the number of multiplications per second required by the system

Q1. 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 99-tap FIR.

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 and round the number of operations to the nearest integer.

Please tell the approach on how to start this question.

The generic order of sampling rate change is "upsample", "filter", "downsample". That means that we need to run the filter at the upsampled rate, i.e 5000 but given that it is 99tap filter so shall i directly multiply 99*5000=495000. is it okay wrt the asked question or am i missing something

• This question appears to be homework. Complete answers to homework are off-topic, but specific questions about homework are acceptable if they include enough detail. Please edit the question to include more background about what you don't understand. Sep 13 '20 at 8:49
• IT WOULD BE A GREAT HELP IF YOU CAN TELL THE APPROACH TO SOLVE THIS QUESTION.
– dsp
Sep 13 '20 at 9:33
• Hi DSP, your question for approach isn't any more narrow. Explain what you understand, and what exactly you need help with to come up with an approach of your own. (Also, "CAPS LOCK" is the internet way of shouting, and I don't think you meant to shout at me ;) ) Sep 13 '20 at 9:36
• sorry sir i do not mean to shout on you
– dsp
Sep 13 '20 at 9:42
• don't worry, nothing bad happened :) Sep 13 '20 at 9:42