Exercise relating to FIR filter
A digital filter deals purely with samples, and this is reflected throughout the analysis of the filter -- most remarkably, the properties of the filter like its passband, stopband, bandwidth, etc are given in radians per sample or equivalent units, rather than Hz and/or radians per second (as is the case with analog filters). In the end, if it's an FIR filter it's just a set of coefficients convoluted with the incoming sampled signal, sample by sample.
Suppose that the initial design specification were for a filter with a 5 kHz cutoff due to noise around 7 kHz. The engineer would design a digital filter with a cutoff of pi/2 radians per sample knowing that the sample rate was 20 kHz. Now, if those filter coefficients were used in a system operating at 40 kHz sampling rate, that cutoff of pi/2 radians per sample now corresponds to a 10 kHz cutoff, or a different filter than the desired one altogether which no longer attenuates the noise. The filter would thus need to be redesigned to attenuate the same noise.