Having Trouble With Designing IIR Filter on Frequency Transformation

Hello all,

As written in title, I am having trouble with frequency transformation.
There are three problems I am encountering right now.

(1) Over-specification band pass filter
I designed a 4th order chebyshev low pass filter which does satisfy given specification, in which
- pass band edge frequency fp = 6500 Hz,
- stop band edge frequency fs = 7500 Hz,
- pass band ripple Ap = 1 dB,
- stop band attenuation As = 10 dB, and
- sampling frequency fsamp = 50 kHz.

However, after transforming this low pass filter to band pass filter with
- low pass band edge frequency fpl = 7500 Hz and
- high pass band edge frequency fph = 8500 Hz
I got the 8th order filter with the gain characteristic shown in the graph attached to this thread.


Obviously, it's over my specification and I wonder why this happens and want to get a filter that follows given specification.

(2) Peaky band pass filter
When I designed a 13th order chebyshev low pass filter and created band pass filter using frequency transformation,
I got the 26th order filter with peaky ripple, which is over than 10 dB...

(3) Low pass band band pass filter
When I designed a 9th order chebyshev low pass filter and created band pass filter using frequency transformation,
I got the 18th order filter with pass band gain lower than -40 dB...


As written in (1), the low pass filter DOES satisfy given specification, but the band pass filter does not.
The formula I used to do frequency transformation is below

z^-1 =
z^-2 - (2*a*k*z^-1)/(k+1) + (k-1)/(k+1)
-----------------------------------------
(k-1)*z^-2 /(k+1) - (2*a*k*z^-1)/(k+1) +1


Can anybody help??


Regards,
Yukihiro

I solved this problem by myself.
I was designing the filter by maple and changing digits in maple helped me.

for me this is the forum to ask about?
thank