A interpolator which increase sampling rate by L times is followed by an anti-imaging filter, the filter is said to have a cutoff frequency of Fs/2L. Is Fs here is the frequency before or after interpolation?
Also during rational sampling rate conversion, the filter in between the interpolator and decimator is said to have cutoff at min(Fs/2L, Fs/2M). But clearly Fs isn't same for both of them. The interpolator changes the sampling rate before the signal passes through the decimator.
The classical up-fir-down system for rational sample-rate conversion
$$ x[n] \longrightarrow \boxed{\uparrow L} \longrightarrow \boxed{ h[n] } \longrightarrow \boxed{\downarrow M} \longrightarrow y[n] $$
has the following specification for its discrete-time lowpass filter $h[n]$ which is a serial cascade of two lowpass filters: the interpolation filter $h_i[n]$ with a gain $L$ and cutoff frequency $\pi/L$ radians (per sample), and the decimation filter $h_d[n]$ with unity gain and cutoff frequency $\pi/M$ radians (per sample). The two filters are convolved, and the result is represented by the single filter $h[n]$ with a gain of $L$ and cotoff frequency of $\omega_c = \min\{ \pi/L, \pi/M \}$ radians per second.
If the original sequence $x[n]$ was sampled at $F_s$ samples per second, then the expander stage will increase the sample rate by $L$, yielding an intermediate sample rate of $F'_s = L \times F_s$. Since the filtering is applied after the expansion and before the decimation, it will be applied at the intermediate high sample-rate $F'_s$. Therefore, the effective analog frequency (in Hz) for the cutoff frequency of the lowpass filter $h[n]$ will be: $$ \begin{align} f_c &= \frac{\omega_c}{2\pi} F'_s \\ \\ &= \frac{ \min \{ \frac{\pi}{L},\frac{\pi}{M} \} }{2\pi} F'_s \\ \\ &= \frac{ \min \{ \frac{\pi}{L},\frac{\pi}{M} \} }{2\pi} L \times F_s \\ \\ &= \min \{ \frac{F_s}{2}, \frac{L F_s}{ 2M} \} \\ \\ \end{align} $$
If $L < M$, then $f_c = \frac{ L F_s}{2M}$, else, $f_c = \frac{F_s}{2}$.
