Re: Odd length Hilbert FIR Implementation

Al Clark wrote:

...

The basic question is why does the hilbert filter with length 4i+1, for example 9 or 13 have better performance than a fir filter of length 4i-1, for example 7 or 11, even though the number of non zero coefficients is the same for the 4i+1 & 4i-1 filters. In the 4i+1 case, the first and last coefficients are zero, which allows the filter size to be reduced to a 4i-1 length.

The 4n+1 filter has two more points. It's just that the end two being zero allows you the efficiency of not including them in the computation. Try it with a low-pass. The same thing happens but it's harder to see in the plots. Unless the window includes a pedestal, windowed FIRs are always better with a window that's wider than the raw coefficients by two.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
.

Relevant Pages

  • Re: Odd length Hilbert FIR Implementation
    ... >> coefficients for each tap of the filter. ... >> be 2i nonzero coefficients and 2i-1 zero coefficients. ... >> Window. ...
    (comp.dsp)
  • Re: Odd length Hilbert FIR Implementation
    ... even tap coefficients are zero, and the odd coefficients are proportional to 1/i before the window is applied. ... Note that the end coefficients are zero if k is even and the window will make them zero if k is odd, so there are only N taps needed in the delay line, as Al said. ...
    (comp.dsp)
  • Re: Odd length Hilbert FIR Implementation
    ... odd- length FIR filter with antisymmetrical coefficients. ... zero coefficients are the same. ... because the window value is zero there. ...
    (comp.dsp)
  • Re: Odd length Hilbert FIR Implementation
    ... coefficients for each tap of the filter. ... be 2i nonzero coefficients and 2i-1 zero coefficients. ... because the window value is zero there. ...
    (comp.dsp)
  • Re: Odd length Hilbert FIR Implementation
    ... length 4i-1, for example 7 or 11, even though the number of non zero ... filter size to be reduced to a 4i-1 length. ... Unless the window includes a pedestal, ... it interesting to compare a fir filter with twice the length using ...
    (comp.dsp)