User's Manual - Cornell Lab of Ornithology - Cornell University

for L i ~ L;1. From the denition of [i] wehave the following equation.L;1Xi=0[i] 2 = N f U 2It is sometimes desirable to choose the spectrogram parameters to makethe graph of [i] 2 as rectangular as possible. Accordingly we dene thequantity by the equation P L;1i=0 [i]2 x[i]P 2L;1= 1 L;1Xi=0 [i]2 Li=0x[i] 2From this we derive thefollowing approximation for the energy E.E ==~L;1Xi=0L;1Xi=0p[i]tp[i]t +X~L;1Xi=Lp[i]t= 1 R 1 L;1x[i] 2 + E Lf s=i=01L 1 Rf s L= LRf s =L;1Xi=0P L;1x[i] 2 + E Li=0 [i]2 x[i]P 2L;1+ E Li=0 [i]2XL;1L[i] 2 x[i] 2 + ERf s N f U 2 Li=0X= (L=f N f ;1s) 1RN f U 2 NN f ;1X= n=0XN f ;1+n=0N2 X;1k=0n=0N2Xk=; N 2 +1 jX(n k)j 2 + E L2[k]TRN f U jX(n fs2 k)j2 NTRN f U jX(n N fs2 2 )j2 N f s f s+ E L