In a digital communication receiver, matched filter(SRRC filter) is used. In different literatures, the location of the matched filter is mentioned in two different places. One is just after the ADC followed by the resampler of a timing recovery system, and the other one is after the resampler of timing recovery process followed by a timing error detector (TED).
To my understanding, practically it should be after the resampler. Lets say, the interpolation factor is $4$ at the transmitter side, that means $4$ samples per symbol. So, if the Symbol rate is $2\textrm{ MHz}$, the sample rate is $8\textrm{ MHz}$.
Now, in the receiver side, let's say the ADC I am using is sampling at $40\textrm{ MSps}$ i.e the sample rate is $40\textrm{ MHz}$, which is $20$ times the symbol rate, or $5$ times the transmitter sample rate. It is only after resampling that we will get back our original transmitter sampling rate, so that SRRC filter (with oversampling rate $4$) can be employed. Otherwise, if we use before the resampler, we have to use a SRRC filter (with oversampling rate $20$), which will increase the number of filter coefficients and hence the hardware cost.
Is my understanding correct?