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  • FIR filter design

    From Tom Killwhang@21:1/5 to All on Sat Sep 5 17:37:58 2020
    I am trying a simple example using frequency sampling. Therefore I have N=16 weights.
    W=[w0 w1.....w15]
    and I make then as follows

    W=[1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 ]
    as magnitude and the phase is -k*pi*(n-1)/N where k is from 0 to N/2
    giving a frequency sampling complex vector of

    H=[h0 h1 h2 ....h15]

    Now according to textbooks I have to have conjugate symmetry but exactly how does this work with the dc bit? The only way I could get it to work so I had real weight coefficients of the filter was to let the frequency coefficients be
    h0=1 and then h15=conj(h1), h14=conj(h2), h13=conj(h3), h12=conj(h4).

    Then my time-domain coefficients were real and it worked. I read that h15 should be the dc bit ie h15=h0 but this doesn't work.

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  • From dbd@21:1/5 to gyans...@gmail.com on Sat Sep 5 19:44:51 2020
    On Saturday, September 5, 2020 at 5:38:03 PM UTC-7, gyans...@gmail.com wrote:
    I am trying a simple example using frequency sampling. Therefore I have N=16 weights.
    W=[w0 w1.....w15]
    and I make then as follows

    W=[1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 ]
    as magnitude and the phase is -k*pi*(n-1)/N where k is from 0 to N/2
    giving a frequency sampling complex vector of

    H=[h0 h1 h2 ....h15]

    Now according to textbooks I have to have conjugate symmetry but exactly how does this work with the dc bit? The only way I could get it to work so I had real weight coefficients of the filter was to let the frequency coefficients be
    h0=1 and then h15=conj(h1), h14=conj(h2), h13=conj(h3), h12=conj(h4).

    Then my time-domain coefficients were real and it worked. I read that h15 should be the dc bit ie h15=h0 but this doesn't work.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From dbd@21:1/5 to gyans...@gmail.com on Sat Sep 5 19:49:25 2020
    On Saturday, September 5, 2020 at 5:38:03 PM UTC-7, gyans...@gmail.com wrote:
    I am trying a simple example using frequency sampling. Therefore I have N=16 weights.
    W=[w0 w1.....w15]
    and I make then as follows

    W=[1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 ]
    as magnitude and the phase is -k*pi*(n-1)/N where k is from 0 to N/2
    giving a frequency sampling complex vector of

    H=[h0 h1 h2 ....h15]

    Now according to textbooks I have to have conjugate symmetry but exactly how does this work with the dc bit? The only way I could get it to work so I had real weight coefficients of the filter was to let the frequency coefficients be
    h0=1 and then h15=conj(h1), h14=conj(h2), h13=conj(h3), h12=conj(h4).

    Then my time-domain coefficients were real and it worked. I read that h15 should be the dc bit ie h15=h0 but this doesn't work.

    Take a look at the IEEE Proceedings paper by harris at: http://web.mit.edu/xiphmont/Public/windows.pdf

    On the second page follow the definition of concepts like "DFT-even" for how to align sampled data with DFTs for desired symmetries.

    Dale B. Dalrymple

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