Let me just add, that in case of having a non-oversampled linearly
interpolated fractional delay line with exactly 0.5 sample delay (most
high-frequency roll-off position), the frequency response formula is
not sinc^2, but rather, sin(2*PI*f)/(2*sin(PI*f)), as I discussed
earlier.
In that case, the results are slightly different:
#---- Tcl code -------------------------------------------------------------
set pi 3.141592653589793238
set freqs {1/4. 1/8. 1/16. 1/32. 1/64. 1/128. 1/256. 1/512. 1/1024.}
set amt 2
foreach freq $freqs {
set amp [expr sin(2*$pi*$freq)/(2*sin($pi*$freq))]
set db [expr 20.0 * log($amp)/log(10)]
puts "[format %-8s ${amt}X:][format %f $db] dB"
set amt [expr $amt*2]
}
#---- End of code ----------------------------------------------------------
Results:
2X: -3.01 dB
4X: -0.688 dB
8X: -0.169 dB
16X: -0.0419 dB
32X: -0.0105 dB
64X: -0.00262 dB
128X: -0.00065 dB
256X: -0.000164 dB
512X: -0.000041 dB
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