Hello Rick, I worked out the math and here is the solution. For two stage interpolation I = I1 x I2, the optimum value of I1 can be given by I1 = (fp + fs + sqrt(I*Fs*(Fs - fs - fp)))/Fs where various quantities are: fp = passband freq in hz fs = stopband freq in hz Fs = sampling freq at the input side. I = overall interpolation ratio. For example if we take fp = 1khz, fs = 3khz, Fs = 8khz and I = 128 and substitute in above equation we get I1 = 8.5, (nearest integer value and also a value which is ratio of 128 is 8). Hence 1st stage interpolation should be by a factor of 8 and second stage interpolation should be by a factor 0f 128/8 = 16. I1 = 8; I2 = 16; This will minimize the number of taps for both filters put together. The above equation has been arrived using Bellangers formula to compute filter order. More accurate equation can be derived using Hermann order equation but that procedure will be very cumbersome and might not be useful for hand calculations. Sometimes approximations help. Regards Bharat Pathak Arithos Designs ~dsp simplified.
Two stage interpolation : Optimum Order
Started by ●January 28, 2008