# FIR coefficients for Bessel analog filter

Started by May 23, 2006
```Dear all,

I've only done a basic course in digital filters. But I'm required to
implement a digial filter in FPGA to approximate an analog Bessel
filter of order 5 and cutoff frequency of 15.5kHz.

I used besself(5,2*pi*15.5e3) in Matlab to get the s-domain transfer
function and plotted out the frequency response of the analog filter. I
tried using the fdatool in Matlab to get the FIR coefficients and I
observed the spectrum of the signal I got, and it was very different
with the spectrum derived using the analog filter.

Can anyone provide me a set of FIR coefficients that best approximate
this Bessel filter specs? I understand that the Bessel filter has a
flat magnitude response at passband and it decays at 6n dB/octave where
n is the filter order. It also has a constant group delay at the
passband. But I can't seem to deisgn a digital filter which matches
these characteristics.

```
```leck wrote:

> Dear all,
>
> I've only done a basic course in digital filters. But I'm required to
> implement a digial filter in FPGA to approximate an analog Bessel
> filter of order 5 and cutoff frequency of 15.5kHz.
>
> I used besself(5,2*pi*15.5e3) in Matlab to get the s-domain transfer
> function and plotted out the frequency response of the analog filter. I
> tried using the fdatool in Matlab to get the FIR coefficients and I
> observed the spectrum of the signal I got, and it was very different
> with the spectrum derived using the analog filter.
>
> Can anyone provide me a set of FIR coefficients that best approximate
> this Bessel filter specs? I understand that the Bessel filter has a
> flat magnitude response at passband and it decays at 6n dB/octave where
> n is the filter order. It also has a constant group delay at the
> passband. But I can't seem to deisgn a digital filter which matches
> these characteristics.
>

The characteristic that Bessel filters desirable is near-constant group
delay in the passband. Analog Bessel filters sacrifice transition
sharpness to achieve it.

Symmetric FIR filters have exactly constant group delay in the passband.
Their transition sharpness and freedom from passband ripple is improved
by adding length, equivalent to an analog filter's order. In general,
symmetric FIRs out-Bessel Bessels. Exactly matching a Bessel's curves
can only make them worse.

http://www-k.ext.ti.com/SRVS/Data/ti/KnowledgeBases/analog/document/faqs/bes.htm

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```Hi,

In fact I'm deliberately trying to obtain the slow rolloff in
attenuation in the stopband and yet have no ripples in the passband. I
find that when I use the FDAtool in Matlab, the filter always has a
very sharp transition in the stopband. Anyadvice on how to obtain a
symmetric FIR which decays at 6n db/octave in the stopband? Thanks very
much.

```
```leck wrote:

> Hi,
>
> In fact I'm deliberately trying to obtain the slow rolloff in
> attenuation in the stopband and yet have no ripples in the passband. I
> find that when I use the FDAtool in Matlab, the filter always has a
> very sharp transition in the stopband. Any advice on how to obtain a
> symmetric FIR which decays at 6n db/octave in the stopband? Thanks very
> much.

Unless the turnover frequency is low compared to the sample rate, you
can't get many octaves. (F_s/2 is an upper limit.) If it is low, an IIR
is more appropriate to the application. You may find useful design
formulas at http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```