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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LTI system output given input and frequency response

The question I'm trying to understand is as follows: A linear time-invariant continuous-time system has the frequency response function $$H(\omega)=\frac{1}{j\omega+1} $$ Compute the output response $...
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83 views

Find the error in phase angle and dB gain Function Transfer

This is a question paper that I've tried to solved but seems I am missing something. My attempt: $$ |G|_{w=0} = K$$ So, $\require{cancel}|G|_{w=0.5a} = \dfrac{K}{\left|1+\dfrac{j0.5\cdot \cancel{a}...
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91 views

Modal analysis and frequency response function - interpretation needed

For couple of weeks now, I have been trying to measure cutting forces during machining processes. The system which I am currently examining is highly distorted at high frequencies due to its ...
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467 views

get poles and zeros of frequency response

I am working on a python based LTSPICE project. I would like to get poles and zeros of AC simulation data. Is there a way to get them under use of the magnitude and phase out of the frequency ...
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114 views

Magnitude and phase response and cut-off frequency of a moving average filter

The frequency response of a typical moving average filter of length $N$ is given by $H(\omega)=\frac{1}{N}\frac{\sin(\omega N/2) e^{-j \omega ((N-1)/2)}}{\sin(\omega/2)}$. Firstly, isn't the cut off ...
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56 views

Compensate for microphone?

I have trained a machine learning model to recognize a specific audio event from mel spectrograms, and it works pretty well on a hold-out test dataset. I now want to run the model on a device and feed ...
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130 views

Fourier Spectra : Significance of the Negative Amplitude [duplicate]

For example, for an aperiodic gate pulse, the Fourier Transforms for the continuous time case is a sinc function, while the discrete time case gives a sine over sine periodic kind of a function. In ...
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81 views

I need to insert an underwater acoustic channel model to an existing code that compared between OFDM and GFDM

The acoustic channel model that I have will output the channel impulse response. However, my signal is modulated in frequency domain (by doing fft). Hence, I want to obtain a frequency response of the ...
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158 views

Difference between the two forms of input-output relationships of an LTI system

$$y(t)=f(t)*h(t)\tag{1}$$ $$y(t)=H(s)e^{st}\tag{2}$$ $$H(s)=\int_{-\infty}^{\infty}h(t)e^{-st}dt\tag{3}$$ Let $f(t)$ in Eqn $(1)$ be $e^{st}$. In many worked out examples, I have found that the two ...
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Frequency response of a microphone using a sine sweep

I want to determine the frequency response (magnitude, phase) of a microphone. I have another "good" reference microphone whose frequency response I know. I understand that I can use a good speaker ...
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Characterization of transfer functions with no local peaks

Assume that you are giving an arbitrary amplitude frequency response $A(\omega)=|H(j\omega)|$ Is there a characterization that ensures that $A$ is monotone? i.e, $A$ has a global maximum at $\omega=0$...
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Is a LTI filter completely characterized by its frequency response

I know that we use the frequency response to determine the properties gain and phase delay of a filter. However, I was wondering if this is enough for a complet characterization of the the filter for ...
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141 views

Understanding the magnitude of frequency response filterbank based on elliptic filters

I've implemented a 10-channels filterbank with octave-scaled second-order elliptic filters using the Python's library scipy.signal. Here is the magnitude of the frequency response: Can someone ...
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Phase response of $H(f)=e^{-j2{\pi}ft_0}$

Given is the impulse response: $$h(t)=\delta(t-t_0)$$. I calculated $$H(f)=e^{-j2 \pi ft_0}=|H(f)|\cdot e^{j\varphi(f)}$$. Now, the magnitude response of $H(f)$ is: $$\begin{align} |H(f)| &=\...
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942 views

Frequency Axis of Discrete Fourier Transform (DFT) with Odd Number of Data Points

I am trying to understand the logic behind making a frequency axis in DFT. I am using for time based light absorbance. When we have even number of data points (N= even integer), collected over a ...
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Plotting the frequency response of a FIR filter

I am trying to figure out the mechanics of plotting the frequency response of a FIR filter. For example, I have used an algorithm (Parks-McClellan), to generate a low pass FIR filter with an even ...
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How to design a a filter and how to determine the poles and zeros on the basis of following informations?

A sinusoidal signal of 300Hz frequency,3V amplitude is contaminated with line frequency (50Hz,1V). Design a digital filter including poles and zeros to remove the interference component. Consider the ...
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Mathematical operations with given discrete frequency response function

Let's say I have a given discrete frequency response function H(w) and corresponding n frequencies as MATLAB arrays, ranging from 0 to 512 Hz. If I do an n-point FFT on a discrete time domain signal ...
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713 views

Output of an LTI system given its transfer function and input

Given the transfer function $$T(s) = \frac{100}{1 + \frac{s}{10^{6}}}$$ and the input $$v_i(t) = 0.1 \sin(100t)$$ find the output, $v_o(t)$. My approach was to use $v_o(t) = \mathcal{L^{-1}}\left\{T(...
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1answer
870 views

How do bode plots work with unstable systems work?

If I had a system with right-half s-plane poles, how would a frequency response work? Since a purely imaginary value for s, would cause the Laplace transform to diverge for such a system, what meaning ...
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374 views

Relationship between Frequency response, magnitude spectrum and gain

I have been reading quite a lot of DSP related materials online and offline (books etc.) lately. I come across the terms frequency response and ...
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287 views

Term for integral multiples of fundamental period?

As we know that a signal has fundamental frequency and integral multiples of fundamental frequency are known as harmonics I am curious about the term that will be used for integral multiples of ...
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Nyquist Plot for transfer functions with poles at the origin

I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states "If f(...
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MATLAB - How do I get the Filter Function to get the output Energy Spectrum?

The image was from a question I posted on reddit, so ignore the title. I'm trying to write a program that plots these graphs I know that the first plot is just a plot of the source-signal so the "...
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58 views

Discrete Time Fourier Analysis

Suppose we're given the following: $ x[n] = 2 + (-1)^n $, and are given the impulse response $ h[n] = u[n] a^n $, of an LTI system where $ |a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...
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Plotting the Phase Response

I would appreciate it very much if someone would be able to provide some clarity on plotting phase responses. For instance, given that the frequency response of a filter can be written as $$H(\exp(j*...
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559 views

Fourier Transforms, symmetry, real/imaginary

I was hoping to clarify if the following was correct: A real function (neither even nor odd) in time exhibits conjugate symmetry in frequency, so the real part of the frequency response is even, and ...
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1answer
493 views

Phase contribution of complex poles

I am struggling with understanding the phase contribution of each individual pole. Let's say we have a system (minimum-phase system if it makes a difference) and it has poles located at: and What is ...
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445 views

How to detect the maximum resolvable spatial frequency of camera?

I am trying to calculate the minimum line pixel width that can be distinguished from noise as shown in the camera test chart in Figure 1 where the thinner lines on the left are getting more and more ...
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324 views

Digital filter design of time series for specified frequency response function

I am currently working with vibration measurements in structures. In the netherlands there is a guideline for verifying vibration measurements for damage to machinery. This is the so-called "SBR ...
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266 views

finding phase and group delay from frequency response

(From Schaum's Outlines, DSP, second edition, problem 5.25, second part of problem) What's the procedure to find the Phase and Group Delay of: $$ H(e^{j\omega}) = e^{-j\theta}\left( \frac{e^{-j(\...
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336 views

Numerical Calculation of impulse response out of frequency response

Currently I work on my Masterthesis which deals with structural dynamic simulation. As a part of it I have to filter a Signal with a FIR-Filter. From that Filter I know the Frequency Response (picture)...
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166 views

Sensor rise time compared to experimental step input rise time

I have a dynamic calibration system. With it, I am applying a experimental step input to a pressure sensor. The goal is to measure the step response of the sensor and use it to calculate the frequency ...
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Is it wrong to first calculate the whole system's Frequency response and then apply input to it?

Having a system like below, which (i think) is LTI, and $H(e^{j\omega}) = \begin{cases} 1 & |\omega|\leq \frac{\pi}{2} \\ 0 & |\omega| \gt \frac{\pi}{2} \end{cases} $ I've ...
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Get the discrete-time poles and zeros from continuous-time poles and zeros

How do you implement the following function: $$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$ where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
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What exactly is Savitzky-Golay differentiation filter?

I could understand Savitzky-Golay filter as being smoothing filter, but then there also seems to be Savitzky-Golay differentiation filter, though for some reason, details do not seem to be clear. So ...
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Frequency response of numerical differentiation by polynomial interpolation / finite difference

One can use polynomial interpolation (or finite difference) to do numerical differentiation. However, there seems to be a surprising lack of interest in obtaining frequency response of this numerical ...
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system identification: MATLAB tfestimate gives different results for different Fs

So I have an experimental data; A is a chirp signal (sweep sine wave) and B is the response of the system. I identify the system as follows in MATLAB: ...
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208 views

Computation of parameter filter to match a given frequency response

I'm looking for the practical way to compute the parameters ($a_1$, $a_2$) of a digital filter to match a certain frequency response. I'm studying the 12-poles filter of the vintage component SP0256 ...
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194 views

what happens If I change the phase and magnitude of a signal

I have a speech signal. I want to know what happens when I make some changes on the phase of its frequency reaponse. When I set its phase to zero I observed that the new signal is even and the ...
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542 views

How to prove these two definitions of the minimum phase transfer function are same?

There are so many definitions of the minimum phase transfer function, and these are two of them. The transfer function of the system which has no zeros or poles at right half plane. The transfer ...
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603 views

Find the impulse response from the frequency response

So I'm having a problem here which gives me the frequency response and asks for the impulse response: $H(\Omega ) = e^{-j\frac{\pi }{2}}$ for $\Omega>0 $ and $H(\Omega ) = e^{j\frac{\pi }{2}}$ for ...
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141 views

Given a plot of both the magnitude $|H(\omega)|$ and its angle, How can you find the $H(\omega)$?

I'm specifically trying to use an inverse Fourier Transform to find $h(t)$, but I'm finding it difficult to get $H(\omega)$ in the first place. I'm under the impression from my textbook that $H(\...
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492 views

Why the frequency response plots (of causal filters) only show positive frequency?

Take an example of the below plot for an LPF (Source : WikiPedia) The plot starts from $0$. We know that the fourier transform of any signal brings in negative frequencies due to complex exponentials ...
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Advantage of using DFT and IDFT hardware for modulation

I am doing a course in communications and while discussing multicaruer modulation to break down a signal into smaller bandwidths (for BW to be less than coherence bandwidth), there was mention of ...
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302 views

Is it right to talk about dynamic range on frequency domain?

I'm comparing three frequency response's plots from simulations and experiments and I observed that two of them look like clamped to a DC component, where the max dB value is i.e. 100 and the min is ...
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284 views

What does the amplitude in a frequency response of a signal signify?

Well according to my understanding it tells the concentration of signals at a particular frequency but what does the number really mean? Suppose in a frequency response graph i have such a relation :: ...
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106 views

3-tap FIR filter: simple expression for $H(e^{j\omega})$ using trigonometric identities

We have a linear time-invariant system described by the input-output relation $$y[n] = x[n] + 2x[n - 1] + x[n - 2]$$ Below is my approach to analyze this system. The impulse response of this system ...
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332 views

Z Transform - Do i always need 2 poles for every “peak”?

I am quite new to digital signal processing (and also Z transforms). I am reading about frequency response modelling and have some questions do we always need a pair of poles for each "peak" in the ...
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Phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$

I want to find the phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$ for the interval $0\leq \omega \leq \pi$. Method 1: $H(e^{j\omega})=1-\left(...

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