Software Appendix
for
Wiener Transfer Functions

Abstract

This appendix provides links to the IDL routines and supporting functions used to extract and use Wiener filter estimates for the transfer function.

Key words: transfer function, Wiener filters, behavioral dynamics, linear systems analysis, Monte Carlo, pigeons.

This appendix follows an IDL batch processing script that first extracts a Wiener filter transfer function from data collected during a measurement phase (phase 3) and then predict the behavior on a test phase (phase 4). The processing script itself is at b558_analysis.bat. (Any text shown in with a tt font are filenames, pathnames, or IDL variables, listings segments, or command lines.) The data used are for Bird 558 from JSU's E42 experiment and can be obtained from Palya et al.'s (2002) web appendix. The processing script assumes that the data files are located in a subdirectory named bird_558.

The first several lines of the batch processing script just set filenames and some control variables so the Phase 3 data can be read in for processing:

file_path = ':bird_558:'

r_in_file = 'b558_p3_input.txt'
r_in_vari_file = 'b558_p3_input_var.txt'
b_out_file = 'b558_p3_output.txt'
b_out_vari_file = 'b558_p3_output_var.txt'

n_t_funs = 4096
seed = 2866595l

ndata = 256
trial = 2000.

monte_wien_t_fun = monte_carlo_wien_t_fun(file_path, r_in_file, r_in_vari_file, $
b_out_file, b_out_vari_file, n_t_funs, seed)
;
SAVE, monte_wien_t_fun, FILENAME = file_path+'b558_monte_wien_t_fun.dat'
;
plot_t_fun, ndata, trial, monte_wien_t_fun, $
'Bird 558, Phase 3 Monte Carlo Wiener tranfer function', file_path, $
'b558_monte_wien_t_fun.ps'
plot_t_fun_ps, ndata, trial, monte_wien_t_fun, $
'Bird 558, Phase 3 Monte Carlo Wiener tranfer function', file_path, $
'b558_monte_wien_t_fun.ps'

• read_blk_ave_4_data_1024_v2.pro which reads and block averages by four a data file.
• gen_monte_carlo_256.pro which returns a 256 element Monte Carlo copy of the input array using a 256 element standard deviation array to control the range of IDL's Gaussian random number generator RANDOMN.
• simple_t_fun.pro which returns the simple transfer function given by the expression b_meas(f)/r_meas(f) from R_meas(t) and B_meas(t).
• ave_t_fun.pro which returns an averaged transfer function and its standard deviation from an array of individual transfer functions
• wiener_t_fun.pro which returns individual Wiener filter transfer functions using a common SNR(f) array.

• b_out_pred_simp is based on the transfer function used in Palya et al.'s original analysis of E42. The simple read function read_256_t_fun.pro restores the E42 transfer function from the data file b558_tfun_v1_p3.dat. Note that ILD's CONJ function is required since the E42's analysis used the Numerical Recipes's FFT routine which is defined with the opposite sign convention used by IDL's FFT routine.
• b_out_pred_wein is based on the Wiener filter transfer function computed above.

; phase 4
r_in_file = 'b558_p4_input.txt'
r_in_vari_file = 'b558_p4_input_var.txt'
b_out_file = 'b558_p4_output.txt'
b_out_vari_file = 'b558_p4_output_var.txt'

; restore the original E42 transfer function for a comparison
e42_conj_t_fun_alt = CONJ(read_256_t_fun('b558_tfun_v1_p3.dat'))
;
predict_from_t_fun, file_path, r_in_file, r_in_vari_file, b_out_file, $
b_out_vari_file, e42_conj_t_fun, times, b_out, b_out_vari, b_out_pred
b_out_pred_simp = FLOAT(b_out_pred)
;
predict_from_t_fun, file_path, r_in_file, r_in_vari_file, b_out_file, $
b_out_vari_file, monte_wien_t_fun, times, b_out, b_out_vari, b_out_pred
b_out_pred_wein = FLOAT(b_out_pred)
;
plot_predict_v3, ndata, times, b_out, b_out_vari, b_out_pred_simp, $
b_out_pred_wein, 558, 4, file_path
plot_predict_v3_ps, ndata, times, b_out, b_out_vari, b_out_pred_simp, $
b_out_pred_wein, 558, 4, file_path