Worst case processing loss

The worst case processing loss of a system is the sum of the processing loss (processing gain) and the scalloping loss of the system.

The scalloping loss is a measure of the maximum loss of power in the system that occurs because of the choice of frequency inputted into the system. The processing loss is a measure of the loss of power in the system, because of the system itself. The sum of the two is the worst case processing loss (i.e., due to the choice of system and to the choice of frequency).

For example, suppose that we are using the Hann window on a signal before spectral analysis with the discrete Fourier transform. The equivalent noise bandwidth of the Hann window is 1.5, which means that its processing loss is 10 log10 (1/1.5) = -1.761 dB. The scalloping loss is -1.42 dB. The worst case processing loss then is -3.18 dB.

In computing the worst case processing loss, confusions usually arise because: 1) the processing gain and the scalloping loss must be expressed in decibels to be additive (if both are not in decibels, they should be multiplied); 2) the decibel measure for the processing loss is the measure for power and not amplitude; and 3) the processing loss may be defined as the ratio of the coherent gain over the equivalent noise bandwidth, but, when worst case processing loss numbers are published, they would usually assume a coherent gain of 1.

Worst case processing loss for common windows

The following is the worst case processing loss of some common windows (in dB, with the window definitions on this site).

 Bartlett-Hann -3.15 BlackmanExact BlackmanGeneralized Blackman  α = 0.05  α = 0.20  α = 0.35 -3.48-3.44 -3.25-3.59-4.21 Blackman-Harris -3.85 Blackman-Nuttall -3.81 Bohman -3.55 Dolph-Chebychev  ω0 = 0.1  ω0 = 0.2  ω0 = 0.3 -4.00-4.94-5.58 Flat top -5.78 Gaussian  σ = 0.3  σ = 0.5  σ = 0.7Approximate confined Gaussian  σ = 0.3  σ = 0.5  σ = 0.7Generalized normal  α = 2  α = 4  α = 6 -3.71-3.04-3.16 -3.71-3.04-3.01 -3.04-3.24-3.43 Hamming -3.10 Hann -3.19 Hann-Poisson  α = 0.3  α = 0.5  α = 0.7 -3.27-3.33-3.40 Kaiser  α = 0.5  α = 1.0  α = 5.0 -3.41-3.04-3.49 Kaiser-Bessel -3.57 Lanczos -3.03 Nuttall -3.87 Parzen -3.07 Planck-taper  ε = 0.2  ε = 0.4   ε = 0.5 -3.22-3.15-3.31 Poisson  α = 0.2  α = 0.5  α = 0.8 -3.70-3.45-3.27 Power of cosine  α = 1.0  α = 2.0  α = 3.0 -3.01-3.19-3.47 Rectangular -3.92 Sine -3.01 Triangular -3.07 Tukey  α = 0.3  α = 0.5  α = 0.7 -3.06-3.11-3.31 Ultraspherical (x0 = 1)  μ = 2  μ = 3  μ = 4 -3.02-3.08-3.26 Welch -3.02

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