Signal Processing

Questions tagged [impulse-response]

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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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RT 60 from Impulse response

I have already the impulse response of an acoustic environment in the form of a series of signals over 300 samples. I have tried the procedure given in this platform - i.e. low pass filtering, Hilbert ...
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Derivation of Strehl ratio

I am in trouble proving the following fact: The Strehl ratio is the ratio of the volume of the aberrated OTF (optical transfer function) and the ideal OTF, i.e. \begin{align} \mathcal{S}=\frac{\int\...
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Unexpected results of deconvolution with scipy.deconvolve

Below I have plotted the signal (Lifetime decay) I am trying to deconvolve from a known impulse response function (IRF), as well as the IRF itself. I'm using scipy.signal.deconvolve. Please note for ...
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54 views

Is it ok to resample impulse response?

I have some room impulse response at 48kHz sampling rate. I have recording at 16kHz sampling rate. I want to apply impulse response on the recording. What I do now is downsample impulse response 48kHz ...
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Finding the system impulse response for 2D system

Im taking a class on medical imaging, but my previous signal processing course did not really cover 2D systems in the greatest of detail. Therefore, I wanted to ask a quick question on determining the ...
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Real time estimation of room impulse response using the sine sweep method

I am working on real time Room Impulse Response estimation using sine sweep. $x(n)$ is my sine sweep signal. $f(n)$ is its amplitude modulated inverse. $beep$ consists of 3 sine sweeps with a delay ...
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How can we find Room Impulse Response in real-time using Sine Sweep Method?

I want to calculate the room impulse response in real-time using sine sweep method. For that, I generated a sine sweep $x$ & its amplitude modulated inverse signal $f$. Then I played that $x$ ...
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78 views

How to use deconvolution technique to find out impulse response?

I have been working to find out room for impulse response. I am using Logarithmic sweep sine wave as input say $x(n)$ and my recorded signal is $y(n)$. I know the room impulse response is ...
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Question on system response (plots) for different values of proportional gain

Given are the Plots of the response of the system for different values of the proportional gain K_p How can I determine which plot corresponds to which values of K_p? i.e. How do I analyze which plot ...
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58 views

Impulse response $h[n]$ of a non linear I/O equation

my question concerns an assignment that was given to us at school. We have been given a list of I/O equations and it is required, for each of them, to find the impulse response $h[n]$ and the ratio ...
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65 views

FFT on impulse response: phase doesn't look right, Python

I want to analyze an arbitrary impulse response. Basically, a list of tap coefficient. In general, "tap1" will give me a BW limitation. I want to add more taps and see what it does to the ...
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32 views

Time delay of direct path in RIR measurement

I am trying to measure an RIR using my laptop and a JBL Flip 5 speaker. I have tried, both, the Matlab tool and a python code shared on gihub. My final goal is to compare with the image method and ...
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49 views

Question about impulse response of an ideal lowpass filter

Consider an ideal lowpass filter with a cutoff frequency of $\omega_c$. Following shows its impulse response: $$h[n] = \frac{1}{\pi n}\sin(\omega_cn)$$ Also, some references shows $h[n]$ as: $$h[n] = \...
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57 views

Definition of frequency response

I studied various signal processing materials for a long time, and I have a question. Considering an LTI filter, one can define its frequency response by evaluating its transfer function $H(z)$ on the ...
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103 views

Audio signal arrival timing, impulse response, and reverberation

I'm building an application that requires determining the arrival time of an audio signal with a very high degree of accuracy (within 1ms would be ideal) using commodity smartphone hardware. I found ...
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26 views

DTFT of $(-1)^{n}\frac{\sin((7\pi / 8 )n )}{\pi n}$

The DTFT without $(-1)^{n}$ is relatively easy but with $(-1)^{n}$ I am not sure how it would be solved. I hope anyone can help
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A system having impulse response $ h(t)=u(t) $ stable or not?

I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess) I proceeded as$$ \int_{-\...
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32 views

Pulse shaping with root-raised cosine filter for a non-Gaussian channel

I am here to check whether my line of thinking is correct. Root-raised cosine (RRC) filtering is one way to minimize intersymbol interference (ISI). Hence, we apply matched RRC filters on both sides ...
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129 views

Calculation of inverse impulse response in the frequency domain

I want to calculate the inverse impulse response of a LTI system in the frequency domain. I generate a simple impulse response $g$. For this I generate a vector of 100 zeros. I set the value of the ...
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91 views

Why is particular solution zero for an impulse excitation signal?

We were being taught the impulse response for a series RC Circuit- consisting of simply one resistance, one capacitor, and an impulse excitation all in series. I get that the homogeneous part of the ...
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Numerically finding impulse response from a wave equation

I'm developing a song synthesizer (like Yamaha's Vocaloid). I decided to mimic the acoustics of human speech. I modeled the space between articulators as a solid of revolution, and came up with the ...
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43 views

RMS level from impulse response

I am trying to quantify the average differences between several impulse responses over the frequency range and over octave bands. So, I am doing (in Matlab): ...
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154 views

Impulse response for an LTI system

I'm new to signal processing and working my way through a textbook. There is an exercise where a causal LTI system is given that responds to a rectangular pulse. I have an exercise where a causal LTI ...
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72 views

Output of a stable LTI system (discrete)

Consider an LTI (linear and time invariant) system that is BIBO (bounded input bounded output) stable and is such that $x[n] = 0$ for all $n < 0$ (note: this is sometimes referred to as a relaxed ...
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58 views

The plot of instantaneous power of the Dirac function

I am very confused. I have tried researching this question for the last two weeks and I cannot get a conclusive answer. I was wondering how would I go about plotting the instantaneous power in the ...
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Optimal control to maximize the ratio between two systems

I have two (or more) systems with analytic (but somewhat big and unwieldy) step responses $H_1(t)$ and $H_2(t)$ both of the same form (eq. A6a onwards in https://doi.org/10.1016/S0302-4598(97)00093-7),...
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86 views

Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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632 views

This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?

My DSP professor uses the freqz() function to find and plot the frequency response and I think it's wrong but I want to make sure before I point it out. Take this ...
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An Impulse in Complex Envelope (i.e. baseband) Notation?

In complex envelope notation, a modulated RF signal, say v(t), is represented in complex envelope notation as v(t) = Re{ g(t)e^(jwct)}, where wc is the carrier angular freq, g(t) = x(t) + jy(t), and g(...
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44 views

Calculate impulse response when output contributes in input

I have an exercise in which I need to find the impulse response for this given system: $$y(n)=\frac{1}{2}y(n−1)+x(n−1)+x(n)$$ As per my knowledge, I need to find the homogenous solution. My homogenous ...
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54 views

Output of a linear time-invariant(LTI) system

I am very confused about one of the questions I received during an exam. How do I solve this question?
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63 views

Finding the impulse response given response to another signal

I was trying to solve this question : I respresented $x(t) = u(t+1)-u(t-1)$ writing the convolution as $[u(t+1)-u(t-1)]*h(t) = y(t)$ I then used the property of differentiation to convert from the ...
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61 views

Impulse Response of real coefficient, LTI System

I'm trying to obtain the impulse response $h[n]$ of a system whose frequency response is $H(e^{j\omega})=R(\omega)e^{-25j\omega}$. I believed that $h[n]=h[n-25]$, would be the correct answer, however ...
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4answers
155 views

What is the correct gain of an RRC Filter?

Breaking my brain all morning with this reading previous questions and googling ... I have made an RRC filter from the equation on wikipedia. It works fine and I compared it to commpy library in ...
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68 views

Setting up RRC filter and useful equations

I have looked at previous answers but cant seem to get everything I need in one place to help me and my textbook doesnt explain this in practical terms. Signal Parameters: $F_s = 44100$ $R_s = 300$ $...
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54 views

Impulse Response for an Anti Causal Linear Shift Invariant System

I have a system given by $$y[n] - \frac{1}{4} y[n-1] - \frac{1}{8} y[n-2] =3x[n] $$ I'm asked to determine the impulse response of both an anti-causal and a causal Linear Shift Invariant System ...
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78 views

What is impulse response in simple AWGN channel?

Assume a sender and receiver communicate through an AWGN channel. Let $x(t)$ be a transmitted signal and $y(t)$ be a received signal and $z(t)$ be the Gaussian noise. It is known that $y(t) = kx(t-\...
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83 views

Is Step the same as an Impulse + 1/s?

Isnt a Step (as a Transfer function -> $ \frac{1}{s} $) and Impulse (trans fcn -> 1) therefore Impulse + $ \frac{1}{s} $ should be equal to a Step in Simulink ...
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70 views

What is the decay rate (time constant) of two One-Pole LPF's cascaded in series?

If you have a One-Pole LPF, and set the cutoff frequency to $\frac{1}{2πt}$ where $t$ is the time to $\frac{1}{e}$ amplitude, it will provide an exponential decay in response to a step function (eg. ...
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42 views

Is there an equation that will graph the shape or predict the maximum amplitude of a single sample impulse fed through a One-Pole LPF?

If you feed a single sample impulse of a given amplitude through a One-Pole LPF you get an envelope that looks like this: The output of the LPF from its peak will settle into an exponential decay ...
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226 views

DC gain from an impulse response

I am studying for my exam in signal processing. For one of the old exam sets, a discrete impulse response of a filter is given as $h[n]$ \begin{bmatrix} -3&0&-3&0 \end{bmatrix} With a ...
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125 views

Impulse response $h[n]$ from input and output signal using cross correlation on Matlab

I have two signals on Matlab, one being input and the other output. I want to know if taking the cross correlation of these signals would give me the impulse response?And if so, will taking the ...
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Deconvolution with noisy measurement of impulse response function

I observe a noisy 1D signal that has passed through some linear time-invariant filter: $$z(t) = (h\star x)(t) + n(t)$$ where $h(t)$ is the filter, and I am hoping to recover $x(t)$. $n(t)$ is some ...
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94 views

Digital Signal Processing Filters Problem

Hello I need some help with this question. $$𝑦[𝑛] = 𝑎_1𝑥[𝑛 − 𝑘_1] + 𝑎_2𝑥[𝑛− 𝑘_2] + 𝑏_1 𝑦[𝑛− 𝑘_3]$$ Set $a_1, a_2$, and $b_1$ to any positive or negative real numbers of your choice. Set $...
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Extrapolation of band-limited frequency data

I'm now studying "How to do accurate transform from band-limited frequency data specifically S-parameter data of high speed interconnect to the causal impulse response in time domain. There are ...
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178 views

Finding impulse response $h(t)$ by impulse matching; problem understanding Example 2.3 in "Linear systems and signals", Lathi 3rd edition

Before the example it has been stated that in a system described by $$ Q(D)y(t) = P(D)x(t), \quad (1.) \iff \\ (D^N + a_1D^{N-1} + ... + a_{N-1}D + a_N)y(t) = (b_{N-M}D^M + b_{N-M+1}D^{M-1} + ...+b_{N-...
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167 views

Stability of a system in time-domain

Consider a system for which the input $x(t)$ and output $y(t)$ are related by the differential equation $$\frac{d^2y(t)}{dt^2} + \frac{3}{2}\frac{dy(t)}{dt} - y(t) = x(t) \tag{1}$$Determine $h(t)$ for ...
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The impulse response of a LTI discrete system is $h[n]=\big(\frac{1}{3}\big)^n u[n]$. Find the response of this system to the input $x[n]= e^{jnπ/4}$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $1.2503 e^{jnπ/4 -0.2991}$, and is found by computing $H(Ω)$ and evaluating this at $Ω=π/4$. when I try ...
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141 views

Single-sided Z transform with difference equations and the system function

I am working on this problem: Given an impulse response, find the system function, find the difference equation representation, find pole-zero plot, find output $y[n]$ if the input is $x[n] = 0.25^n *...
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38 views

Impulse invariance vs. DT representation of a CT system: Where is the inconsistency?

Suppose you have a continuous-time (CT) system $h_c(t)$, bandlimited to $B$. Your goal is to represent the system as a discrete-time (DT) system $h[n]$, sampled at $f_s \leq 2 B$. Clearly $h[n]$ won't ...

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