## Wednesday 17 September 2014

### Zero Crossing Frequency/Period Measuring Function

Following on from my last post I have now finished coding the first two versions of this function, which are shown in the code boxes below.
``````DEFUN_DLD ( iq_zc_period_indicator_v1, args, nargout,
"-*- texinfo -*-\n\
@deftypefn {Function File} {} iq_zc_period_indicator_v1 (@var{Realpart,Quadrature})\n\
This function takes two input vectors of the real part and quadrature of price,\n\
the analytic signal, and outputs the period calculated from the zero crossings of\n\
the two input vectors.\n\
@end deftypefn" ) {
octave_value_list retval_list ;
int nargin = args.length () ;
int vec_length = args(0).length () ;

// check the input arguments
if ( nargin != 2 )
{
error ( "Invalid input argument(s). Inputs are two vectors, the realpart and quadrature." ) ;
return retval_list ;
}

if ( vec_length < 50 )
{
error ( "Invalid input argument length(s). Input vectors must be > 50 in length." ) ;
return retval_list ;
}

if ( args(1).length () != vec_length )
{
error ( "Invalid input argument length(s). Input vectors differ in length." ) ;
return retval_list ;
}

if ( error_state )
{
error ( "Invalid input argument(s). Inputs are two vectors, the realpart and quadrature." ) ;
return retval_list ;
}
// end of input checking

// inputs
ColumnVector inphase_1 = args(0).column_vector_value () ;
ColumnVector quadrature_1 = args(1).column_vector_value () ;
ColumnVector f_hat ( vec_length ) ;
ColumnVector inphase_1_state ( vec_length ) ;
ColumnVector quadrature_1_state ( vec_length ) ;

for ( octave_idx_type ii (0) ; ii < 50 ; ii ++ ) // Start the initialising loop
{
f_hat(ii) = 20.0 ; // a default period length
inphase_1_state(ii) = 0.0 ; // assuming exactly on zero cross line
quadrature_1_state(ii) = 0.0 ; // assuming exactly on zero cross line
} // end of initialising ii loop

double latest_i_1_zc_time = 49.0 ; // as the "current" bar is bar no. 49
double previous_i_1_zc_time = 49.0 ; // as the "current" bar is bar no. 49
double latest_q_1_zc_time = 49.0 ; // as the "current" bar is bar no. 49
double previous_q_1_zc_time = 49.0 ; // as the "current" bar is bar no. 49

// get the initial states of the inphase_1 and quadrature_1 vectors. A value of
// 1 is assigned if > 0, -1 for < 0 & 0.0 if == 0
inphase_1_state(49) = inphase_1(49) > 0.0 ? 1.0 : ( inphase_1(49) < 0.0 ? -1.0 : 0.0 ) ;
quadrature_1_state(49) = quadrature_1(49) > 0.0 ? 1.0 : ( quadrature_1(49) < 0.0 ? -1.0 : 0.0 ) ;

for ( octave_idx_type ii (50) ; ii < vec_length ; ii ++ ) // Start the main loop
{

// first, assign current states for the inphase_1 and quadrature_1 vectors on this
// new (ii) bar
inphase_1_state(ii) = inphase_1(ii) >= 0.0 ? 1.0 : ( inphase_1(ii) < 0.0 ? -1.0 : 0.0 ) ;
quadrature_1_state(ii) = quadrature_1(ii) >= 0.0 ? 1.0 : ( quadrature_1(ii) < 0.0 ? -1.0 : 0.0 ) ;

// check for a change in state, which indicates a zero crossing
if ( inphase_1_state(ii) == 1.0 && inphase_1_state(ii-1) == -1.0 )
{ // inphase_1 has crossed up over the zero line
latest_i_1_zc_time = double(ii-1) - inphase_1(ii-1) / ( inphase_1(ii) - inphase_1(ii-1) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_i_1_zc_time - previous_i_1_zc_time ) * 2.0 ; // calculate the period from times of zero crosses
previous_i_1_zc_time = latest_i_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else if ( inphase_1_state(ii) == -1.0 && inphase_1_state(ii-1) == 1.0 )
{ // inphase_1 has crossed down over the zero line
latest_i_1_zc_time = double(ii-1) + inphase_1(ii-1) / ( inphase_1(ii-1) - inphase_1(ii) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_i_1_zc_time - previous_i_1_zc_time ) * 2.0 ; // calculate the period from times of zero crosses
previous_i_1_zc_time = latest_i_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else if ( quadrature_1_state(ii) == 1.0 && quadrature_1_state(ii-1) == -1.0 )
{ // quadrature_1 has crossed up over the zero line
latest_q_1_zc_time = double(ii-1) - quadrature_1(ii-1) / ( quadrature_1(ii) - quadrature_1(ii-1) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_q_1_zc_time - previous_q_1_zc_time ) * 2.0 ; // calculate the period from times of zero crosses
previous_q_1_zc_time = latest_q_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else if ( quadrature_1_state(ii) == -1.0 && quadrature_1_state(ii-1) == 1.0 )
{ // quadrature_1 has crossed down over the zero line
latest_q_1_zc_time = double(ii-1) + quadrature_1(ii-1) / ( quadrature_1(ii-1) - quadrature_1(ii) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_q_1_zc_time - previous_q_1_zc_time ) * 2.0 ; // calculate the period from times of zero crosses
previous_q_1_zc_time = latest_q_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else
{ // neither the inphase_1 or quadrature_1 have crossed the zeroline on this bar
f_hat(ii) = f_hat(ii-1) ; // set to most recently calcualted zero crossing period length
}

} // end of main ii loop

retval_list(0) = f_hat ;

return retval_list ;

} // end of function``````
and, almost identical to the above
``````DEFUN_DLD ( iq_zc_period_indicator_v1_1, args, nargout,
"-*- texinfo -*-\n\
@deftypefn {Function File} {} iq_zc_period_indicator_v1_1 (@var{Realpart,Quadrature})\n\
This function takes two input vectors of the real part and quadrature of price,\n\
the analytic signal, and outputs the period calculated from the zero crossings of\n\
the two input vectors.\n\
@end deftypefn" )

{
octave_value_list retval_list ;
int nargin = args.length () ;
int vec_length = args(0).length () ;

// check the input arguments
if ( nargin != 2 )
{
error ( "Invalid input argument(s). Inputs are two vectors, the realpart and quadrature." ) ;
return retval_list ;
}

if ( vec_length < 50 )
{
error ( "Invalid input argument length(s). Input vectors must be > 50 in length." ) ;
return retval_list ;
}

if ( args(1).length () != vec_length )
{
error ( "Invalid input argument length(s). Input vectors differ in length." ) ;
return retval_list ;
}

if ( error_state )
{
error ( "Invalid input argument(s). Inputs are two vectors, the realpart and quadrature." ) ;
return retval_list ;
}
// end of input checking

// inputs
ColumnVector inphase_1 = args(0).column_vector_value () ;
ColumnVector quadrature_1 = args(1).column_vector_value () ;
ColumnVector f_hat ( vec_length ) ;
ColumnVector inphase_1_state ( vec_length ) ;
ColumnVector quadrature_1_state ( vec_length ) ;

for ( octave_idx_type ii (0) ; ii < 50 ; ii ++ ) // Start the initialising loop
{
f_hat(ii) = 20.0 ; // a default period length
inphase_1_state(ii) = 0.0 ; // assuming exactly on zero cross line
quadrature_1_state(ii) = 0.0 ; // assuming exactly on zero cross line
} // end of initialising ii loop

double latest_iq_1_zc_time = 49.0 ; // as the "current" bar is bar no. 49
double previous_iq_1_zc_time = 49.0 ; // as the "current" bar is bar no. 49

// get the initial states of the inphase_1 and quadrature_1 vectors. A value of
// 1 is assigned if > 0, -1 for < 0 & 0.0 if == 0
inphase_1_state(49) = inphase_1(49) > 0.0 ? 1.0 : ( inphase_1(49) < 0.0 ? -1.0 : 0.0 ) ;
quadrature_1_state(49) = quadrature_1(49) > 0.0 ? 1.0 : ( quadrature_1(49) < 0.0 ? -1.0 : 0.0 ) ;

for ( octave_idx_type ii (50) ; ii < vec_length ; ii ++ ) // Start the main loop
{

// first, assign current states for the inphase_1 and quadrature_1 vectors on this
// new (ii) bar
inphase_1_state(ii) = inphase_1(ii) >= 0.0 ? 1.0 : ( inphase_1(ii) < 0.0 ? -1.0 : 0.0 ) ;
quadrature_1_state(ii) = quadrature_1(ii) >= 0.0 ? 1.0 : ( quadrature_1(ii) < 0.0 ? -1.0 : 0.0 ) ;

// check for a change in state, which indicates a zero crossing
if ( inphase_1_state(ii) == 1.0 && inphase_1_state(ii-1) == -1.0 )
{ // inphase_1 has crossed up over the zero line
latest_iq_1_zc_time = double(ii-1) - inphase_1(ii-1) / ( inphase_1(ii) - inphase_1(ii-1) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_iq_1_zc_time - previous_iq_1_zc_time ) * 4.0 ; // calculate the period from times of zero crosses
previous_iq_1_zc_time = latest_iq_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else if ( inphase_1_state(ii) == -1.0 && inphase_1_state(ii-1) == 1.0 )
{ // inphase_1 has crossed down over the zero line
latest_iq_1_zc_time = double(ii-1) + inphase_1(ii-1) / ( inphase_1(ii-1) - inphase_1(ii) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_iq_1_zc_time - previous_iq_1_zc_time ) * 4.0 ; // calculate the period from times of zero crosses
previous_iq_1_zc_time = latest_iq_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else if ( quadrature_1_state(ii) == 1.0 && quadrature_1_state(ii-1) == -1.0 )
{ // quadrature_1 has crossed up over the zero line
latest_iq_1_zc_time = double(ii-1) - quadrature_1(ii-1) / ( quadrature_1(ii) - quadrature_1(ii-1) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_iq_1_zc_time - previous_iq_1_zc_time ) * 4.0 ; // calculate the period from times of zero crosses
previous_iq_1_zc_time = latest_iq_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else if ( quadrature_1_state(ii) == -1.0 && quadrature_1_state(ii-1) == 1.0 )
{ // quadrature_1 has crossed down over the zero line
latest_iq_1_zc_time = double(ii-1) + quadrature_1(ii-1) / ( quadrature_1(ii-1) - quadrature_1(ii) ) ; // calculate time of zero cross
f_hat(ii) = ( latest_iq_1_zc_time - previous_iq_1_zc_time ) * 4.0 ; // calculate the period from times of zero crosses
previous_iq_1_zc_time = latest_iq_1_zc_time ; // update the previous_zc_time to equal the latest_zc_time
}
else
{ // neither the inphase_1 or quadrature_1 have crossed the zeroline on this bar
f_hat(ii) = f_hat(ii-1) ; // set to most recently calcualted zero crossing period length
}

} // end of main ii loop

retval_list(0) = f_hat ;

return retval_list ;

} // end of function``````
The first measures the period every quarter of a cycle, based on a half period measure of zero crossings, and the second every quarter of a cycle based on quarter cycle measurements. The screen shot below shows typical performance on ideal sine and cosine inputs (top pane) with the period measurements shown in the lower pane.
It can be seen that they both perform admirably within their respective theoretical constraints on this ideal input. The subject of my next post will concentrate on the inputs that can be realistically extracted from live price data.