How to perform Hilbert transform by using fir hilbert transformer coefficient

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I just read a paper which gives a 7-element FIR Hilbert transformer:
[-0.1270413, 0 -0.6012845, 0, 0.6012845, 0, 0.1270413]
This can be found in "On the Behavior of Minimax FIR Digital Hilbert Transformers" by Rabiner and Schafer, 1974. I want to know how to use the transformer coefficients to perform Hilbert transform, equivalently to using matlab function hilbert() that is based on fft.
For example, I have simple harmonic signal:
y = ac*cos(2*pi*fx*x)
The hilbert() function can be used to obtain the amplitude ac by:
ac = abs(hilbert(y))
My question is how to obtain the amplitude by using the 7-element hilbert transformer?

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