Questions tagged [biquad]

Biquad is referred to either analog or digital second order filters

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What procedure to find the parameters of a given filter prototype to fit a desired frequency response?

To model the frequency response of a system, I am looking for a method to fit the response of cascaded bi-quad filters to the response of that system using an optimization algorithm. The $S$-domain ...
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How to implement cascaded biquad transfer functions in Python/SciPy

I am trying to implement in python/Scipy the biquad filter with the following S-domain transfer function: $$ H(s)=\frac{w_0^{2N-1}(s+w_z)}{[s^2+(w_0/Q)s+w_0^2]^N} $$ My problem here is that because of ...
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Discrepancy in frequency response of biquad filter (in Python)

I have written a simple biquad filter class but when I check its frequency response, I get different results with different methods. If I check it "empirically" (by taking the FFT of its ...
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2 votes
2 answers
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What is the $Q$ of successive Second-Order Sections of an $N$th-order Butterworth low-pass filter?

What if you had an $N$th-order Butterworth lowpass filter filter with -3 dB frequency of $\Omega_0$? $$ \Big| H(j\Omega) \Big|^2 = \frac{1}{1 + \left(\frac{\Omega}{\Omega_0}\right)^{2N}} $$ The number ...
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3 answers
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ELI5: How do biquad filters like bandpass "know" the frequency of a signal?

I understand the code behind biquads, but I fail to understand how 5 coefficients in a biquadratic formula can isolate frequencies so precisely, especially considering it only takes the last two ...
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High pass biquad cascade transposed direct form II low frequency accuracy

I'm quite new to DSP and I'm trying to implement high pass biquad cascade in transposed direct form II. Currently my implementation has very poor accuracy at cutoff frequencies that are less than 5kHz ...
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1 answer
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How to optimally normalize filter coefficients?

I have designed an IIR filter in Matlab that comprises the following biquads ...
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Derive Time-Domain Biquad Coefficients from Z-Domain

I'm trying to derive the time-domain coefficients of a biquad filter based on its z-domain coefficients. The purpose is to import externally-generated EQ filters (in z-domain) into Max/MSP (in time-...
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3 answers
263 views

Biquad cascading frequency response

I am implementing EQ lines in my filter. I need to do biquad with slope 24 db/oct, 36/oct and bigger so I would like to cascade several biquads. I am stuck with calculating frequency response of two ...
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Direct form 1 filter equation for a biquad filter

In general, we all know that the direct form 1 equation for a biquad filter is given by $$y(n) = b_0x(n) + b_1x(n-1) + b_2x(n-2) - a_1y(n-1) - a_2y(n-2)$$ But when it comes to practical applications ...
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Converting cascaded biquads to parallel biquads

I need to convert a fourth-order IIR filter made using two cascaded second-order sections with the transfer function: $$ H(z) = \frac{b2_{1}z^{-2} + b1_{1}z^{-1} + b0_{1}}{a2_{1}z^{-2} + a1_{1}z^{-1} ...
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766 views

Calculating the true values of biquad filter coefficients from normalized form

I have a C code in which the IIR filter(BiQuad) uses only 4 (normalized) coefficients per stage (a2/a0,a1/a0,b2/b0,b1/b0) instead of 6 coefficients (a0,a1,a2,b0,b1,b2). I know that the value of a0 is ...
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IIR Cascaded Filter Response, Unexpected Results

I am attempting to understand how to manipulate portions of a cascaded series of biquad notch filters in a control system I am working with. As part of determining the composite response of all the ...
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609 views

How do you calculate the group delay in samples of a Biquad Filter at a given frequency from the coefficients?

If I have a BiQuad all-pass filter with a given set of coefficients such as: g: 0.903228 a1: -1.88142 a2: 0.903228 B1: -2.08299 B2: 1.10714 And my operation per ...
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Biquad high-pass filter not working as expected

I'm trying to implement a high-pass filter using the the coefficients described in RBJ's well-known EQ cookbook (see https://www.w3.org/TR/audio-eq-cookbook/). However, when I run white noise through ...
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1 vote
1 answer
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bibliography about implementation of IIR filters

I need to implement a 6th order IIR filter. The filter I need to implement is the A-weighting. I've simply used the bilinear function of Matlab with an fs of 20Khz. I need to implement this over the ...
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Biquad Filter Non-Linearity

I'm using a biquad filter algorithm in my project. I got 3, 16 size variable arrays summing into one and then gets filtered. Now i want to filter each array seperately and sum after that, which if the ...
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Biquad Type-II Coefficient Generation

I have a Biquad II filter implementation in my embedded environment and I'm trying to find some equations to generate the coefficients for it. I have already found the Audio Eq Cookbook, which simply ...
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1 answer
217 views

Why does my low pass filter diverge below 7000 Hz?

I'm trying to create a LPF, using language JAVA. My first aim is to understand how filters design is working and the second one is to create a "home made" equalizer with "home made" filters. To help ...
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Known problems with IIR DF2 when using 64-bit floating point processing?

So far I was using DF1 for biquad filters for audio DSP, but it turns out that it is possible to gain significant performance gains using the new AVX/AVX512 instruction sets using DF2. Are there any ...
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2 votes
1 answer
194 views

Biquad and polarity flipping

Assuming normalized biquad coefficients: $$ H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}} {1 + a_1z^{-1} + a_2z^{-2}} $$ And taking the definition of flipping the polarity as multiplying every tap in a ...
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Issue with the Massberg Analog-Matched Low Pass Filter

Implemented the filter mentioned in title using Octave and couple sources Vicanek and Zeitlin (LPF.cpp). Got filter working otherwise but, ... when tested the responses against 'analog model' of the ...
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How would I calculate the state-variables of digital biquad filter (direct form II transposed) at steady-state?

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration For example, let assume the filter is fed a constant input of ...
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Help with audio EQ cookbook BPF filters and Q

I am fairly new DSP, and am using maths that I have not used in 20-30 years. I have been working with Cookbook formulae for audio EQ biquad filter coefficients by Robert Bristow-Johnson and am having ...
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Can a Goertzel filter response be mapped to a Direct Form II Biquad IIR Filter

I am looking at the structure of the Goertzel Filter, and it seems like I can map its coefficients to the standard implementation of the CMSIS DSP Biquad Cascade IIR Filter. Is this possible or should ...
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MATLAB's $\tt dsp.ParametricEQFilter$ bandwidth question

Consider the following code: ...
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Biquad Treble Shelf filter gain being weird

Trying to compute Biquad Coefficients for use in a codec chip TLV320AIC3100. Bass Shelf(boost and attenuation) work as expected. Treble Shelf attenuation works as expected but Treble Shelf boost is ...
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Is it possible to combine two or more Biquads?

I've wrote a Equalizer, and now it apply the Biquads in serie (cascade), I was just thinking if i can combine the biquads it will more efficient than applying one-per-one. Is that possible?
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3 votes
4 answers
1k views

Avoiding clicks with changing biquad coefficients

I have a DSP application that filters a signal with five cascaded biquads whose coefficients are determined by the Audio EQ Cookbook formulae (Thanks for this work, Mr. Bristow-Johnson btw). Each ...
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119 views

PeakEq center frequency does not match frequency response

Following the Cookbook i calculed these coefficients: ...
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1 answer
1k views

How do scaling of the coefficients for the poles of a biquad filter affect the gain?

Given a digital filter consisting of a chain of digital biquad filters. Given a digital biquad filter with a normalized Direct form 1 difference equation: $ y_n = b_0x_n + b_1x_{n-1}+b_2x_{n-2} - ...
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Software implementation recipe of cascaded Biquad IIR filter

I have been given the task of measuring the performance of Biquad IIR filters on a new CPU that we are evaluating. What I know is that the Biquad filters can be cascaded to form higher order filters. ...
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3 answers
711 views

IIR biquad real-time filter just output noises

I've implemented a IIR filter but it outputs only noise (like FM radio out of tuning) and I can't see what's wrong. This is the processing function: ...
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1 answer
987 views

Biquad filter from Matlab to C using "tf2sos"

This is a biquad implementation I use: ...
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1 answer
877 views

4th order high-pass filter on a DSP: standard or biquads?

I have two C implementations of 4th order high-pass filter (fs = 16 kHz, cut-off=100 Hz, designed using Matlab ...
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1 vote
1 answer
144 views

What's the point of MATLAB's scaling array for secord-order-section filters?

I'm currently working on a project where I'm implementing different filter types (e.g. iirs - direct form 1, 2, transposed 1, 2, etc.). I just recently started attempting to implement a second order ...
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1 answer
479 views

Two question about RBJ Peak filter

I'm new into DSP and Filters in general. Its the first step ahead I do from learning and using a 1-pole IIR basic Low Pass Filter. I'm about to implement for my VST audio application (using C++ and ...
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Filter long audio data using cascading biquad filter

I would like to lowpass filter a long pcm wav file. I designed a 20 order butterworth lowpass filter in Octave and transform the zero pole gain data to a series of second order sections. Then I am ...
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2 votes
1 answer
574 views

Biquad cookbook formula for broadcast FM de-emphasis?

Can a simple IIR biquad filter be used as an audio de-emphasis filter for broadcast FM radio? If so, how does one translate the filter requirements (50 uS time constant in the U.S.?) into parameters ...
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Is there any audio DSP without biquad constraint?

I found a codec with audio DSP, ADAU1772. It supports 32 biquads, that is $32\cdot5=160$ parameters. I need to calculate filter coefficients on-line. The result is in transfer function form, i.e., $...
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2 votes
1 answer
1k views

Prewarping both resonant frequency $f_0$ and bandwidth (or $Q$) when using bilinear transform

RBJ's Audio EQ cookbook takes into account only frequency prewarping when case Q is used for bandwidth. Why not $Q$ prewarping as well with some of those filter ...
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1 vote
1 answer
393 views

Biquad coefficients using Magnitude (or Phase) Invariance Mapping Method

I'm trying MIM (Magnitude Invariance Method) and PIM (Phase Invariance Method) for to improve biquad LPF response at low sampling rates. I'm looking some help and examples of usage if available. ...
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3 votes
2 answers
1k views

Is there a method to calculate the maximum gain of a biquad?

Given an IIR expressed as a biquad: $$ H(z) = {b_0 + b_1 z^{-1} + b_2 z^{-2} \over 1 + a_1 z^{-1} + a_2 z^{-2}} $$ Is there a way to calculate the maximum gain the biquad attains over the range $0$ ...
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1 vote
2 answers
791 views

How to calculate biquad coefficients for the partial (1%, 10%) applying of pre-emphasis effect

I'm using sox to emulate RIAA pre-emphasis and de-emphasis effects on audio files. For pre-emphasis I call it like this: ...
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Combining IIM and MZT transformation

Split from thread: Correcting Impulse Invariance Method Back to this subject. Matt L suggested combining IIM and MZT b-coeffs to get the filter response improved at hihger frequency area. Couldn't ...
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Biquad Filter Optimization

I would like to try optimize a bit more the biquad filters indended for RIAA/non-RIAA equalization at low samplerates (44.1/48kHz). Are there any open source optimization libraries (C, C++ or C#) out ...
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1 answer
94 views

Calculating the product of discrete transfer functions

I'm trying to construct a higher order IIR from a biquad cascade, I know this is generally frowned upon, but it's necessary as the coefficients will be embedded into a larger formula used in a FDTD ...
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2 answers
875 views

Regarding BIQUAD IIR implementation in MATLAB

I want to implement a high pass filter (order 4) in MATLAB using cascade form. ...
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1 vote
2 answers
145 views

Transform one-pole cascaded system into a biquadratic section

I have two cascaded one-pole sections with the same coefficient b for both sections. $$ y_A[n]=x_A[n]+b\cdot(y_A[n−1]−x_A[n])\\ y_B[n]=y_A[n]+b\cdot(y_B[n−1]−y_A[n]) $$ The final output of the system ...
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4 votes
1 answer
704 views

Discrete-time Biquad filter: Relation between peak frequency and pole frequency

This question arose from a discussion in the comments to this question and its answer. The author of that question discussed a discrete-time second order filter described by the following difference ...
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