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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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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41 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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38 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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27 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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65 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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98 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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60 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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52 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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53 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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28 views

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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58 views

How frequency response related to a transfer function

Can anyone explain how frequency response related to a transfer function?
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80 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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51 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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93 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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28 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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55 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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121 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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34 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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62 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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43 views
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77 views

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 ...
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109 views

Find frequency/phase response of a microphone

I am trying to find the frequency/phase response of two cheap microphones bought off Ebay. Basically, I want to graph the frequency responses and phase responses of both microphones on the same axis ...
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63 views

System response: LTI system for $x[n] = \sin(\frac{\pi n}{4})$

Consider the LTI system with frequency response $$H(e^{j\omega}) = \frac{1-e^{-j2\omega}}{1+\frac{1}{2}e^{-j4 \omega}}, -\pi < \omega < \pi$$ Determine the output $y[n]$ for all $n$ if the input ...
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68 views

Frequency response of a (rectangular) integrator

A very simple question which can't really figure out: I have a simple discrete time rectangular integrator with Z transform H(z) = 1/(1-Z^(-1)) Plotting the frequency response with Matlab using ...
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How to filter signals with non-uniform sampling rate?

I have a digital signal that was made from analog one by staggering sampling rate: $\tau_i = \begin{cases}\tau_{even}& \text{if } i = 2n\\ \tau_{odd} & \text{if } i = 2n+1\end{cases}$ And I ...
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Matlab's invfreqs won't fit at low frequencies

I'm wondering of anyone can explain why invfreqs() is unable to fit a polynomial to the data in the image below. The red line is the measured frequency response of an analog system. I should mention ...
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28 views

Treating the measured frequency response of a system as a DFT

I have frequency response data of an analog system that I would like to turn into a digital filter in Matlab. Is it kosher to think of my frequency samples as constituting a DFT of the system impulse ...
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113 views

BPSK modulation under bandlimited channel

I modulated signal using BPSK modulation and I have series of -1 and 1. Now I have to pass these signal from band limited channel that has frequency response of the form ...
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44 views

Phase plot in Bode Diagrams

I'm studying the transfer function of an aircraft that relates the pitch angle, $\theta$, with the horizontal stabilizer angle, $\delta$. $$ H(s) = \dfrac{\theta (s)}{\delta (s)}$$ I have computed ...
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227 views

Sine sweep vs impulse response

What kind of pros and cons does these method for identifying a system have? I seem to have a hard time finding literature discussion in this issue. I am operating on a linear system, or the linear ...
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61 views

FIR/IIR approximation of known frequency response

I have two different sets of data from compatible signal sources but recorded off two different transmission line characteristics. I am trying to equalize out the transmission line in the two data ...
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46 views

what is the name of this curve

I was drawing a high pass filter response ,in a polar coordinates, the function is (z+1)/z and then it is 2+2*cos(w) the plot is ...
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Finding the output of frequency response

Suppose the input to an FIR system is $x[n]=e^{j(2\pi n/7 -\pi/2)}$ Define a new signal $y[n] = x[n]-x[n-1]$ . The signal $y[n]$ can be expressed in the form $y[n] = Ae^{j( 2 \pi f n + \phi)}$ ...
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74 views

Relationship between values of frequency magnitude and values of time amplitude in an audio signal

I have an audio signal in wave format, with its time amplitude values located between -1 and 1. When I compute its fft (in respect to the whole signal) and then extract its absolute value to plot the ...
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78 views

custom Nearly-Linear-Phase IIR filter computation gone wrong

I'm using the code in this book :Algorithms for the constrained design of digital filters with arbitrary phase and magnitude responses to compute nearly-linear-phase IIR EQs. fvtool() shows the ...
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140 views

Frequency response of FIR (MTI delay line canceller) with non constant period

Short question How to plot the magnitude of frequency response of the delay line canceller with non constant period using GNU Octave? Or more directly: how to plot magnitude of frequency response of ...
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147 views

Plot the frequency response of MTI delay line canceller using Octave

I try to plot the frequency response of the delay line canceller (FIR filter which used for MTI). The delay line canceller has the following structure: ...
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119 views

Calculation frequency response of digital filter with known structure

Short question What are main stages (steps) of calculation frequency response of digital filter by their structure? Detailed question Let suppose that there is discrete FIR filter with known ...
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220 views

Manual Extraction of Filter Phase Response with MATLAB using sweep sine

I'm currently at a loss for why my code seems to not be working. I'm doing a sine sweep on a filter to calculate its freq and phase response. The frequency response checks out, however the phase ...
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167 views

Measuring frequency response range of piezoelectric disc

How can I measure the frequency response range of a piezoelectric disc below. I don't have an oscilloscope but I do know how to program in matlab / octave I was thinking of creating a swept signal ...
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2k views

Difference between “freqz()” and “plot(abs(fft()))” in matlab

I've plotted the response of a High Pass Filter x=[1 -1]; freqz(x) gave me where as the magnitude plot for the fft gave me Why are the two plots different? Both are frequency responses, then ...
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88 views

why wavelet coefficients are zeros after decomposition

I am learning wavelet theory for image processing. To understand the theory, I write one Matlab program to decompose one black-white image. The program is as follows ...
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Find impulse response and frequency response through given filter [duplicate]

I cannot find anything truly helpful in my book, and I find mostly theoretical answers and not practical. So I am posting the exact exercise I want to solve, and through it I hope I'll work some ...
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78 views

Magnitude value of filter frequency response

Can someone help me with this problem: Suppose we filter signals with the below pre-emphasis filter: $$y[n]=x[n]-0.8x[n-1]$$ I have to calculate the impulse response of the filter (ok easy) and ...
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238 views

Formulas to plot Frequency Impulse Response Coefficients

I made this question newbie:Plotting FFT and Impulse Response Coefficients, using Java I have the IRC: Impulse Response Coefficients: $h(k), k = 0, 1,.., N-1$ Low Pass: ...
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169 views

How can we calculate the frequency response of each filter of a Discrete Wavelet Decomposition filter bank?

I am using the Multilevel Wavelet decomposition. The decomposition results in a filter bank such as the following: Specifically, I am using one of the Daubechies wavelets, ...
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Implications of $X( -j\omega ) = X^*(j\omega)$

What are the implications of: If $x(t)$ is real and $x(-t) = x^*(t)$, then $X(-j\omega) = X^*(j\omega)$ and $X(j\omega)$ is real. I am trying to understand it and I would like to research it ...
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For a standard second order transfer function, what is the equivalent time domain significance of $\zeta>0.707$?

In frequency domain $\zeta>0.707$ implies no resonant peak in frequency response. But I am unable to correlate what is the exact time domain effect of this? If $\zeta=0.707$ acts like an ...