Re: FIR Hilbert Transformer

Thanks RBJ for explaining. I have another related question, and hope you or some one else can explain.

We can transform an even length FIR differentiator to a Hilbert transformer by just making few changes to the signs of the impulse response coefficients. If we just assign negative sign to the first half of the coefficients and positive sign to the second half, we get a HT. Why does it happen? What actually happens to the frequency (magnitude) response of differentiator by making these changes to the impulse response coefficients?

I can understand the transformation of differentiator to halfband lowpass filter, that we take derivative of the differentiator's frequency response (multiply impulse response coefficients with indices), squeeze to half (insert zeros in impulse response) and scale (set middle coefficient to 1/2 etc). How can we explain transformation of differentiator to HT?

Ishtiaq.
.