The document discusses methods for detecting Dual-Tone Multi-Frequency (DTMF) signals. It compares the Direct Fourier Transform (DFT) method, Fast Fourier Transform (FFT) method, and Goertzel algorithm for calculating the DFT. The Goertzel algorithm reduces arithmetic operations compared to the DFT and FFT for certain applications. The document also proposes improving DTMF detection by varying the number of samples analyzed between 80-85 instead of a fixed number, to further reduce computations.

1. Detection of DTMF signals Tomasz Marciniak E-mail: Tomasz.Marciniak @put.poznan.pl

2. OUTLINE 1. DTMF signaling 2. Calculation methods 3. Comparison of arithmetic operations 4. Improving of DTMF detection

3. DTMF signaling

4. DTMF signaling

5. DTMF signaling Example of DTMF application

6. DTMF generation Recommendation Q24

7. Calculation of DFT Direct method Multiplications: 2 N Additions: 2( N -1)

8. Calculation of DFT FFT method We can: calculate two -point DFT’s for two real signals using one -point FFT algorithm, or calculate one -point DFT (for one real signal decimated into two real signals) using one -point FFT algorithm.

9. Calculation of DFT FFT methods Calculation process - four stages: Pacing and bit-reversal of input N -point complex FFT Separation of odd and even parts Generation of final output

10. Calculation of DFT FFT methods Disadvantages of FFT algorithms: compute all output samples of the DFT , the spectrum density depends on the number of the input (output) samples, the FFT needs an accumulation of the all input samples , before beginning of the transformation , they require memorizing many powers of the complex coefficient .

11. Calculation of DFT Goertzel algorithm

12. Goertzel algorithm

13. Comparison of real arithmetic operations FFT – time division Goertzel algorithm DFT – (direct) Number of additions Number of multiplications Method

14. Comparison When Goertzel is more effecitive? Goertzel FFT

15. Comparison When Goertzel is more effecitive?

16. Comparison When Goertzel is more effecitive?

17. Improving of DTMF detection Q: How we can reduce the number of DFT computations? A: By reduction of the number N of the analyzed samples .

18. Improving of DTMF detection

19. Improving of DTMF detection Typical solution : N =205 Proposed solution : Calculation energy for 80  N  85 and next correction

20. Improving of DTMF detection

21. Improving of DTMF detection Tests

22. Improving of DTMF detection Tests

23. Improving of DTMF detection Tests 0.56 Varying block 80  N  85 with correction 13.62 Varying block 80  N  85 3.73 Constant block N =80 1.30 Constant block N =205 0.31 Constant block N =1024 Difference between energy levels [%] Type of calculation