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

Reply by dbd●September 5, 20202020-09-05

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.

Reply by Tom Killwhang●September 5, 20202020-09-05

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.