# Efficient Detection Approach for DTMF Signal Detection
## 1 Introduction  
Dual-tone multi-frequency (DTMF) signals [1; 2; 3; 4] were developed by Bell Labs for the purpose of automatic fulfilled long-distance calls. DTMF signal and the detection of DTMF have been widely used in modern communication systems. In a public switched telephone network (PSTN), the DTMF technique is applied to telecommunication signaling over analog telephone lines in the voice-frequency band among telephone handsets, other communications devices, and a switching center. Recently, the DTMF technique has also been widely applied to household intelligent alarm systems [5], remote control systems [6; 7], VoIP systems [8], and so on. Standardized by International Telecommunications Union (ITU) [9], the DTMF technique uses eight different frequency signals transmitted in pairs to represent 16 different figures and symbols, as tabulated in Table 1. It consists of two mutually exclusive frequency groups: the low-frequency group (<1 kHz) and the high-frequency group (>1 kHz). Four low-frequency tones (697, 770, 852, 941 Hz) are assigned to rows, while four high-frequency tones (1209, 1336, 1477, 1633 Hz) are assigned to columns. Thus, each pair of frequencies corresponding to the column and row are adopted as a unique DTMF tone. In addition, with a permitted frequency tolerance of approximately \(\pm\) 1.5% of the tone frequency in ITU specification for valid DTMF tones, the frequency components in the exterior of \(\pm\) 3.5% must be rejected, while those between \(\pm\) 1.5% and \(\pm\) 3.5% can be either accepted or rejected. Hence, a tone detection must be conducted over the frequency range of \(\pm\) 3.5%. Consequently, a tone detection algorithm is necessary at the receiving end to recognize a received DTMF signal. In the literature, DTMF detection algorithms [10; 11; 12; 13; 14; 15; 16] can be categorized into two types, namely, the discrete Fourier transform (DFT) based approaches [10; 11; 12] and the Goertzel-based algorithms [13; 14; 15; 16]. In the former approaches, the frequency response of a received signal is calculated by the DFT formula, and then determines the tone frequency thereof. However, for the purpose of computational complexity reduction, only the frequency bin that corresponds to a detected tone is calculated. Such an approach is referred to one-point DFT detection approach as well. On the other hand, the Goertzel-based algorithms were demonstrated to provide a way for efficient evaluation of individual terms of the DFT. The Goertzel-based algorithms are widely used in DTMF signal detection, due to the advantage of a considerable computational time saving during a detection procedure. However, one thing that these two detection types have in common is that a tone detection task is performed at a single point each time, meaning that there is an inevitable and significant rise in the required computational load. Alternatively, a number of studies [17; 18; 19; 20] were published with a focus on the applications of tone detection algorithms to the design of field-programmable gate array (FPGA), very large scale Integration (VLSI) chips and digital signal processor (DSP) processors. As a matter of fact, the detection algorithms involved in the above-stated references belong to either DFT or Goertzel algorithm-based ones. In addition to the computational complexity, quantities, e.g., chip area occupied, power dissipation, and more, need to be taken into account in chip design. Not as in chip design, the computational complexity is the first priority issue when porting a tone detection code to a hardware platform, and the Goertzel algorithm stands as the most advantageous candidate in terms of the computational complexity. If a tone detection code can be ported to a hardware platform, say an embedded system platform, via programming, then the hardware cost can be kept down, that is to say, a tone detection chip is not required in the embedded platform.