19 votes
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Calculation of Reverberation Time (RT60) from the Impulse Response

Encouraged by Hilmar, I've decided to update the answer with all the steps necessary to calculate the Reverberation Time from a scratch. Presumably, it will be useful for others interested in this ...
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  • 10.5k
13 votes
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How do real-time convolution plugins process audio so quickly

Real-time low-latency partitioned convolution reverb with a long impulse response works by dividing the impulse response into unequally sized partitions. The shortest partitions (blocks) are at the ...
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11 votes
Accepted

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 ...
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  • 80.4k
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 ...
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  • 80.4k
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. $\theta(\Omega)= a\Omega$ ...
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  • 303
9 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 - ...
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  • 41.4k
9 votes

Can two different impulse responses give the same frequency response?

No. The impulse response and frequency response of an LTI system are related by the Fourier transform, which is one-to-one.
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  • 23.7k
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 &...
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8 votes

What is the relationship between passivity of impulse response and passivity of the system?

Let me clarify some definitions first. There is no such thing as a "passive impulse response", there are only passive systems. If you like, you can call the impulse response of a passive LTI system "...
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  • 80.4k
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; ...
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7 votes
Accepted

Deconvolution Using Response to an Heavy Side

If we can assume no noise (Or the SNR is very high) you can get the response by applying the inverse filter in frequency domain. Lets say $ y [n] $ are the signal samples. Given $ x [n] $ the samples ...
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  • 41.4k
7 votes
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find impulse response from step response

You can find the impulse response Let's take the case of a discrete system. If $s[n]$ is the unit step response of the system, we can write $$s[n]= u[n]\ast h[n]$$ where $h[n]$ is the impulse ...
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7 votes
Accepted

How to obtain impulse response from the differential equation of a system?

It looks like your transfer function is correct, but there's a small mistake in your partial fraction expansion: $$H(s)=\frac{2}{(s+4)(s+2)}=\frac{1}{s+2}-\frac{1}{s+4}\tag{1}$$ The corresponding ...
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  • 80.4k
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......
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  • 26.8k
6 votes
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Check if a filter is IIR or FIR

In the general case you have $$H(z)=\frac{P(z)}{Q(z)}$$ where $P(z)$ and $Q(z)$ are polynomials in $z$. If - as is the case in your example - $Q(z)$ just has one single term, $H(z)$ is definitely ...
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  • 80.4k
6 votes

Can two different impulse responses give the same frequency response?

To add on to what has been said, what you're asking is, if you have $h_1$ and $h_2$ as impulse responses of a LTI systems (continuous-time or discrete time) and $H_1$, $H_2$ their respective frequency ...
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  • 3,272
6 votes
Accepted

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, $\cdot$ ...
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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 ...
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  • 5,780
6 votes

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 ...
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  • 5,780
6 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 ...
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  • 10.5k
6 votes
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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 ...
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  • 80.4k
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 ...
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  • 32.6k
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 ...
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5 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 ...
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5 votes

How to obtain impulse response from the differential equation of a system?

Let me provide a method, for part a, applied only for finding the impulse response $h(t)$ of an LTI system characterised by an LCCDE of the form $ \sum_{k=0}^{N}{ a_k {{d^k y(t)}\over {dt^k}}} = \...
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  • 26.8k
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}^{...
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  • 1,742
5 votes
Accepted

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 ...
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  • 26.8k
5 votes
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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. ...
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  • 5,780
5 votes
Accepted

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 ...
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  • 5,780
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 ...
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