The answer is option 'A' (Interpolation).

Interpolation is the process of increasing the sampling rate of a signal. It involves adding new samples between existing samples to create a higher-resolution representation of the signal. In sampling rate conversion by a rational factor, the sampling rate is changed by a rational number, which can be expressed as a ratio of two integers.

Sampling Rate Conversion:

Sampling rate conversion refers to the process of changing the sampling rate of a discrete-time signal. It is often necessary when combining or processing signals with different sampling rates, or when converting between analog and digital domains.

Rational Factor:

A rational factor is a ratio of two integers, where the numerator represents the new sampling rate and the denominator represents the original sampling rate. For example, if the original sampling rate is 100 Hz and the desired sampling rate is 200 Hz, the rational factor would be 2/1.

Interpolation:

Interpolation is the process of estimating new samples between existing samples. In the context of sampling rate conversion, interpolation is used to increase the sampling rate by inserting additional samples. These additional samples are computed using mathematical techniques such as linear interpolation, polynomial interpolation, or spline interpolation.

Decimation:

Decimation, on the other hand, is the process of reducing the sampling rate of a signal. It involves removing samples from the original signal to create a lower-resolution representation. Decimation is not performed in sampling rate conversion by a rational factor.

Sampling Rate Conversion by Rational Factor:

In sampling rate conversion by a rational factor, interpolation is always performed to increase the sampling rate. The interpolation factor is equal to the numerator of the rational factor. For example, if the rational factor is 2/1, the interpolation factor is 2.

Decimation, on the other hand, is only performed when the rational factor is less than 1. In such cases, the decimation factor is equal to the denominator of the rational factor.

Therefore, in the given options, only interpolation (option 'A') needs to be performed in sampling rate conversion by a rational factor.