# Efficient Detection Approach for DTMF Signal Detection
## 4 Experimental Results  
The MFD detection approach is proposed here as an efficient way to improve the computational complexity required in a DTMF signal detection. In this work, performance is compared in terms of computational load and detection accuracy among the presented MFD, DFT, and a Goertzel algorithm. Tabulated in Table 4 is the computational load comparison among various methods. Since single point detections are performed by a DFT approach and a Goertzel algorithm, \(M\) operations are required to detect the DTMF signals with a frequency shift, depending on the tone frequencies. In contrast, one-time detection is performed in this proposal, resulting in a considerable computational load reduction. In most cases, the value of \(N\) is specified at 512 when performing a DTMF detection task. Accordingly, the number of total operations required for each tone frequency among various methods is presented in Table 5 for the purpose of further analyzing the computational load comparison. Simultaneously, in comparison with the DFT approach, a comparison of the computational saving (CS) versus the tone frequency between a Goertzel algorithm and the proposed approach is given in Table 6. In addition, these experimental results confirm that this proposal provides a CS of 66.67%-87.50% and 55.69%-83.38% in total operations, respectively, compared with the DFT and the Goertzel algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **DFT** & **Goertzel** & **Proposed** \\ \hline Multiplications & \(2 NM\) & \(M(N+2)\) & \(2N\) \\ Additions & \(M(2N-2)\) & \(M(2N+1)\) & \(2N-2\) \\ Total & \(M(4N-2)\) & \(M(3N+3)\) & \(4N-2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational load comparison among various methods; discrete Fourier transform (DFT). Figure 6: Flowchart representation of the proposed detection approach. For each detection procedure of a DTMF signal, an overall operation required and an overall CS comparison with the DFT approach as a benchmark are respectively given in the last row of Tables 5 and 6 as well. The proposed detection algorithm gives a remarkable computational load reduction in comparison with the Goertzel and DFT approaches. Subsequently, an experiment of detection accuracy versus signal-to-noise ratio (SNR) is conducted in this work. In each SNR level experiment, a total of 16,000 test samples are produced for detection experiment. Each DTMF signal in Table 1 has 1000 test samples, and each sample is a DTMF signal with white Gaussian noise (WGN). Presented in Table 7 is the comparison on the detection accuracy versus SNR among various approaches. It shows that the accuracy of the proposed approach drops at SNR of 0 dB, while the DFT and the Goertzel algorithm remains a 100% accuracy. However, according to ITU standard [9; 10], the signal strength is specified to be 15 dB SNR and higher. In such a condition, a 100% accuracy in DTMF signal detection is provided by the presented \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency** & \multicolumn{2}{c}{**Computational Saving (\%)**} \\ \cline{2-3}
**(Hz)** & **Goertzel** & **Proposed** \\ \hline
697 & 24.78 & 66.67 \\
770 & 24.78 & 75.00 \\
852 & 24.78 & 75.00 \\
941 & 24.78 & 75.00 \\
1209 & 24.78 & 83.33 \\
1336 & 24.78 & 83.33 \\
1477 & 24.78 & 83.33 \\
1633 & 24.78 & 87.50 \\ \hline Overall & 24.78 & 80.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the computational saving (CS) versus the tone frequency with DFT approach as a benchmark. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**SNR (dB)**} & \multicolumn{2}{c}{**Detection Accuracy (\%)**} \\ \cline{2-3}  & **DFT, Goertzel** & **Proposed** \\ \hline
5 & 100 & 100 \\
4 & 100 & 100 \\
3 & 100 & 100 \\
2 & 100 & 100 \\
1 & 100 & 100 \\
0 & 100 & 99.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison on the detection accuracy versus signal-to-noise ratio (SNR).