# Tag Info

Accepted

### Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?

You've made an understandable mistake. You are probably looking at this picture: That is not the unit circle, and it isn't even in the $z$ domain. What you are looking at is the locations of the ...
• 8,638

### Signal processing in Python vs C++ (band-pass filter)

Not really an answer but too long for a comment. Standard software development and debug techniques should solve this Don't use code on real data before it has passed all unit tests First write the ...
• 32.6k
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### 4th order high-pass filter on a DSP: standard or biquads?

The two solutions in a floating point implementation are assumed to be identical, with the two BiQuads being a factored version of the standard difference equation. The BiQuad is the better way to go ...
• 37.7k
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### What is the largest "safe" order for the digital Butterworth filter of a given signal?

One cause is that higher order Butterworth filters have poles closer to the unit circle. This nearby infinite gain point increases the likelihood of numerical instabilities. (e.g. rounding/...
• 34k
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### Are IIR filters (and specifically Butterworth filter) causal?

Yes, Butterworth are IIR. The decay from an impulse technically lasts forever. Yes, all [implementable] IIR are causal. Yes, because of #1 and #2. Don't use ...
• 15k

### Mapping of Classic Filters for Digital Filter Design

I'm convinced that depending on the problem we're trying to solve, we can and should use both approaches: the transformation of classic analog filter designs, and the direct design in the digital ...
• 80.4k
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### SOS-matrices' order does not correspond to given parameter when designing bandpass with scipy.signal.butter

Your expectations are reasonable. However, the definition of order in the design routine is confusing. It's the same in Matlab/Octave. For lowpass or highpass ...
• 80.4k
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### Mapping of Classic Filters for Digital Filter Design

and simulation where "copying the analog" would result in the better solution. That' missing the point a bit. It's not that one cares much about matching or copying the "analog" ...
• 32.6k

### Filter design by distributing poles and zeros on parametric curves

Throughout the answer I will use the mathematical notations, that is, the mathematica equivalent of expressing the magnitude response of a filter in frequency domain. For this, $x$ will be used ...
• 1,488

### Mapping of Classic Filters for Digital Filter Design

How to Massively Reduce the Resource Requirements in FIR Filter Approach The two answers provided by Matt and Hilmar are both excellent and provide great insight in answering the question. I am ...
• 37.7k
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### Weird results when using MATLAB's $\tt butter$ function?

The answer to your question can mainly be found in the Matlab documentation. The butter function can design filters either in the analog domain as well as in the discrete domain. In order to make an ...

### Butterworth band pass filter

You need to specify your filter design specifications parameters consistently for either an analog or a digital filter. With your posted code, the butterord ...
• 1,732
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### A few conceptual questions about filter, pole, and bilinear

The poles of low pass and high pass Butterworth filters are indeed the same if both filters have the same cut-off frequency. The difference between the two lies in the numerator. A low pass filter has ...
• 80.4k

### Higher-order (Butterworth) filters

If you want to increase the "selectivity" of your filter, I recommend to use a Papoulis-Legendre filter instead of Butterworth. It is the behaviour which present the sharpest slope at cut-off.
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### Higher-order (Butterworth) filters

Increasing the number of degrees of freedom with the order allows more flexibility in the overall design, to fulfill as much a possible wished properties: ripples in the pass-, stop-band, accomodate ...
• 30.2k

### Why does sampling frequency affect the filter results?

Limited numerical precision. The higher the sample rate, the closer the poles move to the unit circle, the closer to the unit circle, the less stable the filter is. There are different implementation ...
• 32.6k

### Higher-order (Butterworth) filters

When a filter is used, we usually design a specific sort of filter: low pass, high pass, or bandpass. That design assumes an ideal filter that has unity gain in the passband and zero gain in the stop ...
• 22.9k
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### Butterworth filtering behaving unexpectedly -MATLAB

The effect you observed is mainly due to spectral leakage. It is a property of the DFT and it is only indirectly related to the Butterworth filter. Note that there are an integer number of periods of ...
• 80.4k
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### Can't make sense from VHDL butterworth filter implementation

The filter structure is a digital leapfrog and the structure looks like this picture (note: the picture is a different order than the code): These filters are ...
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### If a filter has a non-linear phase lag will the output signal be distorted?

I think your question comes from several misunderstandings. The fact that the phase lag of a system becomes more negative for large frequencies does not mean that there's more distortion of larger ...
• 80.4k
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### How to plot magnitude and phase response of 2 cascaded filters in Matlab?

Using MATLAB/Octave as the tool, the following approach lets you plot the magnitude & phase samples of the DTFT of the cascade of the two discrete-time LTI filters using their LCCDE coefficient ...
• 26.8k
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### Apply butterworth filter (lowpass) to a signal

I found a way to fix the issue by changing the calculations, so it seems like I had the wrong Nyquist frequency and therefore the wrong cutoff frequency. I hadn't realised that the Nyquist frequency ...
• 83
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### Butterworth Polynomial from Butterworth Filter

The denominator of the transfer function of an analog Butterworth filter is a (non-normalized) Butterworth polynomial. Also the numerator is just a constant (i.e. the coefficients of higher order are ...
• 4,872

### How to implement a filter associated to a specific wavelet

You've mentioned Butterworth filters for doing the wavelet analysis using bior6.8. If you want to perform the Discrete Wavelet Transform using some specific wavelet,...
• 10.5k

### How to choose order and cut-off frequency for low-pass Butterworth filter?

an $n$th-order Butterworth filter in the $s$-domain has a magnitude function that is two straight lines connected with a soft corner at $\omega_0$ and -3 dB. the straight line at the left is a flat 0 ...
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### Butterworth filter transfer function in time domain

A plot of the normalized impulse responses, for the n = 2 through 10 Butterworth low pass filters, are given by H.J. Blinchikoff, A.I. Zverev, "Filtering in the Time and Frequency Domains", Wiley-...
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### Butterworth filter transfer function in time domain

There's no need to use numerical methods here. The most straightforward way to compute the output is to see that the filter's impulse response is given by h(t)=\sum_{k=1}^Nr_ke^{s_kt}u(t)=\sum_{k=1}...
• 80.4k
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### How to determine the type of a digital filter given its expression?

Seeing that the paper cites the author of the paper as inventor of the "SuperSmoother" filter, and this filter was (supposedly) good for this specific use case, there's no indication this ...
• 26.6k