Questions tagged [frequency-response]

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system.

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Behavior of tanh IIR filters

If we insert a tanh function (or any other activation function) between the feedback summation and the unit delays, how will such an IIR filter behave for values of $|a| < $1 and $a > ±1$ ? The ...
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Why the bandwidth of the system with the minimum-order observer is higher than the full-order observer?

In Ogata's Modern Control Engineering (5th Ed., page 786) it says: The bandwidth of the system with the minimum-order observer is higher than that of the system with the full-order observer, ...
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Eigenfilters in Matalb [closed]

I have to implement an eigenfilter for an arbitrary frequency response in MATLAB. I have this algorithm: $N$ - order of the filter $M = N/2$ $c(\omega) ...
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FFT and frequency response

There is a system (consisting of several LTI analogue filters) whose input and output signals are being recorded at $20 \ \mathrm{kHz}$ (the sampling period is in the range of 10 times the system's ...
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Frequency response of $\mathrm{sinc}[n]$

In this image the frequency response of a discrete time filter given as $h[n]$. Can someone explain how the magnitude of the frequency response is found ?
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What is the frequency response function for the Bode Plot pictured here?

I've forgotten how to get the frequency response function out of a Bode Plot. The phase component of $H(j\omega) = e^{j\pi/2}$, right? But I am having trouble finding $|H(j\omega)|$. How would I get ...
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What is the frequency response function for an input through a differentiator and mixer?

Through the differentiator, the frequency response will be $j \omega X(j\omega)$, but what about through a mixer with $\sin(\omega_ct)?$ Will it be $$\frac{1}{2j} j\omega\left[X(j(\omega-\omega_c))-...
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identifying overshoots in given state space system with step inputs

Suppose I have the following state space system: $$ \dot{x}(t) = Ax(t) + Bu, \quad y(t) = Lx(t), \quad x(0) = x_0 $$ where $A$, $B$ and $L$ are real matrices, $u$ is a constant real vector (so that ...
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For 2D signals can it be said that the frequency response is the same as the Fourier transform?

Say I have a signal: [1, 1 , 1; 1 100 1; 1 1 1];, I wanted its frequency response, then can I take its FFT? Why does MATLAB have two functions to do the same ...
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Zero-phase vs Linear-phase vs Nonlinear-phase System

I don't understand what is the difference between these. I'm trying to figure out how to classify this system's phase response: Would someone please tell me what it is and how you can tell?
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BIBO stable LTI system frequency response for this input signal?

For an LTI system with bounded input and bounded output, I have the input $$x(t) = 5 + \cos(12t+\pi/4)$$ and output $$y(t) = 6\sin(12t)$$ It is said that the magnitude of the frequency response $|H(...
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Does the frequency response assume the zero input response to be 0?

I'm a bit confused about the frequency response and the state of a system. Is it simply the ratio of the output of the zero state response to the input of the zero state response? Or does it include ...
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Does a filter need to completely attenuate high frequencies to be considered low-pass?

I'm looking at a system with a frequency response that is: $$H(e^{j\omega})=\tfrac{1}{4}(2\cos(\omega)+\cos(2\omega)+2)$$ I think the magnitude of this system looks like this (not sure what is the ...
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Inverse a frequency response

I haven't recorded a precise impulse response, but I have carefully written the attenuation/boost of a recording chain for every third of octave: ...
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Matlab freqz and custom implementation differences

I am making some homemade tools on Matlab. I made function that plot the frequency response of a discrete transfer function (just like freqz does). When I compare ...
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Analogue filter analysis (band-pass)

The transfer-function: $$G(s) = \frac{\beta s}{s^2 + \beta s + \omega_0^2}$$ is to be used in an application that requires the magnitude of the frequency response to be of the band-pass form. ...
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Magnitude and phase of $-\delta[n]$?

I was reading this document and it shows the computation of the magnitude and phase of $h[n]=-\delta[n]$. We can get the DTFT as: $$H(e^{j\omega})= -1$$ So the magnitude will be $1$, and according ...
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Modelling the amplitude and phase through an amplifier

I am writing a software simulator to simulate a real physical acoustic interferometer. I now want to write the module to model the microphone amplifier(s). I'd like to be able to specify the frequency ...
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Fourier transform relationship

I am having trouble understanding the relationship between a frequency function and it's Inverse Fourier transform. The Frequency function is $$\frac{1+0.8(e^{-j 2\pi f}+e^{j 2\pi f})+0.64}{1+1.4\...
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Harmonic oscillation and Fourier

I am back to college after 6 years of professional life and I need help with the following problem [...] The standard form of the function is $S_{E}(t) = e^{j2\pi f_k t}$, whose derivation ...
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How to implement a time-varying filter?

I'm working on a 10-second sound, sampled at 44.1 khz. I want to do filtering, and have a desired EQ (equalization) curve that varies over time, as suggested here (here $f0=250\ Hz$) How to ...
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Design of a digital A-weighting filter with arbitrary sample rate

I want to A-weight a time series with arbitrary sample rate. An analog A-weighting filter is defined exactly by IEC 61672-1. But there's no definition for a digital filter. One method is to use the ...
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Unexpected result after calculating the response of a system in frequency domain

I'm implementing a Python script that calculates the response of a system given an input. The system is $y(t) = x(t-2)$, i.e. it delays the signal by $2$, and the signal is $x(t) = \sin(3t)u(t)$. As ...
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Definition of Ideal Low pass filter (Time Continous)

Actually I got confused about definition of frequency response of Ideal low-pass filters because in some books they mention that phase of H(f) should be linear in pass band and it's value is $ -2\pi ...
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Finding frequency respone of a differential/integral LTI system

So suppose that we have an LTI system defined by the differential/integral equation below, where $x(t)$ and $y(t)$ denote the system input and output, respectively. How would I find the frequency ...
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Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
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What is the Autocorrelation of the Impulse Response if the Magnitude of Frequency Response is >1

So by the DTFT pairs, if the magnitude of the frequency response of a signal is 1, then the autocorrelation is the Kroneker Delta Function. What if I find that the magnitude of the frequency response ...
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Frequency Response with Delta Function?

I am trying to find frequency response and magnitude of the frequency response of the following system impulse response: $$h[n] = 2\delta [n] + 2\delta [n-1]$$ I understand, that through the DTFT: $$...
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Equalizing frequency response in software

I'm playing audio through a speaker which I know to have a non-flat frequency response, with particularly poor response in the low ($<1\textrm{ kHz}$) ranges. My plan to get around this problem is ...
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841 views

How do I identify a notch filter given the transfer function?

I am studying for an exam, and a problem that my professor gave produces a transfer function that looks like the following: $$H(z)=\frac{z^2-j}{z^2-\frac{1}{4}j} = \frac{\left(z-e^{j\frac{\pi}{4}}\...
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Equalize Speaker using Frequency Response Curve

I have a speaker for which I know the frequency response curve (-5dB at 600Hz, -3dB at 700Hz, ... +5dB at 10kHz). This response curve is not as flat as I would like, and so I want to write a script ...
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Difference between transfer function and frequency response? [duplicate]

AFAIK both represent the ratio of the output response $Y(j\omega)$ to the input excitation $X(j\omega)$: $$H(j\omega)=\frac{Y(j\omega)}{X(j\omega)}$$ Are there any difference?
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calculating DC value from positive frequency with its DC undefined

Is there a way of calculating DC value from just the positive frequency that has its DC undefined ? Simply if we remove the DC and the negative frequency components of the signal is there a way to ...
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Continuous and discrete-time raised cosine filter properties in frequency domain

In communication systems, the raised cosine (RC) filter is split into root-raised cosine (RRC) filter at the transmitter and the receiver. The combined response of both RRC filters is the RC filter. ...
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Generate impulse from random frequency response [closed]

This code supposed to generate random frequency response which could be used as impulse...But it fails to pack correctly when going from fft domain to real signal time domain, the other half is left ...
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Why must I take abs of filter frequency response?

I was playing with filters in SciPy and noticed something that I'm not that familiar with: I'm using the code: ...
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316 views

How to measure the frequency response of an acoustic filter by input and output signals

I am trying to measure the frequency response of acoustic filter. I sample the sound before propagation in the filter and after by 2 different mics. And now I am trying to find the system (the ...
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2answers
494 views

Windowing before viewing a filter frequency response?

It is well known that it is a good idea to apply windowing to a signal, before obtaining its DFT and viewing its frequency response. But is it a good idea to apply windowing to the impulse response ...
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Butterworth filter approximation: derivation and output poles

I am having trouble understanding the exact derivation of the butterworth filter and how it results in the output of the poles. I have researched multiple lecture series and textbooks and this is my ...
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How do you convert angular frequency to $\textrm{Hz}$ from MATLAB's $\tt freqz$ function?

Let's say I have used MATLAB's butter function to generate a 3rd order, low-pass, Buttersworth, digital filter. I have a sample rate of $2000\textrm{ samples/second}$, and I want the cutoff frequency ...
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How does constant frequency response relate to equiripple?

The teacher says As a consquence, you can think of the frequency response of a filter as a shark. It must always move and it can never be rest. An important case is equiripple. I am very confused ...
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Calculating phase response of filter with latency

I have an LTI filter that I want to treat like a black box. It has a latency of 24 samples. This is what I'm doing (which works for a filter with no latency): Send unit impulse through my filter ...
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Non-causal FIR. Is that possible?

I know that a FIR (Finite Impulse Response) filter has the same quantity of poles than zeros. And I believe all the poles are at $z=0$. And a FIR filter is always stable, so it's ROC has to include ...
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Generalized linear-phase filter

I know I can write the frequency response of a Generalized linear-phase system as: $$H(e^{j\omega}) = A(\omega) e^{-j\left(\alpha \omega - \beta\right)}$$ where $A(\omega)$ is real. I need to prove ...
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DTFT and Inverse DTFT Homework Problem

I'm trying to solve this signals homework problem: So for part a, since multiplication in the time domain is convolution in the frequency domain, I just used a DTFT table, found the DTFT for $\left(\...
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The frequency response function (FRF) fails to detect the antiresonance of a system

I am trying to identify a vibrational systems by computing the frequency response function (FRF) of the system when a chirp signal is applied to its input. After comparing the FRF computed and the ...
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System identification/ Filter estimation to mimic frequency equalizer of audio with Scipy

At the current problem I'm working on, I have two signals: One "original" signal that contains audio (voice). The second signal is the same audio file but edited with a frequency equalizer, for ...
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Compensating Loudspeaker frequency response in an audio signal

I have been working on a project in which I was required to work on the audio signals recorded from the loudspeaker kept in front of a filter. So, to simply explain it: $$\boxed{\rm LoudSpeaker} \...
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How to filter a signal knowing the frequency response of a system in MATLAB?

I have a signal of period $T_0=8$, let's say $x(t)$, and it has the following Fourier coefficients: $$ a_k=\frac{1}{4} \mathrm{sinc}^2\left(\frac{3k}{8}\right) e^{ik\frac{\pi}{2}} $$ for $1\le|k|\le6 ...
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Classifying Discrete time filter

So let's say i have this frequency response of a digital filter: My question is how can i classify this type of filter ( low pass, high pass,...)?

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