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In Strang's Wavelets and Filter Banks, Problem 1.3.6 asks,

If $H_0$ is the response of a lowpass filter, what is the response $H_1$ of a corresponding highpass filter? If $h(0), \dots, h(N)$ are coefficients of $H_0$, what are the coefficients of your $H_1$?

I have gone through the section several times, and all I can find, as defining feature of lowpass and highpass filter, is the frequency response function being $1$ (and $0$) at frequency $0$, and $0$ (and $1$ respectively) at frequency $\pi$. These features do not reference one another, i.e., there is no clear definition of a "pair" of filters. I do not see any defining relationship between the two of a pair anywhere in this section. What am I missing here?

bobeyt6
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YAC
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    I would guess that $H_0(f)=1-H_1(f)$, which means they have the same frequency where they pass half the signal. It should be defined in the text. – Ross Millikan Jan 19 '23 at 02:06

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