15 votes
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If the convolution of two signals is a unit impulse, what does this tell us?

It tells us that the systems are inverses of each other. The DFT of $$h_1[n]*h_2[n]= \delta[n]$$ is $$H_1[k] \cdot H_2[k] = 1 $$ so we get $$H_2[k] = \frac{1}{H_1[k]}, H_1[k] = \frac{1}{H_2[k]}$$ In ...
Hilmar's user avatar
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12 votes
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Who first understood the importance of poles?

If you consider poles of an integral transform domain to be important to the solution of differential equations: (as usual,) Euler did it first, 1753. One "importance" of poles is that they're part of ...
Marcus Müller's user avatar
11 votes

Digital filter coefficients from low-pass to high-pass

You can apply a so-called all-pass transformation to a discrete-time low-pass prototype filter in order to convert it to other standard filters (such as high-pass, band-pass, and band-stop). This is ...
Matt L.'s user avatar
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11 votes
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Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?

There is a relationship between these two concepts. Let the complex function $f(z)$ be analytic on and inside a simple closed curve $C$ in the complex plane. Then Cauchy's integral formula states that ...
Matt L.'s user avatar
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7 votes
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Understanding the $\mathcal Z$-transform

Consider a liner discrete-time system. Assume we can define it in terms of an input-output relation as follows (you can assume a more general model but it is enough for our purpose): $$a_0y[n]+a_{1}y[...
msm's user avatar
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7 votes
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Why does reversing the order of these two transfer functions give me different outputs?

If the input is a unit step, then the output of the first block in system 1 is not zero, but it is a Dirac delta impulse $\delta(t)$. Intuitively, the derivative is infinite at $t=0$ because of the ...
Matt L.'s user avatar
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7 votes
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Basic Questions on Wiener Filtering

The task is to filter x(t) when given y(t), where y(t) = x(t) + n(t). Great but first we need to build an appropriate filter. At this point: No. The task is to filter $y[n]$ to achieve $x[n]$. Your ...
Fat32's user avatar
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7 votes

Filter odd or even harmonics with notch or inverse notch filter

What you are looking for are what we, in the audio space, call comb filters. Comb filters may or may not have a feedback path, just like FIR and IIR filters. In fact, there is a generalized theory ...
robert bristow-johnson's user avatar
6 votes
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Poles and zeros of a transfer function

The "poles-inside-unit-circle" stability criterion only applies to causal systems. Your system is not causal because it uses one sample from the future owing to the $z$ term. The general technique to ...
Atul Ingle's user avatar
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6 votes
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What Is the Transfer Function of a Moving Average (FIR Filter)?

The frequency response of the moving average is called the asinc or psinc, the aliased sinc or periodic sinc (sinc for cardinal sine), or the Dirichlet function. Since the sum of the moving average ...
Laurent Duval's user avatar
6 votes
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Transfer function intuition

Normally, in electrical enginnering, we apply the term "transfer function" and "filter" to an operation that belongs in the class we call Linear Time-Invariant systems (LTI). Sometimes you might read ...
robert bristow-johnson's user avatar
6 votes
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Is this system causal or not?

Note that in this case you can see that the system is causal only from the given implementation. It's important to understand that you can't see it from the difference equation (if no initial ...
Matt L.'s user avatar
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6 votes
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Transfer function with blackbox modelling is too slow compared to real expectation

In your original code you defined the sampling interval to be $T_s=0.05$ (idd1 = iddata(ddout, ddin, 0.05);). Yet, according to the data file, the time step between ...
Matt L.'s user avatar
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6 votes

Filter odd or even harmonics with notch or inverse notch filter

If the OP is actually interested in selecting only one individual frequency from the even or odd harmonics, then a moving average filter (MAF) would be ideal since this can provide a null at every ...
Dan Boschen's user avatar
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6 votes
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How accurate is the dominant poles approximation in higher order control systems?

It depends entirely on how close the less dominant poles are to the dominant poles. A simple way to understand what is happening is consider poles on the real negative axis for continuous time systems:...
Dan Boschen's user avatar
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6 votes
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Why does scipy introduce its own convention for H(z) coefficients?

I agree with the OP's annoyance in that two conventions are used and believe it comes down to what is commonly used in filter design vs what is commonly used in control systems. However the only ...
Dan Boschen's user avatar
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5 votes

Converting mel spectrogram to spectrogram

Nowadays the easiest thing would be to use librosa for this task. It has the mel_to_stft function which does exactly what you want. As others have mentioned, this ...
jojeck's user avatar
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5 votes
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determining type of filter given its pole zero plot

You'd have to figure out the frequency response of the filter. Here are two methods. I prefer Method 2 because it's quick and dirty, and you don't really care about the exact gain values in the ...
Atul Ingle's user avatar
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5 votes

determining type of filter given its pole zero plot

In this answer I'll try to show you how to qualitatively evaluate a given pole-zero plot by just looking at it. Of course, this method has its limits, but for relatively simple pole-zero plots you can ...
Matt L.'s user avatar
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5 votes
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Why do we assume zero mean noise in sensor data?

The brutally honest answer here is: The noise is considered zero-mean because that's what the author decided to do. Without looking deeper into the signal model employed, it's impossible to answer. ...
Marcus Müller's user avatar
5 votes

A question about the meaning of pole in time domain

Let $H(s)$ be a transfer function of the form $$H(s) = \frac{1}{s-p}$$ where $p$, which is a pole of $H(s)$, can be written as a complex number $a+jb$. Taking the inverse Laplace transform of $H(s)$ ...
anpar's user avatar
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5 votes

What Is the Transfer Function of a Moving Average (FIR Filter)?

The following figure is borrowed from Frequency Response of the Running Average Filter: This is the gain applied to different frequencies (normalized to interval 0-$\pi$), for running averages of ...
Laurent Duval's user avatar
5 votes

Can someone explain waveshaping to me?

In the audio domain, waveshaping is simply applying a memoryless nonlinear function to an input signal. $$ y(t) = g\big( x(t) \big) $$ The waveshaping function, $g(x)$, is most often a continuous ...
robert bristow-johnson's user avatar
5 votes

What is the zero in this transfer function?

$$2s+1=2\left(s+\frac12\right)$$ That's all I can say.
Matt L.'s user avatar
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5 votes
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Missing delay in heavyside step function

We know that $\displaystyle \frac{\sin(\theta (n+1))}{\sin(\theta)} u[n+1]$ has value $0$ for $n < -1$ since $u[n+1]=0$ for $n < -1$. At $n=-1$, $u[n+1]$ jumps to value $1$, but $\sin(\theta (n+...
Dilip Sarwate's user avatar
5 votes

Compensating the Group Delay of an Analog Filter using DSP

It's often easier to design FIR filters for compensating group delay. At the same time they could also compensate the magnitude if necessary. The easiest method is to use a complex least squares ...
Matt L.'s user avatar
  • 90k
5 votes

How to realize Poles and zeros at infinity??especially through transfer function?

It's actually quite straightforward: positive powers of $s$ (or, in discrete-time, $z$), correspond to poles at infinity. Negative powers give you zeros at infinity. Let's look at some examples. In ...
Matt L.'s user avatar
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5 votes
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Poles and zeros form of a transfer function

The two expressions are generally not identical. In the special case $K=L$ they're equivalent, otherwise they differ by a (positive or negative) power of $z$: $$\frac {\displaystyle\prod_{k=1}^K (1 - \...
Matt L.'s user avatar
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5 votes
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Why does causality imply that the system function is analytic?

New answer: I provide a new answer because I believe that this is a clearer and more direct way of explaining the relation between causality of the impulse response and analyticity of the ...
Matt L.'s user avatar
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