Estimating the frequencies of multiple signals in noise is an important problem in signal processing. We can estimate these frequencies, using subspace techniques such as Multiple Signal Classification (MUSIC) [1], adaptive techniques such as Least Mean-Square (LMS) estimation [2], or fast implementations of discrete Fourier transform (DFT) such as the Goertzel algorithm [3]. The choice of the technique is based on a trade-off between the observation time and the available computational resources.
We apply MUSIC, LMS-based normalized Direct adaptive Frequency Estimation Technique (DFET) [4] (NDFET) [5], and the Goertzel algorithm to the detection of dual-tone multiple frequencies (DTMF). We evaluate their performance and compliance with standards through MATLAB simulations and real-time embedded digital signal processor implementations. We coded the ADSP-2101 implementations manually, but we used the Ptolemy 0.6 rapid prototyping environment [6] to generate the Motorola 56001 implementations. A key benefit of using a tool like Ptolemy is that the DTMF decoders can be reused in other designs and retargeted to VHDL, C, and other implementations.