Re: Amplitude response of a Biquad Filter

"rkthebad" <raviyenduri@xxxxxxxxx> wrote in
news:J8KdncyPSKDCkGveRVn-ug@xxxxxxxxxxxx:


rkthebad wrote:


Apart from the conditions that you mentioned above, I found one
more
stability condition in a textbook.
Condition is : |a2| < 1 and |a1| < 1 + a2.
I did not venture too much into the math, but I am guessing your
conditions might come down to this after simplification.

the second one looks different, but the first is the same.

whatever, i am convinced that the criteria i stated:

1. if (a1/2)^2 >= a2 then |a1/2| + sqrt((a1/2)^2 - a2) < 1

2. if (a1/2)^2 < a2 then a2 < 1

is both necessary and sufficient.

if it's case 1. then

sqrt((a1/2)^2 - a2) < 1 - |a1/2|

(a1/2)^2 - a2 < (1 - |a1/2|)^2 = 1 - |a1| + (a1/2)^2

which comes to

|a1| < 1 + a2

so you're right, it's the same thing (except, it's a "either or" not
*both*). thanks for pointing that out.

But, wouldn't it be sufficient to see whether the poles of the
quantized
filter are inside the unit circle?

that's precisely what i was doing. take a look at the math, that is
all that it is.

r b-j


Here is one strange thing that I observed. Can anyone explain why?

I am trying to see the actual response of the designed 5-band
equalizer. I put a gain of +12 dB for all the bands. Then I vary the
sampling frequency of the system. It is observed that at a sampling
freq. of 48 kHz, the first band (with fc = 300 Hz) does not show a
gain of +12 dB. Instead, it only shows a gain of +9 dB. Why is this
so?

Thanks,
~ R K



I think you are a victim of 16 bit precision. The low frequency bands
with high Q are the first place where the problem is likely to occur.

This kind of problem illustrates why the Motorola 56K (24 bits) and
later

the SHARC (32 bits) became so popular in high performance audio.

I think you already found improvements by changing filter topology (DFI

vs DF2). If you have enough MIPs, you can rewrite the algorithm with
double precision math with your 16 bit processor or move to a higher
precision processor.





--
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com

Al,
You are right. Because of the 16-bit quantization, I am losing
precision
compared to the floating point architecture. But, the above mentioned
problem, I am experiencing even in the floating point implementation.
The
problem is the same when I tried to compute my coefficients using MATLAB
or Microsoft VC++. Is 48 kHz tooo high a sampling freq. compared to the
300 Hz band?

Thanks,
~ R K


Everyone,

I am able to get a *decent* output through my 5-band equalizer. But, I
am sacrificing the bass content till 500 Hz. Now, I know for sure that
there is serious problem with a high sampling frequency and my first band
(if below 500 Hz). I would have to find a way around this. Any suggestions
will be definitely helpful.

Thanks to everyone.
~ R K

.

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