LowPass Filter coefficient calculation

Davids Question

Mar 12, 2018 00:00

Hi all,

I am checking the Low Pass Filter coefficient to use on my micro-controller,

I have researched some topic, like https://ez.analog.com/message/21166?commentID=21166#comment-21166

and the wiki: https://wiki.analog.com/resources/tools-software/sigmastudio/toolbox/filters/general2ndorder

I use the excel to verify my formula is correct or not (check with the SigmaStudio compiler window).

I can not get the correct A1 and A2 value but I can get the correct B0, B1 and B2, so I don't know where is wrong.

like this example:

excel:

Fs: 48000

f0: 1000Hz

Gain: 0

Q: 1.41

boost: 0

and the

omega(w0): (2 * Pi() * f0 ) / Fs = 0.130899694

sin(w0): 0.130526192

cos(w0): 0.991444861

alpha( this is from the SigmaStudio Filter Wiki):

alpha = sin(w0) / (2 * Q) = 0.046285884

like below pic:

from the above calculation,

I can get the similar B0/B1/B2:

SigmaStudio:

from mine excel:

but to check the A1 and A2, the value is not correct, I follow the Wiki formula and the reference topic,

so I am not sure which is the correct answer. I don't know my formula is wrong or not.

Here is mine A1 and A2 formula:

A1 = -2 * cos(w0) = -1.982889723

A2 = 1 - alpha = 0.953714116

from the SigmaStudio compiler window A1 and A2 value:

A1= 1.8951700925827

A2 = -0.911523461341858

from the above I can sure is completely different.

Please help me on this.

Thanks you all !

Regards,

Alvis

filter parameter

filter coefficient

sigmastudio

dsp filter

formula

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matthijs Reply

Mar 15, 2018 00:00

Here's a python script that produces the correct coefficients for a few flavors of biquad:

#!/usr/bin/python3

from math import pi, cos, sin

fS = 48000

f0 = 1000 / fS # normalized frequency
Q = 1.41 # quality factor

ζ = 1/(2*Q) # damping ratio
x = cos(2*pi*f0)
y = sin(2*pi*f0)

def transform(L, C, H):
L *= 1 - x
C *= ζ * y
H *= 1 + x

c0 = (L + H)/2 + C
c1 = L - H
c2 = (L + H)/2 - C

return (c0, c1, c2)

(b0, b1, b2) = transform(1, 0, 0) # low-pass
# (0, 1, 0) # band-pass
# (0, 0, 1) # high-pass
# (1, 0, 1) # notch
# (1,-1, 1) # all-pass

(a0, a1, a2) = transform(1, 1, 1)

# normalize a0 coefficient
(b0, b1, b2) = (b0/a0, b1/a0, b2/a0)
(a0, a1, a2) = (a0/a0, a1/a0, a2/a0)

# print dsp coefficients
print("b2 =", b2)
print("b1 =", b1)
print("b0 =", b0)
print("a2 =", -a2)
print("a1 =", -a1)

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KJBob Reply

Mar 17, 2018 00:00

Alvis,

You need to normalize all your coefficients. To do this, divide each of a1, a2, b0, b1, and b2 by a0 -- see lines 34 and 35 of matthijs 's Python script. I've neglected this myself, it's a common mistake. Interestingly, in your example it makes the coefficients merely 5% too large -- yet results in an enormous response error.

Perhaps the easiest way to test your coefficients is to type them into the IIR Coefficient version of the General 2nd Order Filter, as shown below:

If you prefer to use a spreadsheet, I attached one with various filter types. I just added the Lowpass filter so you'll find it at the far right of the sheet. When you program your microcontroller, remember to flip the signs of the a1 and a2 coefficients before safeloading them.

Best regards,

Bob

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