Question: Sampling rate conversion by a rational factor The sampling rate of a digital signal can be changed through a sequence of upsamping, lowpass filtering, and

Sampling rate conversion by a rational factor

The sampling rate of a digital signal can be changed through a sequence of upsamping, lowpass filtering, and downsampling. In this problem we consider the specific case where the change in rate is a rational number I/D, where I and D are positive integers.

Write a function rationalresample that takes as input

f the values of a continuous function sampled at equally spaced time instants

I the numerator of the rational factor

D the denominator of the rational factor

The output of the function should be

g the samples of the continuous function at I/D times the old rate

Note that the resample and upfirdn functions perform the same operation, but they use an approximate FIR lowpass filter (so zooming in on the results will probably show small oscillations). In contrast, here you should design ideal lowpass filters in the frequency domain, which should make the results smoother.

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