37 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 ...
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27 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 ...
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  • 416
20 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 ...
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  • 481
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 $\Delta f$ ...
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19 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 ...
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  • 80.4k
17 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(\...
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  • 26.8k
14 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 ...
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13 votes
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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 ...
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  • 80.4k
13 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 ...
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  • 151
13 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 Hann ...
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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 ...
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  • 32.5k
12 votes
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3dB-Cut off frequency of moving average

Consider a zero-phase moving average of length $N$: $$\text{y}[n] = \begin{cases} \displaystyle\frac{\text{x}[n] + \displaystyle\sum_{k=1}^{\frac{N-1}{2}}\left(\text{x}[n+k] + \text{x}[n-k]\right)}{N}...
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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 ...
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10 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 ...
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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 ...
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9 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 ...
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  • 80.4k
8 votes

Group delay of the FIR filter

To be precise the group delay of a linear phase FIR filter is $(N-1)/2$ samples, where $N$ is the filter length (i.e. the number of taps). The group delay is constant for all frequencies, because the ...
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8 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. ...
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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. ...
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8 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 ...
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  • 2,576
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 ...
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7 votes
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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 ...
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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} \\ \...
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  • 1,357
7 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 $...
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  • 4,105
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 ...
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  • 34k
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 ...
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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 ...
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7 votes
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How to Classify a Kernel as Low Pass Filter (LPF) or High Pass Filter (HPF)? How to Transform an LPF Kernel into HPF Kernel?

General We assume 2 modes of filters: LPF or HPF. Classifying Filter Type Usually, if it is a well planned LPF and well Planned HPF a simple test will do. Calculate the sum of all coefficients. The ...
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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 ...
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  • 37.6k
7 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 ...
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