Rayleigh's Identity and the Fourier coefficients

Attached is my m file that computes the Fourier coefficients for a function that is referred to as the "Friedlander waveform". In the end I check for convergence by using Rayleigh's identity which I have expressed below formally:

              infinity                                           
               -----                                             
                \                                                
                 )             2      /      2        1      1  \
                /        |f(k)|  = int||f(t)| , t = - - T .. - T|
               -----                  \               2      2  /
            k = -infinity

Lines 54 - 56 computes the error associated with the difference in the expression above. Note in line 56 I had to multiply the summation of the square of the Fourier coefficients by 1/4 to get results to make sense. I am a bit puzzled by this factor which suggests a factor (1/2)^4. I thought the factor of 1/2 was already accounted for in the computation of the Fourier coefficients. Can anyone account for this factor? I do not think it is due to the integral bounds because the function does not exist for -t, but I am not sure.

[John D'Errico]

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"Attached is my modified m file (2 instances) that corrects my original problem. The original problem was attempting to reconcile the cumulative sum of the square of the Fourier coefficients with the integral of the square of the "idealized" waveform function. The cause of the problem is due to both parameters w & T. Both w & T factor in computation of the Fourier coefficients, Ck, lines 35 to 41 in the original m file. w also factors in the integration bounds of the square of the "idealized" waveform function, line 55 in the original m file.

Realizing that the summation of the Fourier coefficients squared must asymptotically approach a finite value which corresponds to integral of the square of the "idealized" waveform function a correction factor, R, is computed in the new m file, line 61. Applying this correction factor in line 62 now reconciles the discrepancy.

After applying this correction I then double-checked the results against other modifications to computing the Fourier coefficients. So I commented out lines 34 through 41 & uncommented lines 16 through 21 and ran the 2nd instance of "peakpress2.m". Now I have a slight discrepancy in comparing the results of q against Q. They will not be identically equal, but should concur within probably 6 significant figures. I am hoping a DEBUGGING GURU might help resolve this discrepancy."