Questions tagged [impulse-response]

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

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Which one is a better impluse response by comparing two given filter length?

I was asked which impulse response $h_1(t)$ or $h_2(t)$ has a better decoding performance for two filter lengths: $l_1 = 50$ and $l_2 = 500$. $$h_1(n) = \cfrac{1}{\sqrt{l_1}}\cos{(0.2\pi n f/f_s)}$$ $$...
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Difference in impulse response output

I followed the two methodology for generating impulse response Method 1: Used the below link reference where I simply convolve the recorded signal by the time reversed sweep signal to get the impulse ...
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Use multichannel noise spatially diffused for multichannel diarization

I'm trying to implement speaker diarization (who speaks when) for mono recording audio (1 channel), but now I'm starting to work with multichannel audio (stereo - 2 channels), so I need for data ...
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Excessive low frequency component of electroaccoustic system impulse response

I'm using GNU Octave to achive speaker to my laptop microphone path impulse response. For this I use NLMS system identification algorithm. I've analyzed impulse response of system with fft to being ...
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Probability of the rate of change of a filtered random process

I am given the following problem: I have a filter with impulse response $h(t) = e^{-10t}, t \leq 0$, and autocorrelation function of the input signal, which is WDS and Gaussian with median equal to 0, ...
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2 answers
192 views

Constructing an input signal whose response is determined by the impulse response

I'm self-studying Signals and Systems by Alan Oppenheim, and I have some trouble understanding the solution to a homework problem. P5.13 tries to find the sufficient and necessary condition on the ...
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Convolution: graphing output y(t) with given input x(t) and impulse response h(t)

I have the following question in my mock exam. My graphing looks as following: Could someone please correct?
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Analog LTI system impulse response

I have the following question in my mock exam! My Answer: I can apply the dirac delta to know the impulse response. Or use the transfer function $H(z) = \frac{Y(z)}{X(z)}$. I am not sure about the ...
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1 answer
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Impulse response out of a modal model, how is it gotten?

I'm reading about modal models and related modelling. For example, I'm reading this paper: Modal Synthesis for Vibrating Objects Kees van den Doel and Dinesh K. Pai I am confused about the theory ...
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How to use deconvolution code with an impulse response to achieve the original signal

I am trying to write a code for my thesis to deconvolve a recording with an impulse response so that I can achieve the original audio signal. I have written a simple code so that I can implement this ...
2 votes
1 answer
226 views

Impulse response of IIR low-pass filter

(Disclaimer. I have started doing some DSP. The last time I worked with this was in the eigthies. And I wasn't much of a specialist then, either.) Is the impulse response different for IIR and FIR ...
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How to calculate impulse response from frequency response whose denominator has an imaginary roots

It is quite easy to solve when the denominator of the frequency response has no imaginary values..... But I do I solve something like this? $$H(\omega)=\frac{1+2e^{-2j\omega}}{1-\frac{1}{15}e^{-j\...
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Finding the impulse response of $y[n]=\tfrac12y[n-1]-\tfrac15y[n-2]+x[n]$

I'm new to signals processing and up until now we'd assume that $x[n]$ is the input and $y[n]$ is the output, and when I wanted to get the impulse response I'd simply replace $x[n]$ with sigma and $y[...
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Simulated Room Transfer Function

I need help obtaining a simulated transfer function in a simulated room. I have created image sources for first and second order reflections, and am assuming a point source for my source. I have the ...
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1 answer
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Channel impulse response vs sampling frequency

As part of my uni assignment I have to figure out what is the impact of sampling frequency on actual channel impulse response. One obvious thing is that the higher sampling frequency is, the more taps ...
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How long should be the Room Impulse Response

I am writing a code to calculate the reverberation time of a room. I am new to the topic. I used sine sweep to excite the room and the response was recorded. Then I got the room impulse response by ...
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Meaning of arrow head in dirac delta?

Images of graphs of dirac delta show an arrow head pointing upwards at t=0, what does that means? Is it referring that at t=0, amplitude is infinity?
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IDFT of voltage frequency response of input resistance of antenna / transmission line is non causal?

Always seem to get this effect when I specifically do the real part of an input impedance over divided by the input impedance in the frequency domain: I have a lossless transmission line with no ...
3 votes
2 answers
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Proving Fourier transform of cosine multiplied with another function

Cheers, I have a impulse response that looks like this: $h(t) = h_1(t) \cdot \cos(8 \pi t)$ and I have to find its frequency response. In order to achieve this I am trying to use the fact that $$x(t)y(...
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1 answer
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Finding if a system is stable

I am doing an exercise where I'm supposed to decide if a system is stable or not. The output is given by $y[n] = x[n- 1 ] + u [n + 2 ]$, with $u[n]$ the Heaviside step function. I know that a system ...
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3 votes
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Prove that exponential sweep sine decay 6 dB per octave

Exponential sweep sine (ESS) is a good excitation signal to measure the impulse response of an acoustic system, such as loudspeaker - room - microphone system. An ESS has the form of $$ x(t) = \sin\...
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Guessing filters from responses to step signals

This is a cross-post from CrossValidated SE where I did get no definite answer. Consider a signal $X$ filtered by a kernel $p$ with finite support $[t_0,t_1]$ and $\int_{t_0}^{t_1}p(t)\,\text{d}t = 1$...
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Measuring the frequency and impulse response of an audio recorder

I would like to test the frequency and transient/step response of the Zoom H5 recorder preamps. If possible, I'd also like to test the preamps for the built-in (exchangeable) XY capsule module, but I'...
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Calculating numerator and denominator polynomials of a transfer function

I was reading this passage in a Doctoral Thesis about Adaptive cancellation. Using MATLAB, if i were to write a simple code, it would look something like this. ...
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Complex Filter (Modelling a Channel ) convolved with complex baseband modulation gives error *Plots inside -Updated*

I have a complex filter that is modelling the channel response, its not symmetrical on 0. The complex filter is convolved with a complex baseband modulation of QPSK. Plot 1 Zoom in on impulse response ...
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How to get the difference equation from impulse response?

I'm trying to solve a problem about filter design. We want to design a equalizer filter which have the following frequency response : How can i get the difference equation from the impulse responce ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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2 votes
1 answer
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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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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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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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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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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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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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