Improve DTMF decoding algorithm

Being new to signal processing era, I have written a Matlab code (using fft) to decode digits from a given noisy DTMF audio file (wav format). Considering the input signal to be in the form of x(n)+αv(n) where x(n) is the noise-free signal, v(n) is white Gaussian noise and α is a constant controlling how much noise is added. My algorithms is working fairly well in my eyes but I am still looking for improvements. Below is a report of how my code is coping with a noisy tone (containing 13 digits for this particular instance):

@alpha=  0.00 --> SNR is    Inf dB  --> (100% recovery )
@alpha=  0.10 --> SNR is  15.90 dB  --> ( 92% recovery )
@alpha=  0.29 --> SNR is  -2.60 dB  --> ( 84% recovery )
@alpha=  0.31 --> SNR is  -3.76 dB  --> ( 76% recovery )
@alpha=  0.37 --> SNR is  -6.83 dB  --> ( 69% recovery )
@alpha=  0.39 --> SNR is  -7.74 dB  --> ( 61% recovery )
@alpha=  0.41 --> SNR is  -8.61 dB  --> ( 53% recovery )
@alpha=  0.44 --> SNR is  -9.84 dB  --> ( 38% recovery )
@alpha=  0.45 --> SNR is -10.23 dB  --> ( 30% recovery )
@alpha=  0.48 --> SNR is -11.35 dB  --> ( 30% recovery )
@alpha=  0.49 --> SNR is -11.71 dB  --> ( 23% recovery )
@alpha=  0.62 --> SNR is -15.80 dB  --> ( 15% recovery )
@alpha=  0.71 --> SNR is -18.15 dB  --> (  7% recovery )
@alpha=  0.79 --> SNR is -20.01 dB  --> (  0% recovery )

My question is whether I can still improve the performance my algorithm or not? For instance, looking at the second line of the generated report above, indicates that my algorithm is not capable of recovering all digits successfully when SNR is still greater than zero. Can I address that?

Answer 1

[Walter Roberson]

abs(LF - LF1) < Freq_Tolerance and like expressions only need to be calculated once. You can assign the result into temporary variables and then use the result in the following tests.

[Hasan Ghorbani]

Thanks for the reply but I am afraid my question was more about the logic of the code in practical sense if you understand what I mean. Small programming tweaks, like what you just mentioned, is not really going to improve the efficiency that much. Let's put it like that, 'I would like to improve the resistivity of my algorithm to noise' or 'what can I do to get desired results in the presence of more noise'.

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BTW: Have I interpreted your answer correctly? you are suggesting to split the existing 'for' loop into two separate loops? Is that right?

[Walter Roberson]

Move the constants out of the "for" loop to before the loop. LF1 never changes, there is no reason to initialize it multiple times.

In your code, if abs(LF - LF1) < Freq_Tolerance then it is not possible for abs(LF - LF2) < Freq_Tolerance and likewise for LF3 . Therefore you can restructure as

if abs(LF - LF1) < Freq_Tolerance
   if abs(HF - HF1) < Freq_Tolerance
     decodedValue = strcat( decodedValue , '1');
   elseif abs(HF - HF2) < Freq_Tolerance
     decodedValue = strcat( decodedValue , '2');
   elseif abs(HF - HF3) < Freq_Tolerance
     decodedValue = strcat( decodedValue , '3');
   else
      decodedValue = strcat( decodedValue , 'E');
   end
elseif abs(LF - LF2) < Freq_Tolerance
   ....
else
  decodedValue = strcat( decodedValue , 'E');
end

I have to question why anything unidentifiable should be 'E', but that's what your current code says.

These tweaks do make a performance difference.

As for the basic method you are using: I have no opinion on that, as I do not work with audio analysis. I do recall seeing some people doing the analysis in quite different ways, including hilbert transform, but it would take me research to find out the advantages and disadvantages of each method.

[Hasan Ghorbani]

I appreciate your help Walter.