Consider a system implementing a rational sampling rate change by 5/7: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency π/7 and a downsampler by 7. The lowpass filter is a 4rd-order Butterworth filter with transfer function
$$H(z) = \frac{b0 + b1z^{-1} + b2z^{-2} + b3z^{-3} + + b4z^{-4}}{1 - a1z^{-1} - a2z^{-2} - a3z^{-3} - a4z^{-4}}$$ Assume that the input works at a rate of 1000 samples per second. What is the number of multiplications per second required by the system? Assume that multiplications by zero do not count.
Since there are 9 filter coefficients and 5000 samples left (after upsampling, filtering, downsampling), 9*5000 = 45000 is my MAC calculation, but that seems to be wrong approach, any other idea to solve this question???