Get a spectrum analyzer eq to see the kick power. take out everything in the kick below 60hz to get rid of that shakiness. and boost a bit around 80-90. take out the highs too for a nice sounding kick. a compressor can take out the peak too for a nice sound.
I'm sorry, but what the hell is kick power? Not trying to be rude, but I assure you a spectrum analyzer can only help you so much (which is usually not at all). A spectrum analyzer will not tell you how something sounds, it will simply tell you about frequency content. It doesn't tell you the formant. It can't tell the difference between a cello and a guitar. It doesn't account for resonance. Furthermore, cutting below 60hz to get rid of shakiness is only applicable if he has shakiness below 60 hz. Taking out the highs for a nice sounding kick is also subjective.
Focus on the attack of the kick. If you don't have enough attack, use a transient plug to increase it slightly, or use a comrpessor with a 5ms (ish) attack to create a stronger transient. As always, some kick sounds are punchier than others in this category. To get more punchy power, boost somewhere between 1kHz and 3.5kHz. I find it's usually around 2-3kHz. As always, highly dependent upon the kick sound you start out with.
I think this is good advice, and I'd like to add to it. It is a huge pet peeve of mine when I don't think the transient of a kick is punchy enough, but sometimes it's not the kick sample itself. It could be the timing of other things. The weird thing about punchy kicks is it may not be punchy across the frequency spectrum. It might just be punchy in the highs or mids. And other things hitting in that area can make the transient sound weird. Culprits I've had are clean electric guitars or cymbals with pronounced transients. If you boost the transient of a kick and it doesn't seem to be punchier, try taking out the transients of other things, or nudging them forward. A cymbal can hit a few MS after a Kick drum and no one will notice, but the kick will sound more powerful and the cymbal will still hit at roughly the same time (assuming the cymbal was a problem in the first place).
sample selection counts for a lot of it. if you start with a weak sample, it will be harder to process it to sound good. but if you just start out with a powerful kick sample you won't need to do much to it. and of course you can layer samples.
This is also true. Having a not punchy kick drum to begin with just means you'll need to work at it. At the same time, if you have a kick drum that sounds punchy and yet it doesn't in your song, than you are putting it in a context in which something is stepping on its transient.
I think you are looking for at least some lows, even though you said you aren't. I just want to make sure you're being objective about punchy. Terms like warmth and crisp can be very abstract sometimes, and I feel like a lot of people just pretend to know what it sounds like, but punch and fat are some objective terms to work with. It's essentially what Chris Carter is getting at. Attack versus sustain. Punch is when a sound is loud, and loses volume quickly. The transient is that first 10ms or so of a sound: the snap of a snare, the consonant of a vocal. It sounds like, to an extent, you aren't just looking for punch, but a little bit of low mid to beef it up, and you feel that without it, the kick doesn't seem punchy (boy I'd love an example). But a kick can be highpassed all the way to 800 and still technically be punchy. It won't make a club shake but it's punchy. Vocals can be punchy too. Punchy vocals are often what come through a dense mix. Those exaggerated consonants poke through dense beats and we sort of fill in the rest for the vowels, which will be much lower in volume.
Arguably, any content below 30hz is not musical and not worth your time. I don't know many people that will debate that, but there may be a few.
More importantly, music is about contrast, and if you want a kick drum to seem punchy without having too much low end, that means the rest of your track has to have even less low end (for the most part). For example, a kick drum with a good amount of low frequency content that has no other sound around it other than a bright synth sounds nice and low. However, that same kick drum hitting at the same time with a piano left hand playing full chords, a bass guitar, and a didgeridoo does not sound like a low end kick at all. The whole thing sounds like a mess of shit, and, to be fair, part of that is because we hear low end in a much different way than anything else on the frequency spectrum. But you could do the same thing with high end. I have never heard anyone praise Flying Lotus's high end, and that's because it's often a mess of sounds. He doesn't do clarity. He doesn't mix for clarity (I honestly don't even know if he mixes his tracks, per se). But his low end is usually spot on, because he leaves it relatively open. Usually just kick and bass, and the bass is usually side-chained to the kick for a lot of compression, so even those items are separated.
So when you think about punch and power, thinking about that kick is important, but it is equally important to think about what is around that kick.
Lastly, and I'm assuming you already don't clip in your DAW, but you need headroom for punch. Because of the nature of punch, a transient being much louder than the rest of the sound, it is going to peak higher than we interpret the volume level to be at (since our DAW's dont measure how we actually perceive loudness). This is versus a sub bass with sustain all the way up. It's just going to peak at a certain point and stay there. So we need headroom. The good news is, headroom is easy with 24 bit recording and not having headroom is one of the dumbest problems anybody has ever had in the digital world. So as long as you're working with a lot of headroom, punch is attainable.