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The impulse response of a dynamic system is its output when presented with a brief input signal, called an impulse.

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38 views

Simple question about Sinc()

Suppose I use the ideal lowpass filter eq to attempt creating a IIR filter using it : $$ h[n] = \frac{\sin(\omega_c \, n)}{\pi \, n}, \qquad -\infty < n < \infty $$ Obviously, I can't really (...
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0answers
15 views

impulse response from frequency and phase spectrum

Is there a generally accepted way of calculating an impulse response of an LTI system from its frequency and phase spectra? Of course, the obvious thing to do is an inverse Fourier transform, but ...
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6answers
121 views

Optimal n-th order IIR approximation to a moving average filter

I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
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2answers
51 views

How to compute the impulse response from incomplete frequency response data?

I need to compute the impulse response of a system, but I only have access to the frequency response data. This data contains the output magnitude of the system (for a fixed input amplitude) at ...
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1answer
30 views

Poles of the transfer function in Z Transform

Given that: $H(z)$ has 4 poles maximum. $H(z)$ has a pole at $z_1=a+bi$ Given that the impulse response $h[n]$ is: Symmetric: $h[n] = h[-n]$ Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$ How we can ...
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1answer
60 views

FIR Impulse response & transfer function

I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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0answers
12 views

Estimation of the frequency response data using Matlab command invfreqz?

I would like to determine frequency response and then impulse response of the displacement equation (eq. 1 please see screen shot of the task below). In this example we study a response of the finite ...
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1answer
57 views

ACF and impulse response

These are questions according to the system identification. I can understand some questions: Is there a relation between autocorrelation function and impulse response? Is it possible to identify the ...
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1answer
34 views

I want to get impulse response of causal system

I want to get impulse response of this causal system on first photo. So I got frequency response on second photo from this system. and now I am trying to transform this frequency response to impulse ...
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0answers
21 views

extracting a room response [duplicate]

So I have a wav file containing a record of a sine sweep played on my pc and recorded by a mic. And I want to extract the room impulse of it, I've looked online but I couldn't find any clear answers. ...
2
votes
2answers
59 views

Frequency response of marginally stable LTI systems

The frequency response of a system is defined as: $$\int_0^\infty{h(t)e^{-j\omega t}dt}$$ where $h(t)$ is the impulse response. But in marginally stable systems, $h(t)$ does not decay so the integral ...
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2answers
42 views

Equalize Speaker using impulse response

So I have this school project where my aim is to improve a loudspeaker in general, my idea is to mesure the impulse response of the room using a mic, then use this mesure to conceive a loudspeaker ...
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0answers
64 views

Multilateration of Sound in 3D Space

TL:DR - How can you find the 3D coordinates of a emitter than transmits an impulse signal? STORY: I'm working on something to improve my bird-watching. I've got a camera that can take pictures of ...
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1answer
64 views

Impulse response of a causal system from transfer function in z-domain

The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$ I need to find the impulse response h[n] of a causal system with x[n] as unit impulse. I have tried to find the impulse response by the following ...
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3answers
80 views

Why use transfer functions than differential equations?

I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths. Why we use ...
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1answer
63 views

Homework Help: What does $h[0] = 1$ represent? What is $\ln \big| H(e^{j \omega})\big|$?

I have been staring at this problem for a week now... Suppose $H(e^{j \omega})$ is the frequency response of a stable and causal minimum-phase discrete-time system with $h[0]=1$ ($h[n]$ is the ...
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1answer
59 views

Calculating impulse response of system

Given is the illustrated circuit diagram of a linear, time-invariant, time-discrete system: How do I show that the total system has the impulse response $h[n] = aδ[n] + bδ [n - 1] + cδ [n - 2]$ and ...
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2answers
283 views

How do I calculate the impulse response of an ideal band-pass filter?

I understand the FR of an ideal BPF is just 1 between the two cutoff frequencies and 0 everywhere else above and below them both. But with arbitrary cutoffs, how would one find the IR of this ideal ...
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1answer
36 views

Add multiple aborption coefficients into virtual impulse response

I've got some code which creates a virtual impulse response of a room with arbitrary dimensions. I want to know, how can I add more than one absorption coefficient into it? ...
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0answers
72 views

BIBO Stability of an impulse response

I am trying to prove if $h_1[n] = 2^{-n} u[n]$ and $h_2[n] = (0.1)^n$ are BIBO stable or not, but I'm not sure if these analysis are correct. I'm having some trouble to understand this specific ...
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2answers
76 views

What is the derivative of the function $s(t)=(1-e^{\frac{-t}{RC}})u(t)$?

What is the derivative of the following function $$s(t)=(1-e^{\frac{-t}{RC}})u(t)$$ with respect to $t$, where $u(t)$ is a unit step function? I am getting $\delta(t)+\frac{1}{RC}e^{-t/RC}u(...
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1answer
134 views

Designing high-pass filters using impulse invariance

One of the main disadvantages of realizing digital filters using impulse invariance is aliasing. According to the Nyquist sampling criterion, in order for the frequency response of the digital filter ...
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2answers
54 views

How do I show an impulse response leads to a zero-phase frequency response?

I'm trying to understand how to show that with real coefficients, the phase response of a filter is 0. Here is the impulse response $h[n] = b_1d[n+1] + b_0d[n] + b_1d[n-1]$ How should I approach ...
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2answers
219 views

How can I calculate Reverberation Time (RT60) from the Room Impulse Response using Python?

I have the following Room Impulse Response(RIR) in wave format here. I wanted to calculate Reverberation Time (RT60) of it by plotting its Energy Decay Curve using this Python code. The RIR is ...
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2answers
38 views

unit step signal as sum of impulses from MIT OCW video

From MIT's OCW on Signals and Systems by A. Oppenheim, at 4:30 mark https://www.youtube.com/watch?v=jGk3w1b7UXQ&index=3&list=PLLNp7XoiSLQYygYw8Mzt763zZCQdzCZcd He said that by forming the sum ...
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2answers
65 views

How to calculate time of arrival using room impulse response

I need to find the timestamp of arrival of a particular signal at a receiver location within a room. The known parameters are the room impulse response h for a ...
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1answer
40 views

impulse response of a system from its step response;confusion

If the step response of a system is given as $$c(t)=(10e^{-5t}-2e^{-10t}+1)u(t)$$ then its impulse response is _______? My Approach: we know: $$h(t)= \frac {d}{dt} c(t)$$ Process(1): $$h(t)= \{ ...
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0answers
53 views

Difference between $H(\omega)$ and $H(j\omega)$ [duplicate]

What is the difference between $H(\omega)$ and $H(j\omega)$, in terms of impulse response. And if so, when do I have to use one or another.
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1answer
44 views

Impulse Invariant mapping [closed]

Can someone help me to better understand the Impulse Invariant mapping? : $$h[n] = T \cdot h(nT)$$ I don't understand why the discrete-time impulse response, $h[n]$, is taken from the sampled ...
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0answers
31 views

BER Graph for a PSK Modulation through a linear channel model

This is the graph that occurs when M-PSK symbols pass through a linear channel with impulse response given in a vector h. The simulation is done in Matlab and I am unsure about the result because of ...
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1answer
217 views

Calculating output of a system given impulse response and input

I'm trying to calculate the output given an impulse response $h(t)=e^{-t}u(t)$ and input $x(t)=\cos(2\pi t)$. I know I need to use the convolution but given that cosine is periodic, I don't see how ...
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1answer
35 views

Proof of $E[y(n)]=E[x(n)]*\sum h(k)$

If $h(n)$ is the impulse response of the discrete LTI system, $x(n)$ is the white noise process with variance $\sigma_x^2$ and $y(n)$ is the output, prove that $$\mu_y = \mu_x*\sum_{k=0}^\infty h(...
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2answers
212 views

How to obtain impulse response from a plot of magnitude of frequency response?

I have a plot of a magnitude response of a frequency response, how can I get the impulse response using only this plot and nothing else?
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3answers
365 views

Impulse Response to LTI

I am new to DSP, and I am self-studying using mostly Proakis. I have a question. There are some examples in the text where you will be given the impulse response of an LTI system, and then asked to ...
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0answers
28 views

Applying the inverse FFT to even out a room's sound - What is the more efficient algorithm?

I have a way (the standard way) to correct for my room's acoustics, but I'm wondering if there's a more efficient algorithm, something that doesn't involve going to the frequency domain maybe? I ...
2
votes
3answers
240 views

Solving for impulse response h[n] given input-output pairs

This is a homework problem that I've worked on and I want to confirm some of my reasoning. I'm given two sets of input-output pairs of a particular system, $S$, that we know is linear time-invariant ...
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1answer
121 views

determine the impulse response of given second order difference equation

$y[n]-3y[n-1]-4y[n-2]=x[n]$ i solved it as follows : 1.first calculated natural-response(ZIR i.e,zero input response) by using characteristic equation it came out as $y_n[n]=[c_1(-1)^{n}+c_2(4)^...
2
votes
2answers
86 views

Is system $h(t) = u(t)-u(t-1)$ LTI or not?

$$y(t) = \int_{0}^{\infty} x(\tau)h(t-\tau) \ \mathrm{d}\tau$$ where $h(t) = u(t)-u(t-1)$. I have some problem with understanding whether system LTI or LTV just looking the impulse response of the ...
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1answer
189 views

Impulse response function from pole-zero graph

I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula: $$ W(s) = \frac{\rm ...
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1answer
153 views

What is the product of Dirac Delta function and $t$? [closed]

$t\cdot \delta (t)$ Does it equal to zero? If so, how can we prove it?
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2answers
128 views

When can the impulse response become zero?

The article Efficient Use Of Sparse Adaptive Filters (Proc. Asilomar Conference, Khong et al., 2006) introduces adaptive filters for the estimation of channels or systems having a sparse impulse ...
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0answers
63 views

IR estimation with cross correlation

I have the input and output of white-noise signal. My overall goal is to estimate the impulse response of a system through cross correlation of my $x$ and $y$. I am doing this through MATLAB for ...
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0answers
32 views

Matched Filter and its Impulse response in signal processing [duplicate]

Why the impulse response of matched filter is a time shifted version of signal?
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0answers
78 views

Room Impulse Response Inverse Problem

This article here talks about a room impulse response generator which takes the source and destination coordinates, sound speed, sampling rate, room dimension and wall reflection coefficients as input ...
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2answers
207 views

Is the system $h(t)=\frac{u(t)}{t+1}$ time-variant or time-invariant?

Following this answer , I tried like this $$h(t)=\frac{u(t)}{t+1}$$ where $u(t)$ is unit step function. I can write the input-output relation like this: \begin{align} y(t)&=\int_{-\infty}^{+\...
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1answer
42 views

Interpretation of system response to unit impulse

I want to understand the meaning of unit impulse response when time flows. An example is given below: In the example the left signal depicts a $\delta[n]$ function value of which is $1$ only at $n=0$....
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1answer
180 views

FIR filter reverse engineering from step response

I am working on a reverse engineering problem - I am trying to reconstruct a filter. I have: The step response of the system. (I could calculate the impulse response by derivating) I know: The ...
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0answers
30 views

Confusion related to Room Impulse Response equation in a research paper

This paper presents a toolbox to simulate Room Impulse Responses (RIRs) based on Image Source Method (ISM). The equation (1) has a windowed sinc function in it, which is given in equation (2). I was ...
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2answers
170 views

Is this system time invariant?

I've been working at this problem for a while now, and can't seem to come to a solid conclusion - is this system time invariant? $y(t) = \int_{-\infty}^{t} e^{-9(t-\tau)} x(\tau)d\tau $ My reasoning ...
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1answer
490 views

How do I calculate the step response of a discrete-time system?

I am given the impulse response $$h[n]=2\left (\frac{1}{2} \right )^n\sigma [n]-\delta [n]$$ where $\sigma$ is the unit step function and $\delta$ is the unit impulse function. I know that $$a[n]=\...