vlt.neuro.spiketrains.spiketrain_sinusoidal

  SPIKETRAIN_SINUSOIDAL - Create a spike train with a sinusoidal rate

   SPIKETIMES = vlt.neuro.spiketrains.spiketrain_sinusoidal(MAXRATE, FREQUENCY,...
       PHASE, RATE_OFFSET, T_START, T_END, DT)

   On top of a background spike rate of RATE_OFFSET, create a
   sinusoidal spike train with a maximum rate MAXRATE, 
   sinusoidal frequency equal to FREQUENCY, with a phase of PHASE radians.
   Time will start at T_START and end at T_END in steps of DT.

   SPIKETIMES will be the spike times generated by a poisson process.

   Example:  Generate a sinusoidal spike train and verify the modulation
   rate with fourier analysis.

     dt = 0.001; t_start = 0; t_end = 50/4; % 50 cycles at 4Hz
     %Generate a spike train with modulation rate of 4Hz and amplitude of 20Hz on
     %a background of 50Hz rate
     ST =vlt.neuro.spiketrains.spiketrain_sinusoidal(20,4,0,50,t_start,t_end,dt);
     % convert back to bins
     T = t_start:dt:t_end; % time bins
     SC = vlt.neuro.spiketrains.spiketimes2bins(ST,T);
     % convert spikes to be instantaneous rates
     SCr = SC/dt;
     [fc,freqs] = vlt.math.fouriercoeffs(SCr,dt);
     figure;
     subplot(2,1,1,'box','off');
     plot(T(find(SC)),SC(find(SC)),'x');
     xlabel('Time(s)');
     ylabel('Spike');
     subplot(2,1,2,'box','off');
     plot(freqs, abs(fc));
     xlabel('Frequency');
     ylabel('Fourier magnitude');
     A = axis; axis([0 10 A(3) A(4)]);