DTMF Touch Tone Decoder Using Microchip PIC Microprocessor using PIC12F683

The PIC 12F683 microprocessors built in A/D converter is used to sample an input audio waveform. The samples are analyzed using the Goertzel algorithm to detect whether any of the 8 tones are present.

The Goertzel algorithm is a signal processing algorithm which is used for detecting a single frequency. It acts as a very narrow bandpass filter.  It produces a very sharp response to frequencies within the pass band, and a much lower response for frequencies outside the pass band.

In my implementation of the algorithm, the samples are taken at a rate of 4 times the frequency to be detected. Using a sample rate of 4 times the target frequency makes coefficients used in the algorithm be equal to 1 or 0. This eliminates the need to perform complicated and time consuming multiplication on an 8 bit micro.  I haven’t included all the mathematical details of the algorithm here, but  a Google search will produce articles on the topic if you are interested in learning more about the algorithm itself.

Due to the restriction that the sampling rate must be 4 times the target frequency, the sample rate required will be different for each of the 8 tones that are used for DTMF. So, the algorithm must be run once for each of the 8 frequencies . This means that a separate set of samples must be taken for each frequency of interest, as each frequency will be tested at a different sample rate.

The sharpness of the filter response versus frequency is proportional to the number of samples taken. The response of the algorithm must be sharp enough that it responds to the target frequency, but does not respond to any of the other 7 frequencies. A value of 120 samples was found to produce a reasonably narrow response in experimentation. There is of course a tradeoff between number of samples and the execution time. In order to detect short tones, the execution time should be as short as possible. But, to make a narrow response the number of samples must be larger, resulting in a longer execution time. The number of samples becomes the limiting factor in how short of a tone can be detected.

Once the algorithm has processed 120 samples, it outputs a value. The magnitude of this value is proportional to the amplitude of the frequency of interest. This resulting value is compared against a threshold to determine if target frequency is present.
Once the algorithm has been run for all 8 frequencies, the microprocessor performs logic on the results to determine if a valid DTMF pair is present. A valid DTMF pair is considered to be present only if 1 row freq and 1 col freq is detected. Other combinations are regarded as invalid.

The graph shows the actual response measured using this algorithm running on a PIC 12F683.  The graph shows the frequency response of all 8 times the algorithm is run.  The x axis is frequency, in Hz.  The vertical axis is the value output by the algorithm.  The input was a 1V sine wave, swept from 600Hz to 1800Hz.  Note that the width of the response is wider for the higher frequency filters.  This is due to the fact that the width of the response is proportional to the sample rate, divided by the number of samples taken.  In this implementation of the algorithm, the sample rate is always four times the target frequency, to simply and speed up the math.  However, the same number of samples is used for each of the 8 target frequencies.  The to make the width of the response the same for each would require using the same sample frequency for each, which would involve more time consuming mathematics, or it would require that the number of samples taken at the higher frequencies be greater, which would lengthen the execution time.  If you were using a microprocessor with real DSP functionality, the extra math could be performed very fast and so it would be something that you would most likely include.

Despite the differences in the width of the response, the operation has been very robust at detecting tones, even in the presence of significant noise.