}{c|}{0.9115}                                                                                   & \multicolumn{1}{c|}{0.9511}                                                                               & 0.9335                                                                                 & \multicolumn{1}{c|}{0.8346}                                                                                  & \multicolumn{1}{c|}{0.8118}                                                                                      & \multicolumn{1}{c|}{0.8415}                                                                                 & 0.8243                                                                                      & 0.8694                                       \\ \cline{2-11} 
                                                                                        & Complexity                        & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d^2   \cdot T\right)$}                                            & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot L^2  \cdot T\right)$}                                  & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot L \cdot h^2 + L\cdot a \cdot   h^2\right)$}                & $\mathcal{O}\left(n^*\cdot d \cdot k^2 \cdot T\right)$                                 & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot f \cdot T\right)$}                                    & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot k^2 \cdot T\right)$}                                      & \multicolumn{1}{c|}{$\mathcal{O}\left(n^*\cdot d \cdot f^2 \cdot k^2 \cdot   T\right)$}                     & $\mathcal{O}\left(n^*\cdot d \cdot f \cdot L \cdot T\right)$                                & $\mathcal{O}\left(n^*\cdot d \log{d} \cdot f \right)$ \\ \hline
\end{tabular}

}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Experimental Setup}\label{subsec:exp_setup}
The WaveDIF model was trained and evaluated on these datasets using an 80-20 train-test split. Prior to extraction of frequency domain feature from the videos, for each frame three channels of input spectra (RGB) were converted to a single channel (Grayscale), and since videos (in real time) can vary in spatial resolution, the videos were resized to $224 \times 224 \times F$ ($F$ is the frame count). Further, since in the classification phase, input to the regression models are sub-band energy values, which are of order $10^8-10^9$, feeding them directly to the model might lead to numerical instability (like arithmetic overflow or 
precision errors). To get rid of that, a log-transformation $\text{log-transform} \left(z\right) = \log \left(1 + z\right)$ was applied. Note that logarithmic
transformation works only for features having values $\ge 0$. 
Since energy values are computed as sum of squared terms (refer to 
Eqn.~\eqref{sub_band_energies}), the features in 
$\displaystyle{\mathbf{F}_v = [\mathcal{E}_{\text{LL}}, \mathcal{E}_{\text{LH}}, \mathcal{E}_{\text{HL}}, \mathcal{E}_{\text{HH}}]}$ will be $\ge 0$;
thus, logarithmic transformation is applicable. 
All experiments were carried out on a system with 16 GiB main memory, 
\texttt{Intel(R) Core(TM) i7-1065G7 @1.30 GHz} processor and an 
\texttt{NVIDIA GeForce MX330} Graphics Processing Unit with 2 GiB in-built 
memory.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[]
\caption{\label{ablation}Ablation Study: Impact of DFT Filtering and Sub-band Energy Components on WaveDIF's Accuracy}
\renewcommand{\arraystretch}{1.2}
\resizebox{\linewidth}{!}{%
\begin{tabular}{|c|c|c|c|c|c|cc|}
\hline
\multirow{2}{*}{\textbf{Model   Variant}}  & \multirow{2}{*}{\textbf{\begin{tabular}[c]{@{}c@{}}DFT \\ Filtering\end{tabular}}} & \multirow{2}{*}{\textbf{$\mathcal{E}_{\text{LL}}$}} & \multirow{2}{*}{\textbf{$\mathcal{E}_{\text{LH}}$}} & \multirow{2}{*}{\textbf{$\mathcal{E}_{\text{HL}}$}} & \multirow{2}{*}{\textbf{$\mathcal{E}_{\text{HH}}$}} & \multicolumn{2}{c|}{\textbf{Validation Accuracy}}                                               \\ \cline{7-8} 
                                           &                                                                                    &                                                     &                                                     &                                                     &                                                     & \multicolumn{1}{c|}{ \texttt{FF++} \cite{rossler2019faceforensics++}} & \texttt{CDF2} \cite{li2019celeb} \\ \hline
\textbf{WaveDIF} & \checkmark                                                          & \checkmark                           & \checkmark                           & \checkmark                           & \checkmark                           & \multicolumn{1}{c|}{0.9493}                         & 0.9203                         \\ \hline
\textbf{w/o DFT   Filtering}               & \text{\sffamily X}                                 & \checkmark                           & \checkmark                           & \checkmark                           & \checkmark                           & \multicolumn{1}{c|}{0.8041}                         & 0.8049                         \\ \hline
\textbf{w/o $\mathcal{E}_{\text{LL}}$}     & \checkmark                                                          & \text{\sffamily X}  & \checkmark                           & \checkmark                           & \checkmark                           & \multicolumn{1}{c|}{0.8333}                         & 0.8251                         \\ \hline
\textbf{w/o $\mathcal{E}_{\text{LH}}$}     & \checkmark                                                          & \checkmark                           & \text{\sffamily X}  & \checkmark                           & \checkmark                           & \multicolumn{1}{c|}{0.8402}                         & 0.8390                         \\ \hline
\textbf{w/o $\mathcal{E}_{\text{HL}}$}     & \checkmark                                                          & \checkmark                           & \checkmark                           & \text{\sffamily X}  & \checkmark                           & \multicolumn{1}{c|}{0.8411}                         & 0.8406                         \\ \hline
\textbf{w/o $\mathcal{E}_{\text{HH}}$}     & \checkmark                                                          & \checkmark                           & \checkmark                           & \checkmark                           & \text{\sffamily X}  & \multicolumn{1}{c|}{0.8531}                         & 0.8459                         \\ \hline
\end{tabular}

}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Evaluation Results}
The accuracy of WaveDIF was compared
against a number of state-of-the-art models that work both in 
the frequency and spatial domains (refer to Section~\ref{sec:related}). 
Further, to test the generalizability of the proposed model, it 
was evaluated both in-dataset and cross-dataset, and their 
respective accuracies were noted. One advantage of classifying 
between deepfakes and original videos in the frequency domain is 
the lightweight model requirements, but because of less complex 
model artifacts, it trades off the accuracy (though negligibly). 

The evaluation results of WaveDIF on the 
\texttt{FaceForensics++} and \texttt{CelebDF (v2)} datasets 
have been presented in Table \ref{compar_ff+}, and 
\ref{compar_celeb} respectively. In each table, methods 
are compared based on achieved accuracy, precision, recall, 
and F1-score. Additionally, the complexities of the 
methods have been reported in terms of  number of 
in-dataset samples ($n$),  number of cross-dataset 
samples ($n^*$), feature dimension ($d$), number of epochs 
($T$), number of layers ($L$), transformers’ hidden dimension 
($h$), convolutional networks’ kernel size ($k$), transformers’ 
attention heads ($a$), and frequency domain transformation 
complexity ($\mathcal{O}\left(f\right)$). 
The WaveDIF pipeline (training) takes $n$ 
or $n^*$ data points, and each of them are converted to 
frequency domain in $\mathcal{O}\left(f\right)$ time. Wavelet 
decomposition of the filtered videos is done with $d \times \log d$ complexity 
(due to divide-and-conquer approach of Haar filters). 
Thus, overall, the proposed model's complexity is 
$\mathcal{O}\left(n \cdot d \log d \cdot f \right)$. 


As observed through experiments (Table \ref{compar_ff+}, and 
\ref{compar_celeb}) -- the proposed \textbf{WaveDIF model 
outperforms state-of-the-art deepfake detection models (operating in 
frequency domain) for both in-dataset, and cross-dataset basis of 
testing by $0.7433\%$, and $1.1748\%$ respectively}. Table 
\ref{ablation} gives an ablation analysis of each component in the 
WaveDIF model with respect to both the datasets. Table 
\ref{ablation} related to ablation study 
reveals that DFT filtering and all sub-band energy components 
($\mathcal{E}_{\text{LL}}$, $\mathcal{E}_{\text{LH}}$, $\mathcal{E}_{\text{HL}}$, $\mathcal{E}_{\text{HH}}$) 
contribute to WaveDIF's accuracy. Removing DFT 
filtering from the pipeline significantly lowers accuracy 
(by $\approx 15.31\%$), while excluding any sub-band component 
also reduces performance, with $\mathcal{E}_{\text{LL}}$ having 
the largest impact ($\approx 12.23\%$).

% You must include your signed IEEE copyright release form when you submit your finished paper.
% We MUST have this form before your paper can be published in the proceedings.

% Please direct any questions to the production editor in charge of these proceedings at the IEEE Computer Society Press:
% \url{https://www.computer.org/about/contact}. 