A 50Hz band-pass filter or >50Hz* low-pass filter will pass a single-cycle 50Hz signal. (A kick drum is more than one cycle, although it does decay.) It doesn't matter if it's digital or analog. A basic R-C filter may be just as good as a more-advanced filter for your purposes. If you use an analog filter, you can connect-up your computer speakers or sound system and listen to what you're getting. (The Arduino doesn't have a DAC so you can't listen to an Arduino digital filter.)
Of course, it's cheaper to make a digital filter and a more-advanced digital filter (sharper cutoff, etc.) is just a matter of more software. But you can run-out of processing power, and if you're processor is doing lots of filtering that takes-away from other things you might want to do at the same time.
If you use an analog filter (or no filter at all), a [u]peak detector[/u] (AKA "envelope follower") may be helpful because you Arduino only has to read the "loudness" at maybe 10 samples-per-second instead of reading the "waveform" at thousands of samples-per-second. That frees-up your processor to do other things, but since the peak detector removes all of the frequency-information, you can't use a digital filter.
Of course, there is often bass guitar in music so you can't generally isolate the kick drum. And, "the beat" may be dominated by higher frequencies.
There are beat detection algorithms and you might want to research that. I don't think beat detectors are sas good as the human brain, but I assume (good) beat detectors are "intelligent", or that they use some "fuzzy logic". i.e. When you tap your foot to the beat (or dance), you don't wait for the beat before tapping your foot... You "get into the rhythm", and anticipate the next beat. You might also need some automatic level detection because some songs have a stronger bass drum than others, and some songs are just louder than others, etc.
....I've made a very-crude beat detector (for lighting effects). My non-backed-up computer crashed and I lost the code. But, here's how it works - I use a peak detector (with no filter**) for all of my lighting effects. The beat detector uses the previous peak as a reference, it then has a delay of about 200mS before it can be triggered again. After the delay, another equally-loud beat can be detected immediately, and then the "sensitivity" starts increasing over the following several-milliseconds so the next peak/beat doesn't have to be exactly as loud as the previous one. It isn't perfect, but for my purposes it's "more interesting" than a perfect 1-2-3-4 beat detector.
My beat detector could be improved by using a bandpass filter of about 3-4Hz on the envelope, 3-4 beats per second) and it could be improved even more by making a filter that "tunes" to the actual beat it finds, and maybe even better it I make it anticipate the next couple of beats... But, that's more work and think it's more interesting if my lights to react dynamically to the sound, and only a couple of my effects use beat detection anyway.
- The cutoff frequency of a high-pass or low-filter is defined as the -3dB point. So a "50Hz low-pass filter" will loose some 50hz signal. If you want to get the full 50Hz signal, you need a higher cut-off frequency, depending on the steepness of the filter.
** The use of a peak detector means that it's impossible to do any digital filtering, and all of my effects work form the loudness or "beat". (And, they all automatically calibrate to a moving-average of the loudness or a moving-average of the peak.)
One of my lighting effects is "the worlds simplest effect", and it sort-of reacts to "the beat". I save one a reading from the peak detector (envelope follower) once per second and I make a 20-second moving average. At the same time I'm reading the peak detector in a fast-loop while, comparing to the average. When the reading is above average the light comes-on, and it's otherwise off. The light is on about half the time and off about half the time, blinking to the music.
In the real-world I have more than one light and they can all go on & off together, or I can toggle some-on while the others are off, or I can trigger a random pattern, etc., making this simplest effect into multiple, more-interesting effects.
... Of course, that can be done without the peak detector circuit... You just have to make your software "read the loudness".