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40 votes

Why is a linear phase important?

Let me add the following graphic to the great answers already given, with the intention of a specific and clear answer to the question posed. The other answers detail what linear phase is, this ...
Dan Boschen's user avatar
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31 votes
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Why is a linear phase important?

A linear phase filter will preserve the waveshape of the signal or component of the input signal (to the extent that's possible, given that some frequencies will be changed in amplitude by the action ...
AndyW's user avatar
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22 votes

Why is a linear phase important?

Just to add to what's already been said, you can see this intuitively by looking at the following sinusoid with monotonically increasing frequency. Shifting this signal to the right or left will ...
orodbhen's user avatar
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20 votes
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FIR Filter Design: Window vs Parks McClellan and Least Squares

I agree that the windowing filter design method is not one of the most important design methods anymore, and it might indeed be the case that it is overrepresented in traditional textbooks, probably ...
Matt L.'s user avatar
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19 votes

Why is a linear phase important?

The essence and importance of linear phase property lies in the definition and the effect of group delay $$\tau(\omega) = - \frac {d\phi(\omega)}{d\omega}$$ on the applied signal $x[n]$, where $\phi(\...
Fat32's user avatar
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19 votes
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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 $\Delta f$ ...
Dan Boschen's user avatar
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15 votes

Why is a linear phase important?

The answer to this question is already been explained clearly in the previous replies. Yet I wish to give it a try to present a mathematical interpretation of the same Consider a linear time ...
SakSath's user avatar
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15 votes
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Why would one use a Hann or Bartlett window?

In reviewing fred harris' Figures of Merit for various windows (Table 1 in this link) the Hamming is compared to the Hanning (Hann) at various values of $\alpha$ and from that it is clear that the ...
Dan Boschen's user avatar
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15 votes

A basic question about the use of moving average vs low-pass filters in DSP

A moving average filter can be thought of as a type of low-pass filter that doesn't have any control over its bandwidth for a fixed number of taps. For a finite impulse response (FIR) filter, the ...
Robert L.'s user avatar
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13 votes
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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 ...
Hilmar's user avatar
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11 votes
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Pole-zeros of a real-valued causal FIR system

Note the difference between the zeros at $0.3 \pi$ and at $0.8 \pi$. The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$. At $\theta = 0.8 \pi$, however, the curve is tangent to ...
Juancho's user avatar
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11 votes
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Number of taps needed in an FIR filter to remove DC

See How many taps does an FIR filter need? In your case you'd need more than 1000 taps depending on the allowable ripple, as your cut-off frequency is less than fs/500. Alternatives : use an IIR, a ...
Ben's user avatar
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11 votes
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Minimum Phase - All Pass Decomposition For Large Linear Phase Filters

Computing the polynomial coefficients from the roots of the polynomial is a potentially ill-conditioned problem. However, it turns out that the order of the roots supplied to the ...
Matt L.'s user avatar
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9 votes

FIR filter design for complex signal

In fact you have two signals, and it depends on what you want to achieve, but usually you would just filter both signals (the real and the imaginary part) with the same (real-valued) low pass filter. ...
Matt L.'s user avatar
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9 votes

Vector length output of discrete time convolution

The output $y$ is convolution of $x[n]$ and $h[n]$: $$y[n]=\sum_{l=-\infty}^{l=+\infty} x[l]h[n-l]$$ As you said, let's assume only $h[0],\cdots,h[N-1]$ and $x[0],\cdots,x[M-1]$ are non-zero. When $...
msm's user avatar
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9 votes
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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 ...
DSP Rookie's user avatar
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9 votes
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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 ...
Hilmar's user avatar
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9 votes
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What are the advantages and disadvantages of Kalman filter compared with FIR, IIR and low pass filter to filter data with noise?

Kalman filters really aren't that special, and you seem to be missing the point of a Kalman filter. A Kalman filter is really just a generally time-varying, generally IIR, generally multi-input ...
TimWescott's user avatar
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9 votes
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High Dynamic Range FIR Filters

Like @MattL. and @aconcernedcitizen say, the issue is numerical. Python's scipy.signal.firls uses internally the solver ...
Olli Niemitalo's user avatar
9 votes

Half power frequencies is -6dB or -3dB

The definition of the cut-off frequency is arbitrary. Different design methods use different definitions. If you define the cut-off at $-6\textrm{ dB}$, it means that the amplitude of a sinusoidal ...
Matt L.'s user avatar
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9 votes
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Why the sum of filter coefficients of an FIR filter does not add to 1?

I'm assuming your FIR filters are nonrecursive tapped-delay line FIR filters. For such filters the sum of a filter's coefficients will equal the filter's gain at zero Hz (DC). This property results ...
Richard Lyons's user avatar
8 votes
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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. ...
Matt L.'s user avatar
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8 votes
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What is the difference of windowing functions for FIR filtering?

So, from the discussion in the comments it's clear you know most you need to know. The window method for FIR filter design is based on this idea: We know the "ideal" frequency response $H(f)$ we ...
Marcus Müller's user avatar
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 ...
Matt L.'s user avatar
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8 votes
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FIR filter with no ripple (only one zero at Nyquist frequency)

This answer shows how to get coefficients for zero-phase "maxflat" filters. They do not minimize stop-band energy (as noted by @MattL. in a comment) generally, but may still be useful. With $...
Olli Niemitalo's user avatar
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} \\ \...
Brethlosze's user avatar
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7 votes

FIR Filter Design: Window vs Parks McClellan and Least Squares

Windowed Sinc filters can be adaptively generated on the fly on processors barely powerful enough to run the associated FIR filter. Windowed Sinc filters can be generated in finite bounded time. The ...
hotpaw2's user avatar
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7 votes

FIR Filter Design: Window vs Parks McClellan and Least Squares

I'll show here one benefit of a windowed design and a trick to get the same benefit from Parks–McClellan. For half-band, quarter-band etc. filters windowing retains the time-domain zeros of the ...
Olli Niemitalo's user avatar
7 votes
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Educational purpose - What is the correct way to simulate a multipath fading channel which has ISI

Lets say we want to transmit a sequence of discrete data $\left\lbrace x[n] \right\rbrace$. But because we are living in analog world, the sequence must be modulated. Call $T_s$ is symbol duration ...
AlexTP's user avatar
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7 votes
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Why a pair of complex-conjugate zeros provide a nulling filter? (FIR filter case)

The unit circle on the z-plane represents the frequency axis, similar to the imaginary axis $j\Omega$ on the s-plane for the Laplace Transform in the continuous time case. So the frequency response of ...
Dan Boschen's user avatar
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