The impulse response for a 10-term approximation to a Hilbert transformer is shown in This Figure . The odd-symmetry and zero-valued coefficients are both exploited to generate an efficient FPGA realization. The coefficient data file for the Hilbert transform must contain the zero-valued entries. For example, the .coe file corresponding to This Figure is shown in This Figure .
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In practice, some optimization methods used for designing a Hilbert transform can lead to the presence of small even-numbered coefficients. If the Hilbert Transform filter class is used in the FIR Compiler, you must force these terms to zero.
Just like the half-band filter, the zero-valued entries for a Hilbert transformer can occur at the filter impulse response extremities. However, these values do not contribute to the result.
This condition is detected when the filter is specified. If the number of taps is such that the zero-valued coefficients form the first and last entry of the impulse response, the filter length is reported as an invalid value. The number of taps N for a Hilbert transformer must obey N=3 + 4n, where n = 0, 1, 2, 3,…. For example, a Hilbert transform filter can have 11, 15, 19, and 23 taps, but not 9, 13, 17, or 21 taps.