[Discuss-gnuradio] Please identify this algorithm

[Dennis Glatting]

Newbie alert: I am not a signal processing expert. 

I am looking at this chunk of code and cannot identify the algorithm in
my books. It's probably obvious and I am clueless. Please help identify
the algorithm so I can go off and find and read about it. The code is
using the FFTW library.

Thanks.


I have a block of /float/ samples (i.e., NOT complex I/Q) in
general_work() and will run two DFTs and one inverse DFT. I am sampling
at 48KHz and looking at a 2400Hz tone occasionally present in the
stream. Two important variables are:

SEARCH_SAMPLES = 61 * ( 48000 / 2400)
SEARCH_RANGE   = (N -
SEARCH_SAMPLES)

N is a collected number of samples input to generate_work().


The first DFT is performed across a buffer where the first
SEARCH_SAMPLES of SEARCH_RANGE elements are the cos()/sin() of a 2400Hz
tone at time t (1/48000) and the remaining elements are zero. It goes
like this:

      for( size_t t = 0; t < SEARCH_SAMPLES; t++ ) {
        plan_a_input.get()[t][0] = d_cos2400.get()[t];
        plan_a_input.get()[t][1] = d_sin2400.get()[t];
      }
      for( size_t t = SEARCH_SAMPLES; t < SEARCH_RANGE; t++ ) {
        plan_a_input.get()[t][0] = 0;
        plan_a_input.get()[t][1] = 0;
      }

A DFT is then performed on "PLAN A":

        plan_a = fftw_plan_dft_1d( SEARCH_RANGE,
                                   plan_a_input.get(),
                                   plan_a_dft.get(),
                                   FFTW_FORWARD, FFTW_ESTIMATE);
        fftw_execute( plan_a );


The second DFT, Plan B, is performed across a buffer of the samples to
general_work().

        for( size_t k = 0; k < SEARCH_RANGE; k++ ) {
          plan_b_input.get()[k][0] = d_dm.get()[k]; // Input samples
          plan_b_input.get()[k][1] = 0.;
        }
        plan_b = fftw_plan_dft_1d( SEARCH_RANGE,
                                   plan_b_input.get(),
                                   plan_b_dft.get(),
                                   FFTW_FORWARD, FFTW_ESTIMATE);
        fftw_execute( plan_b );

That's pretty straight-forward and I have plotted the results, which
are as expected. The following is the part of the algorithm, Plan R,
when Plan A and Plan B are mixed with a little math, I do not
understand:

        for( size_t k = 0; k < SEARCH_RANGE; k++ ) {

          fftw_complex mul = {

            ( plan_a_dft.get()[k][0] * plan_b_dft.get()[k][0]) -
            ( plan_a_dft.get()[k][1] * plan_b_dft.get()[k][1]),

            ( plan_a_dft.get()[k][1] * plan_b_dft.get()[k][0]) +
            ( plan_a_dft.get()[k][0] * plan_b_dft.get()[k][1])

          };

          plan_R_input.get()[k][0] = mul[0]/(float)SEARCH_RANGE;
          plan_R_input.get()[k][1] = mul[1]/(float)SEARCH_RANGE;

        }
        plan_R = fftw_plan_dft_1d( SEARCH_RANGE,
                                   plan_R_input.get(),
                                   plan_R_dft.get(),
                                   FFTW_BACKWARD, FFTW_ESTIMATE);
        fftw_execute( plan_R );

What algorithm is going on there?