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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If the frequency response of a system is time-independent, is this system LTI?

Intuitively, I feel like a time-variant system would necessarily have a time-dependent frequency response, and vice-versa. So, is the time-independence of the frequency response necessary and ...
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How to normalize frequency response charts

I want write a simplistic program that can transform a high-quality voice recording in a way that it sounds like it was recorded using a specific low-quality microphone. I have obtained the mic's FR ...
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Output of system given input and frequency response

Given the signal: $$x(t) = −4\cos(2\pi 4t) + 3\cos \left(\pi t − \frac{\pi}{3}\right)$$ By sampling theorem $Fs = 2 Maxf = 8 Hz$ The question ask what is the output of system y[n] when the signal x[...
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Output of system given the input and frequency response [closed]

Given the signal: $$x(t) = −4\cos(2\pi 4t) + 3\cos \left(\pi t − \frac{\pi}{3}\right)$$ 1) $2 Hz$ is in line with what required by the sampling theorem? Not, $2f_{max} = 2 * 4 = 8 Hz$? 2) The ...
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FIR Linear Phase Condition

This is the linear phase condition for FIR filters as expressed by my prof: I don't understand why $G(f)$ can be negative. Isn't the Fourier transform expressed in polar form ? So the magnitude is ...
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Frequency response of each component of a system given its global response

Given the following block diagram, find the frequency responses $H1(f)$ and $H2(f)$. The frequency response of the whole system has to be $H(f)=(\alpha_0+\alpha_1e^{-j2\pi T_1f}+\alpha_2e^{-j2\pi T_2f}...
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87 views

Frequency response of a system given its block diagram

Given the following block diagram, I am asked to find the frequency response $H(f)$ of the system. This is what I have done: The output of the first block is $j2\pi fX(f)$, and after going through $...
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Polynomial Response

I was referring to the below paper from @robert bristow-johnson https://www.researchgate.net/publication/266675823_Performance_of_Low-...
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Frequency response of FM modulation/demodulation chain with phase derivative demodulation

Frequency modulating a carrier by white noise and then demodulating the complex signal using discrete derivative of phase it appears that the discriminator is acting as a low-pass filter. How do I ...
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Is it possible to infer the characteristic curve of a recording device only from (many) recordings?

... with a certain degree of confidence / corridor of accuracy. What do I mean? Case in point: There is the huge archive of digitized Edison wax cylinder recordings. They have annotations, usually ...
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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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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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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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82 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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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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Require explanation for Matlab freqz2

Question I browsed the code of the Matlab freqz2 function (to find out how it is different to simple fft2.) First of all it ...
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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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Finding frequencies(and bandwidth) that works best audio in a certain medium

Complete DSP and coding newbie(learning python). I am trying to find frequencies that can pass through well in a musical instrument tube. I am trying to find audio frequencies(audible and inaudible ...
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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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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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34 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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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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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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251 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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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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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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96 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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55 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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119 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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214 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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109 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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187 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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146 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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148 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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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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295 views

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: ...