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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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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46 views

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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Deriving impulse response from frequency response?

In Oppenheim's Discrete Time Signal Processing the frequency response is given by $$H_d(e^{j\omega}) = \sum_{n=-\infty}^{\infty} h_d[n]e^{-j\omega n}$$ then the impulse response $h_d[n]$ can ...
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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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56 views

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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42 views

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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92 views

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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25 views

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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32 views

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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Power/Amplitude Response of a system

I am currently looking over filters and understand the frequency response of a system, e.g. a low-pass filter. However I am confused by the 'Power/Amplitude response' of a system as detailed in my ...
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Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)

My apologies for perhaps the stupidity of this question. Presume that one has the 'frequency response' $Y_{data}(k)$ of a system and also has an estimated model $Y_{syn}(k)$ that fits the data. How ...
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1answer
20 views

Phase wrapping in Bode plot

I'm trying to model the transfer function of a linear system (a MOEMS mirror) based on a datasheet plot of its response. I'm developing the model in the python-control model and I think that I've got ...
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43 views

Frequency response given poles and zeros

I'm trying to plot the frequency response $H(z)$ of given zeros/poles using the following code in MATLAB: ...
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34 views

getting frequency response from input and output signal

How does one get the frequency response of a filter, given an input signal and the signal output by the filter?
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18 views

concerning the usable frequency band of signal

The spectrum amplitude of the response of instruments is generally trapezoid-shaped, with a flat portion in the middle and decaying at higher and lower frequencies. By deconvolving with the ...
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27 views

How to validate an estimated model in case of output-only data (in frequency domain)?

Before moving to the actual question, I would like to emphasize on the following points (maybe they are obvious to some of you, but I still would like to list them, since they make the difference): ...
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How to eliminate audio device transfer function from recording?

I'm working on a project which requires analysis of filter transfer function of vocal tract. The vocal tract is excited by a source signal that is a frequency sweep. The source signal is provided ...
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69 views

plotting frequency response to window sinc funtion in matlab

I am taking DSP and the instructor explains theory, but has not shown a single example all semester. One problem on the current homework assignment is to plot the frequency response of a windowed sinc ...
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97 views

How to design a variable slope highpass filter

I want to design some specific slope highpass filter to enhance speech; just like $1$ dB/octave, $2$ dB/octave and more. Is there a method to calculate the coefficients by specific slope?
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41 views

How many non-zeros samples in convolution

If I have $b[n]$ of length 30 (30 non-zero samples) and $c[n]$ of length 40 (40 non-zero samples). How many non-zero samples will $a[n]=b[n] * c[n]$ have? (Note '$*$' is a convolution). I think ...
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Can two different impulse responses give the same frequency response?

I have two different impulse response each with different length, is it possible that they have the same frequency response?
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Obtaining a frequency response from other frequency responses

I have loaded six impulses responses (1024 samples each in length) into Matlab, zero-padded the end of each with 1024 zeroes and taken 2048 point DFTs of each using Matlab’s built in ...
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57 views

Signal response in Frequency Hz from angular frequency

I have a filter whose respose I have in angular frequency. ...
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67 views

Lowpass filter impulse response in frequency domain

A Linear Time-Invariant system with impulse response $h_1[n]$ is an ideal lowpass filter with cutoff frequency $\omega_c =\pi/2$. The frequency response of the system is $H_1\left(e^{j\omega}\right)$. ...
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Linear Time-Invariant system frequency response and impulse response given input and output in time domain

I am having difficulty with this question specifically with the $\sin()$ part. So here goes nothing: Consider a Linear Time-Invariant system with input $x[n]$ and output $y[n]$. When the input to the ...
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97 views

Lagrange Multipliers Optimization - Complex Functions

I want to optimize a sum of complex frequency responses (complex sum is SPL, sound pressure level as a complex function of distance) of a number of loudspeakers, say 10. There is a reference, desired ...
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62 views

Find Natural Frequency $\omega_n$

You are testing a new device to determine its characteristics. You find the magnitude of its frequency response shows a peak at 500 Hz, and the measured overshoot of the step response is 40% of the ...
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108 views

Relationship between the Real and Imaginary parts of a LTI causal system

Prelude I am writing an elaborate text on the relationship between the real and imaginary parts of a LTI causal system and how stability, causality and analyticity imposes various constraints on its ...
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112 views

Phase response of moving average filter — how to interpret?

There are many articles on the frequency response of the moving average filter but they all seem to focus on magnitude. However the phase response is intriguing and I find it hard to interpret. The ...
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80 views

Convolution by IIR filter, a case where circular convolution is allowed?

The question is, how to attain the frequency domain representation of any signal (which is finite, non-unit length) convolved with an IIR filter. The correct answer in my opinion is that there is in ...
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108 views

What does this signal filter do? (coming from finance)

In finance, many "indicators" are used in order to make prediction about if a price has an increasing or decreasing trend over time. Among them, MACD is a popular one. There are many slighlty ...
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Is the book wrong? — How to sketch frequency response obtained from H(z)?

This question is directly related to digital signal processing, so I am asking here. How to sketch frequency response obtained from $H(z)$? I'm adding an example and its solution below. I did not ...
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64 views

Frequency dependent frequency shift

I have the Fourier Transform or FFT of a signal, call it $F(f)$. I would like to apply a "frequency-dependent frequency shift" to it. Specifically, frequency $f$ should be shifted to $3f^2$, for all $...
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90 views

Obtain the frequency response of a time domain chirp signal

I have simulation data in the time domain and I need to represent them in the frequency domain. The data have been obtained time integrating the following equation: $m \ddot{x} + c\dot{x} + kx = A \...
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75 views

Discrete-time Biquad filter: Relation between peak frequency and pole frequency

This question arose from a discussion in the comments to this question and its answer. The author of that question discussed a discrete-time second order filter described by the following difference ...
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1answer
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Butterworth High Pass Filter Amplitude Response

I have learned the Butterworth filter, normally it is used for low pass design. And the amplitude response is: $$|H(jw)|=\frac{1}{\sqrt{1+(\frac{w}{w_{c}})^{2n}}}$$ mentioned in this Butterworth ...
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80 views

How frequency response related to a transfer function

Can anyone explain how frequency response related to a transfer function?
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103 views

From lowpass to bandpass

I have to do two frequency shifts: the first: to transform a lowpass filter into a highpass filter I've implemented it in this way: h_hpf=h_lpf.*exp(j*pi*(0:N)) the second: to transform a ...
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74 views

Frequency response and impulse response of black box

I am trying to find out the transfer function of a real life continuous-time black box. First thought is of course to input a delta and get the impulse response as the books have taught us but I ...
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99 views

Limits of convolution

Say we have a function of time ($S(t)$) of the length $T$, and then a customized impulse response (say $I(t)$) of the length $T+N$. The question is, when $S(t)$ is convolved with $I(t$), what are the ...
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36 views

Effect of sampling frequency on DFT?

I don't get it. I have the following form of the DFT: $$ Y_N(e^{j\omega_n})=\sum_{k=1}^{N-1}y(k)e^{j\omega_n k}\quad\omega_n=\frac{2\pi n}{N}\quad n=0,1,...,N-1 $$ But this assumes that the sampling ...
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64 views

How to stabilize a filter

Suppose we have an unstable all-pole filter with transfer function $H(z) = A(z)^{-1}$. What is the best way to design a stable filter with frequency response as close to that of $H$ as possible. (I ...
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400 views

Matlab: plotting magnitude and phase response

I've got the frequency response $H(e^{j\omega}) = \frac{2 + 3.125e^{-2j\omega}}{1-0.9e^{-j\omega}+0.81e^{-2j\omega}}$, and I'm trying to figure out how to plot the magnitude response and the phase ...
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36 views

Polar form of eigenvalue

I greatly appreciate the opportunity afforded by this forum to submit a query. It has been suggested that for a sinusoidal input, represented as 2 phasors, into a Linear Shift-invariant system, the ...
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1answer
67 views

Convolution reverb using a frequently updated frequency dependant impulse response

I am implementing a software to auralize a virtual scene but am kind of a newbie to DSP. The focus should be the calculation of the IR which is frequency dependant. But this means that the renderer of ...
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what is magnitude responce at ω = π/2M for freqz function [duplicate]

what is magnitude responce at ω = π/2M.Code Given is ...
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Frequency response of a rolling linear regression

I am looking for a way to characterise the frequency response of the slope from a linear regression. We are exploring the effect of window length of the regression to the magnitude of the slope of the ...