Bode's Amplitude/Phase relation for discrete time systems
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From: Rune Allnor on 24 May 2010 07:46 On 23 Mai, 17:42, Jerry Avins <j...(a)ieee.org> wrote: > On 5/23/2010 6:50 AM, Rune Allnor wrote: > > ... > > > Done correctly, the end DT filter woks out exactly right. > > For any _one_ frequency. Also, a high band edge is sharpened. No, and that's the point: *Without* the pre-warp the BLT is correct at *one* frequency. *With* the pre-warp, it is correct at *two* frequencies; the pass-band and stop-band corner frequencies. Rune
From: Jerry Avins on 24 May 2010 08:55 On 5/24/2010 7:46 AM, Rune Allnor wrote: > On 23 Mai, 17:42, Jerry Avins<j...(a)ieee.org> wrote: >> On 5/23/2010 6:50 AM, Rune Allnor wrote: >> >> ... >> >>> Done correctly, the end DT filter woks out exactly right. >> >> For any _one_ frequency. Also, a high band edge is sharpened. > > No, and that's the point: *Without* the pre-warp the BLT > is correct at *one* frequency. *With* the pre-warp, > it is correct at *two* frequencies; the pass-band and > stop-band corner frequencies. The BLT is substantially correct at _all_ frequencies well below the sampling frequency. Warping becomes more severe as fs/2 is approached. Prewarping accounts for this by computing where the band edges of the s-plane filter need to be in order to place them properly after bilinear transformation. You can correct as many frequencies as you have degrees of freedom in the design. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Rune Allnor on 24 May 2010 09:11 On 24 Mai, 14:55, Jerry Avins <j...(a)ieee.org> wrote: > On 5/24/2010 7:46 AM, Rune Allnor wrote: > > > On 23 Mai, 17:42, Jerry Avins<j...(a)ieee.org> wrote: > >> On 5/23/2010 6:50 AM, Rune Allnor wrote: > > >> ... > > >>> Done correctly, the end DT filter woks out exactly right. > > >> For any _one_ frequency. Also, a high band edge is sharpened. > > > No, and that's the point: *Without* the pre-warp the BLT > > is correct at *one* frequency. *With* the pre-warp, > > it is correct at *two* frequencies; the pass-band and > > stop-band corner frequencies. > > The BLT is substantially correct at _all_ frequencies well below the > sampling frequency. Warping becomes more severe as fs/2 is approached. > > Prewarping accounts for this by computing where the band edges of the > s-plane filter need to be in order to place them properly after bilinear > transformation. Right. The *two* band edges. > You can correct as many frequencies as you have degrees > of freedom in the design. Wrong. The reason why the pre-warp / BLT combo works, is that the filter designs where they are relevant, are dominated by the bandwidth of the transition band. Rune
From: Jerry Avins on 24 May 2010 09:26 On 5/24/2010 9:11 AM, Rune Allnor wrote: ... > Wrong. The reason why the pre-warp / BLT combo works, is that > the filter designs where they are relevant, are dominated by > the bandwidth of the transition band. I don't understand that. In any case, the warping itself sharpens transitions Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Mikolaj on 24 May 2010 09:43
On 22-05-2010 at 14:56:55 Greg Berchin <gberchin(a)comicast.net.invalid> wrote: (...) > I don't see any reason that a similar expression should not apply to > discrete (...) Be careful about such statements. This is false friend to look for simple similarities. (...) > Even though they are discrete in time, they are continuous in > frequency. (...) Even you can move your feet the sun is hot. No comment... -- Mikolaj |