# Tag Info

## Hot answers tagged infinite-impulse-response

Accepted

### Applying filter in scipy.signal: Use lfilter or filtfilt?

filtfilt is zero-phase filtering, which doesn't shift the signal as it filters. Since the phase is zero at all frequencies, it is also linear-phase. Filtering ...
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### What is the advantage of MATLAB's filtfilt

I found this video to be very, very helpful (it elaborates on Matt's answer). Here are some key ideas from the video: Zero-phase will result in no phase distortion, but will result in a non-causal ...
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Accepted

This is the FIR filter, although it looks like an IIR. If you calculate the coefficients you get finite impulse response: $h=$ This happens due to zero-pole cancellation: $Y(z)-0.5Y(z)z^{-1}=X(z)... • 10.7k 19 votes Accepted ### Filter Order Rule of Thumb My favorite "Rule of thumb" for the order of a low-pass FIR filter is the "fred harris rule of thumb": $$N=\frac{f_s}{\Delta f}\cdot\frac{\rm atten_{dB}}{22}$$ where$\Delta f$... • 38.4k 18 votes ### What kind of filter is that? Is it IIR? Jojek's answer is of course correct. I would just like to add some more information because much too often have I seen the terms "IIR" and "recursive" confused. The following implications always hold: ... • 80.9k 16 votes Accepted ### Single-pole IIR low-pass filter - which is the correct formula for the decay coefficient? The given single-pole IIR filter is also called exponentially weighted moving average (EWMA) filter, and it is defined by the following difference equation: $$y[n]=\alpha x[n]+(1-\alpha)y[n-1],\qquad ... • 80.9k 13 votes Accepted ### Are all IIR filters unstable in nature? Note that for stable IIR filters, the impulse response does approach zero as n goes to infinity. It just never becomes exactly zero. However, the sum of the absolute values is finite. Just as an ... • 80.9k 13 votes Accepted ### FFT-based fast convolution vs IIR filtering For a simple 10-band equalizer, it would be very hard to beat the IIR implementation. For most HW architectures the break-even point between direct FIR convolution and Overlap Add/Save (OLA) is ... • 34k 12 votes ### What is the maximum output of an IIR filter? I would like to know,if there is any way to estitmate what could be the maximum limits of the output Yes. It's$$y_{max} = x_{max} \cdot \sum_{n = 0}^{\infty} |h[n]| $$I.e. the maximum gain is the ... • 34k 11 votes ### best implementation of a real-time, fixed-point iir filter with constant coefficients what is fraction saving? can you write a code.so that i can understand more clearly? Let's call the quantizer operator \operatorname{Quant}\{\cdot\} . So the output of the quantizer, with v[n] ... 10 votes ### Applying filter in scipy.signal: Use lfilter or filtfilt? Answer by @endolith is complete and correct! Please read his post first, and then this one in addition to it. Due to my low reputation I was unable to respond to comments where @Thomas Arildsen and @... • 201 10 votes Accepted ### How to produce a high-pass filter from a low-pass one? The result will indeed be a high pass filter. From your difference equation, the transfer function of the low pass filter is$$H_l(z)=\frac{\beta}{1-(1-\beta)z^{-1}}\tag{1}$$with \beta=1/\alpha. ... • 80.9k 9 votes Accepted ### Is y[k] = y[k-1] + x[k] an integrator? The system$$y[n]=y[n-1]+x[n]\tag{1}$$is an ideal accumulator, i.e., it computes the cumulative sum of the input samples:$$y[n]=\sum_{k=-\infty}^nx[k]\tag{2}$$It is in a way analogous to a ... • 80.9k 9 votes Accepted ### Why can't realisable IIR filters have linear phase? The frequency response of a real-valued discrete-time system with linear phase has the form$$H(e^{j\omega})=A(\omega)e^{-j\omega\tau},\qquad\omega\in [-\pi,\pi]\tag{1}$$where A(\omega) is either ... • 80.9k 9 votes Accepted ### How do software equalizers work? This depends a lot on how you implement it. A single biquad takes about 10 arithmetic operations. (To be precise a Transposed Form II takes 4-5 multiplies and 3 adds, depending on how the gain ... • 34k 8 votes Accepted ### Analytically designing a notch-filter for specified frequency 50 Hz You've designed a causal filter with a notch at \omega_0=100\pi. But the result is probably not what you want. Note that you've designed an FIR (finite impulse response) filter. Its frequency ... • 80.9k 8 votes Accepted ### How does this "simple filter" work? In more standard DSP terms, you have the following filter:$$ y[n] = (1-a) x[n] + a y[n-1] $$where x[n] and y[n] are the input and output signals at time n respectively. The transfer ... • 4,751 8 votes Accepted ### Cutoff frequency of a first order recursive filter That formula for the cut-off frequency is a very inaccurate approximation. In this answer I derived the exact relation between the coefficient of a first order recursive averaging filter and its 3-dB ... • 80.9k 8 votes Accepted ### 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 ... • 38.4k 8 votes Accepted ### Design a linear-phase FIR filter approximating the magnitude of a given IIR filter What you do in step 1 is simply truncate the infinite impulse response to approximate it by an FIR filter. If you use sufficiently many filter taps, the approximation becomes arbitrarily accurate. ... • 80.9k 8 votes Accepted ### Meaning of Phase response of a filter? In simple words? There are many good answers here. I will try to take the reverse approach in order to explain in very simple words what is necessary in order to keep the output's shape same as input's, and what ... • 2,496 8 votes Accepted ### 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 ... • 15.1k 8 votes ### 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 ... • 80.9k 7 votes Accepted ### How to design a filter with custom group delay -- why is it an IIR? As pointed out by Peter K., it is true that many well-known techniques for designing FIR filters actually only design linear phase filters. However, FIR filters are very well suited for delay ... • 80.9k 7 votes Accepted ### Convert a FIR to an equivalent IIR I would say that the answer to your question - if taken literally - is 'no', there is no general way to simply convert an FIR filter to an IIR filter. I agree with RBJ that one way to approach the ... • 80.9k 7 votes ### What's the advantage of adaptive IIR filter against FIR? These are the key differences between FIR and IIR filters, regarding the feature you wish to control are the following:$$ \begin{array}{c|lcr} \text{Feature} & \text{IIR} & \text{FIR} \\ \... • 1,367 7 votes ### Frequency Domain Filtering This is just "faking" the magnitude response of an IIR filter. The output's magnitude spectrum looks just like it has been filtered by the IIR filter with the given frequency response. Although it may ... • 4,115 7 votes Accepted ### Protect an IIR filter from being reverse-engineered Short answer: You can't. If an attacker can insert a signal that covers the whole bandwidth (e.g. a white signal, or at least one that has no spectral zeros) into the system (and he can do that over ... • 26.9k 7 votes ### Single pole IIR filter, fixed point design One thing to consider when implementing an IIR filter, whatever the order, is quantization and limit cycles. Let me show you with a quick example with your original filter$y[n] = a*x[n]+(1-a)*y[n-1]...
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A discrete-time first-order high pass filter with unity gain at Nyquist and a zero at DC is described by the following difference equation: y[n]=\frac{1+\alpha}{2}\big(x[n]-x[n-1]\big)+\alpha y[n-1],...