That's not my understanding ... we just have half wave pulses , very spaced apart (only 4 magnets on a big rotor ) , just need a cap to average it all out.....I think...If I’m not mistaken, there would be no way to avoid reverse polarity across the capacitor. Either it is reversed on normal operation, or when the inductor must dissipate the energy, the polarity is reversed. So don’t you also need a diode? Additionally, just a capacitor could lead to resonance.
@ Sensacel ...certainly a brushless motor would be sensible for high power extraction , but awkward to connect mechanically . I think OP want's an elegant compact design .... the question arises where is the other power going that the human generates in this exercise machine .Why not extract it all electrically ??? I think someone exercising could generate a few 100 watts of electrical power ,and it would be extremely easy to adjust the resistance the exerciser experiences with switches which changes the load on the generator.