Hilbert Transformer Designed Using the Frequency-Response Masking Technique
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From: Clay on 19 Mar 2010 10:29 On Mar 18, 6:23 pm, robert bristow-johnson <r...(a)audioimagination.com> wrote: > On Mar 18, 11:52 am, dbd <d...(a)ieee.org> wrote: > > > > > > > On Mar 18, 6:09 am, "Junglist" <vasily.karpenko(a)n_o_s_p_a_m.gmail.com> > > wrote: > > > > Hello! > > > > I have read article "Optimum Masking Levels and Coefficient Sparseness for > > > Hilbert Transformers and Half-Band Filters Designed Using the > > > Frequency-Response Masking Technique", Yong Ching Lim, NOVEMBER 2005. > > > > There're in example two filters Hb(z) and H1(z). I guess they derived by > > > multiplication classical hilbert impulse function h(n)=[1-cos(Pi*n)]/Pi*n > > > on different windows. What kind of windows is using there? > .. > > Why do you suggest the use of windows here? The frequency response > > masking literature takes advantage of a variety of filter design > > methods, but usually optimizing techniques. > > an implied window can come from any design technique as long as you > can avoid dividing a non-zero numerator by a zero denominator. > > because half-band symmetry let's us ditch the even-numbered taps, any > design that imposes half-band symmetry can have its (properly aligned) > impulse response divided by the ideal > > h[n] = (1 - (-1)^n)/(pi*n) (h[0]=0) > > for odd n, and you have an implied window. > > r b-j- Hide quoted text - > > - Show quoted text - True, but the article refers to Chebyshev approximation and the effect the masking has on its ripple, so I assume he's using a Remez method to obtain his original filters. And then "sharpening" them from there. My 2 cents worth anyway. Clay
From: robert bristow-johnson on 20 Mar 2010 17:06 On Mar 19, 10:29 am, Clay <c...(a)claysturner.com> wrote: > On Mar 18, 6:23 pm, robert bristow-johnson <r...(a)audioimagination.com> > wrote: > > > > > On Mar 18, 11:52 am, dbd <d...(a)ieee.org> wrote: > > > > On Mar 18, 6:09 am, "Junglist" <vasily.karpenko(a)n_o_s_p_a_m.gmail.com> > > > wrote: > > > > > Hello! > > > > > I have read article "Optimum Masking Levels and Coefficient Sparseness for > > > > Hilbert Transformers and Half-Band Filters Designed Using the > > > > Frequency-Response Masking Technique", Yong Ching Lim, NOVEMBER 2005. > > > > > There're in example two filters Hb(z) and H1(z). I guess they derived by > > > > multiplication classical hilbert impulse function h(n)=[1-cos(Pi*n)]/Pi*n > > > > on different windows. What kind of windows is using there? > > .. > > > Why do you suggest the use of windows here? The frequency response > > > masking literature takes advantage of a variety of filter design > > > methods, but usually optimizing techniques. > > > an implied window can come from any design technique as long as you > > can avoid dividing a non-zero numerator by a zero denominator. > > > because half-band symmetry let's us ditch the even-numbered taps, any > > design that imposes half-band symmetry can have its (properly aligned) > > impulse response divided by the ideal > > > h[n] = (1 - (-1)^n)/(pi*n) (h[0]=0) > > > for odd n, and you have an implied window. > .... > > True, but the article refers to Chebyshev approximation and the effect > the masking has on its ripple, so I assume he's using a Remez method > to obtain his original filters. And then "sharpening" them from there. still, an implied window can be derived from the data as long as there are no 1/0 kind of division. even when using Parks-McClellan, you can enforce half-band symmetry, which will make the even samples zero. then the conditions are met and an implied window can be observed. r b-j
From: Clay on 22 Mar 2010 13:00 On Mar 20, 5:06 pm, robert bristow-johnson <r...(a)audioimagination.com> wrote: > On Mar 19, 10:29 am, Clay <c...(a)claysturner.com> wrote: > > > > > > > On Mar 18, 6:23 pm, robert bristow-johnson <r...(a)audioimagination.com> > > wrote: > > > > On Mar 18, 11:52 am, dbd <d...(a)ieee.org> wrote: > > > > > On Mar 18, 6:09 am, "Junglist" <vasily.karpenko(a)n_o_s_p_a_m.gmail..com> > > > > wrote: > > > > > > Hello! > > > > > > I have read article "Optimum Masking Levels and Coefficient Sparseness for > > > > > Hilbert Transformers and Half-Band Filters Designed Using the > > > > > Frequency-Response Masking Technique", Yong Ching Lim, NOVEMBER 2005. > > > > > > There're in example two filters Hb(z) and H1(z). I guess they derived by > > > > > multiplication classical hilbert impulse function h(n)=[1-cos(Pi*n)]/Pi*n > > > > > on different windows. What kind of windows is using there? > > > .. > > > > Why do you suggest the use of windows here? The frequency response > > > > masking literature takes advantage of a variety of filter design > > > > methods, but usually optimizing techniques. > > > > an implied window can come from any design technique as long as you > > > can avoid dividing a non-zero numerator by a zero denominator. > > > > because half-band symmetry let's us ditch the even-numbered taps, any > > > design that imposes half-band symmetry can have its (properly aligned) > > > impulse response divided by the ideal > > > > h[n] = (1 - (-1)^n)/(pi*n) (h[0]=0) > > > > for odd n, and you have an implied window. > > ... > > > True, but the article refers to Chebyshev approximation and the effect > > the masking has on its ripple, so I assume he's using a Remez method > > to obtain his original filters. And then "sharpening" them from there. > > still, an implied window can be derived from the data as long as there > are no 1/0 kind of division. even when using Parks-McClellan, you can > enforce half-band symmetry, which will make the even samples zero. > then the conditions are met and an implied window can be observed. > > r b-j- Hide quoted text - > > - Show quoted text - I wasn't saying you can't do it this way, but rather I was reflecting on the OP's question about what window or how the particular filters in the article were created. Clay
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