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How do impulse response guitar amp simulators work?

When talking about modeling, there are two things that usually get modeled: 1. the guitar amp, and 2. the speaker cabinet. Only the latter is modeled by an impulse response, which means that the ...
Matt L.'s user avatar
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11 votes
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This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?

Your professor is right, and you're almost right too. The filter is clearly an FIR filter, but because its frequency response can be expressed as a geometric series, a recursive implementation is ...
Matt L.'s user avatar
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10 votes
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Why do linear phase filters have symmetric impulse responses?

Actually, I think I see why. $$X(j\Omega) = |X(j\Omega)|e^{-j\theta(\Omega)}$$ $|X(j\Omega)|$ is purely real, and therefore if we take the IFT it is even and symmetric. $\theta(\Omega)= a\Omega$ ...
CAJ's user avatar
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9 votes

Meaning of arrow head in dirac delta?

The arrow head is a symbol. It symbolizes "there's a Dirac delta at this position". That's all its meaning. Is it referring that at t=0, amplitude is infinity? Ahhh, no. You cannot say &...
Marcus Müller's user avatar
8 votes
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Calculating the inverse filter for the (exponential) sine sweep Method

Assuming that your Exponential Sweep Sine was generated using the formula: $$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$ where: $f_1, f_2$ - Initial and final ...
jojeck's user avatar
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8 votes

How do impulse response guitar amp simulators work?

If you're an EE student, you will have encountered the term LTI System (or you certainly will soon enough!): A system that, no matter the absolute time, outputs, given the same input, the same output; ...
Marcus Müller's user avatar
7 votes

Why is the impulse response function of this system 0?

This system $$ y(t) = t^2 x(t) $$ is not LTI and therefore does not have an impulse response of the form $h(t) = \mathcal{T}\{\delta(t)\}$. So your statement $h(t) = t^2 \delta(t)$ is not correct......
Fat32's user avatar
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6 votes

For an LTI system, why does the Fourier transform of the impulse response give the frequency response?

The intuitive answer is that an impulse in time at t=0 contains all frequencies of equal magnitude, so applying an impulse to an LTI system is the same as applying all frequencies at once, thus the ...
Pat Eblen's user avatar
6 votes
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Delayed impulse does not delay spectral response

The convolution theorem ("Multiplication in time is Convolution in frequency") states: $$\mathcal{F}\{x\cdot y\}=\mathcal{F}\{x\}*\mathcal{F}\{y\}$$ where $x, y$ are two time-domain signals, $\cdot$ ...
Maximilian Matthé's user avatar
6 votes

Impulse response of LTI Systems

$h_0(t)$ is inverse Fourier transform of $H(jw)$. Your formula is OK, you can continue your calculation to practice your math manipulation, why not. To check the result, you can remark that $H(jw)$ is ...
AlexTP's user avatar
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What is impulse response (or equivalently the frequency response) of the channel ?

This is a fundamental topic and it needs a lot of explaination. I suggest you use the fading channel object of MATLAB, especially the Channel Visualization Tool. There are lots of examples with ...
AlexTP's user avatar
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What is the time unit of the converted Channel Impulse Response?

Because you don't have background in wireless communications, I will try to answer as simply as possible. What is the time unit of the converted CIR? Just time unit. It can be second, ms, us, etc. ...
AlexTP's user avatar
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Why is the first value in digital first-order IIR filter impulse response not the largest?

A causal first-order IIR filter is characterized by the following difference equation: $$y[n]=b_0x[n]+b_1x[n-1]-a_1y[n-1]\tag{1}$$ with $x[n]$ the input signal, and $y[n]$ the output signal. The ...
Matt L.'s user avatar
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6 votes

Design a LTI system which returns DC value of the input signal

The DC value is simply the mean. Since the signal is periodic you only need to take the mean of one period. This can be simply done with $$h(t)=\left\{\begin{matrix} 1/T, 0 < t < T\\ 0, {\rm ...
Hilmar's user avatar
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6 votes

Meaning of arrow head in dirac delta?

On the wiki page for the Dirac delta function, you can find one meaning of the arrow. It somehow means that is not "defined" as a constant defined value, but more as a factor applied to ...
Laurent Duval's user avatar
6 votes

Algorithm to "serialize" impulse responses

You convolve the two impulse responses. $$h_{cascade}[n] = h_1[n]*h_2[n]$$
Hilmar's user avatar
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5 votes
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Estimate the Filter Coefficients of 1D Filtration (Convolution)

This is a nice question. I will try solving it using 2 approaches (Which are basically the same). The solution is the Least Squares Solution: $$ \hat{h} = \arg \min_{h} \frac{1}{2} \left\| h \ast x - ...
Royi's user avatar
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5 votes
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Understanding an alternative representation for the difference equation of a FIR filter?

Given that $$ u[n-k_1] = \sum_{k=k_1}^\infty \delta[n-k] $$ you can take the difference between two steps with different shifts ($k_1 < k_2$) and obtain: $$ u[n-k_1] - u[n-k_2] = \sum_{k=k_1}^{...
SleuthEye's user avatar
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5 votes
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Can I assume system is LTI when given by DTFT of impulse response

A 1D LTI system is completely characterized by the function $h(t)=T\{\delta(t)\}$ which is denoted as the impulse response of the system. Given an LTI system with impulse response $h(t)$ you can then ...
Fat32's user avatar
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5 votes
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Proper method for generating Channel coefficients in MATLAB

Complex channel coefficient is just a way to represent the independent real coefficients. You just need to generate ...
AlexTP's user avatar
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5 votes

Multiplication of two impulse function $\delta(t)\cdot \delta(t)=?$

The property $$f(t)\delta(t-t_0)=f(t_0)\delta(t-t_0)\tag{1}$$ is only valid for a function $f(t)$ that is continuous at $t=t_0$. Since the Dirac delta impulse $\delta(t)$ is not a function (it is a ...
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

How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?

First of all it seems useful to establish what we mean by an equation like $$\delta(at+b)=\frac{1}{|a|}\delta(t+b/a),\qquad a\neq 0\tag{1}$$ Since the Dirac impulse $\delta(t)$ is a distribution, Eq....
Matt L.'s user avatar
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5 votes
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why only impulse signal for convolution?

Because the impulse response completely characterizes an LTI system. The reason is an arbitrary input $x(t)$ can be written as an infinite sum of time shifted and scaled Delta functions: $$x(t) = \...
GKH's user avatar
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5 votes
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Design a LTI system which returns DC value of the input signal

A constant impulse response won't work because if the input signal has a non-zero DC component, the output will blow up. Note that the input signal has frequency components at DC and at integer ...
Matt L.'s user avatar
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5 votes
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Composing two Impulse Responses

Yes, that's correct. The impulse response of a cascade of two systems is the convolution of the individual Impulses responses. Convolution is commutative, so it doesn't matter in which order you ...
Hilmar's user avatar
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5 votes
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Why is particular solution zero for an impulse excitation signal?

The correct form of the statement should be the particular solution is zero for $t>0$ This is simply the case because the input $\delta(t)$ is zero for $t>0$. So for $t>0$, the impulse ...
Matt L.'s user avatar
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5 votes
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Calculation of inverse impulse response in the frequency domain

Your result is correct, even if it seems a bit counterintuitive. Note that you don't compute the Fourier transform but the discrete Fourier transform (DFT). The system you want to invert has the ...
Matt L.'s user avatar
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5 votes
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Prove that exponential sweep sine decay 6 dB per octave

This JAES paper gives a close form of the Fourier transform of the synchronized swept-sine (SSS) signal which has the same form as the ESS $$ x(t) = \sin \big\{2\pi f_1L \big[\exp(t/L) -1 \big]\big\} $...
ZR Han's user avatar
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5 votes

How long should be the Room Impulse Response

The length of any room impulse response is technically infinite since it's inherently an IIR system. The reverberation time describes the decay rate. During the reverberation time the impulse response ...
Hilmar's user avatar
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