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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Decimation FFT Result

In my Signal Processing class we just learned decimation however after messing around in Matlab trying an example of decimation, I just can't understand what's happening. I get the introducing twi ...
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Why does sampling chirp at peak frequency yield correct frequency response?

Followup; setting Fs = bandWidth in accepted answer's code yields the "correct" frequency response of an LFM chirp: constant magnitude, parabolic phase. ...
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155 views

Applying zero-phase filtering in the frequency domain - also works in real-time?

In my application a filtering in the frequency space is desired. I designed two high-pass filters: $h_1$ Butterworth IIR filter, and $h_2$ FIR. I designed them using Python's ...
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Does chirp have constant magnitude frequency response?

Pg. 223 claims so, yet my results via DFT differ: Is the textbook wrong? My attempted explanations: (code) DFT vs DTFT: "frequency response" is computed via latter. Still, DFT should ...
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228 views

Apply “non-causal” filter buffer-wise, a.k.a “soft real-time filtering”

I am dealing with digital filtering of signals, both offline and in real-time. Typical filtering purposes are highpass filter or bandpass filter. So far I worked on prerecorded signals (e.g. ...
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If you would write the frequency-response in terms of projections through inproducts. How would you do it?

While studying for signals and systems I realised that the most intuitive way of understanding Fourier Series for me, was to see it as a projection (through inproducts) of a signal onto the orthogonal ...
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Notch filter: differences between IIR and FIR filters

I'm trying to understand this great answer from Matt L. . It's said that "One advantage of IIR filters is that steep filters with high stopband attenuation can be realized with much fewer ...
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101 views

Designing appropriate filter by choosing values for $A$ and $B$

Let $$y[n] - ABy[n-1] +A^2y[n-2] = x[n] - Bx[n-1] +x[n-2]$$ Where $A$ and $B$ are constants. Also there are two sounds which have $400$ hertz noise and the sampling rate is $8000$ samples/sec. The ...
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Calculation of gain at certain frequency in case of nth order IIR filter

There is this method for to set 0dB gain to be at wanted frequency (fc) (Octave/Matlab example for biquad LPF): ...
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118 views

Frequency response and sampling theorem for triangular function

The triangular function is defined as follows: $h_l(x) = \begin{cases}1-|x|,&|x|<1;\\0&\text{otherwise}.\end{cases}$ According to ccrma.stanford.edu: "If the output of the interpolator ...
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Deriving of magnitude, phase response and impulse response of transfer function

I have a transfer function as $$H(z) = \frac{-0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z - 0.0625}{z^4}$$ I want to derive magnitude and phase response of this equation. can someone help me from here I ...
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Why notches in sinc filter response

Below response shows sinc1,sinc2 and sinc3 filter response. I understand that notches in the frequency response happens at the output data rate of the sigma-delta ADC. But I am not able to figure out ...
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Calculating the 3dB frequency of an nth order low pass filter and nth order high pass filter

I am using the 6th order high pass filter in the C code. And the cut-off frequency selected for it is 150 Hz and the sampling frequency being used is 32000Hz. Now, I want to calculate the 3 dB ...
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128 views

What is the relationship of S-parameters to frequency response?

I have some S-parameters. I'm reading about frequency response and the impulse response and step response. If I have a set of S-parameters, then is the frequency response for a port (say output port 2,...
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Difference between freqz vs freqresp in scipy?

I'm always confused that scipy has scipy.signal.freqz, but also scipy.signal.lti.freqresp / ...
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Frequency response of discrete PT1 in MATLAB

I want to calculate the frequency response of a discrete PT1 system with T=T1 and K=1. (the code is at the bottom of the question) To validate the magnitude response, I want to use an sinusoidal input ...
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Is it possible to prove that dither VS PWM can result the same output?

Assume that we have a SISO transfer function model $G(s)$ and we want to look how the output looks like when we have a input signal $u(t)$ that looks like this: $$u_1(t) = \left\{\begin{matrix} 50 + ...
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Why when you use any filter, it results first a steepness at the beginning to a certain level?

Is there any tool to avoid that? For instance, I wish after filterin my signal, the filtered signal start from a certain level, in other words, at the offset level. In this case, I've use Butterworth,...
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Fourier Transform of a PSD and response of a PSD input

Does a Fourier Transform of a white noise exist? If so, what is its general form? It is possible to compute the fourier transform of a Power Spectral Density? My problem in detail. I have to compute ...
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Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$

Let $$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$ Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$? If not, what's the reason for ...
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Fourier transform of unit step

I was reading pdf by caltech and in one of its section, Fourier transform of Unit step signal is calculated but I am confused, how this can be possible if region of convergence for Laplace transform ($...
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179 views

impulse response cascaded with time reversed of itself

Consider a filter with real-valued impulse response $h[n]$. The filter is cascaded with another filter whose impulse response is $h'[n] = h[-n]$, i.e. whose impulse response is the time-reversed ...
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Estimation of Group Delay from Noisy Frequency Response Measurements

Consider a linear, time-invariant system. Noisy measurements of the magnitude and phase associated with the frequency response of the system are available over some dense generally non-uniform grid ...
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Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $H(\omega)$. I don't have any clue that how to deal with the ...
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Determining output of a LTI system

Consider following LTI system $$y[n] - 2y[n-1] = x[n]$$ where $x[n]$ is the input to the system and $y[n]$ is the output. Let $x[n] = \cos[n\frac{\pi}{3}] + 2\cos[n\frac{\pi}{2} + \frac{\pi}{4}]$, ...
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Simplifying frequency response equation

I am trying to to find a magnitude and phase response of a FIR filter as in problem 5.18 Digital Signal Processing 4th Edition by John Proakis. I got the frequency response as: $$ H(\omega ) = 1 - e^{...
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LowPass Filter & Window *Img & Code* - Frequency Response has no lobe roll off

Not sure if I am doing something silly but I am not seeing lobe roll off on the frequency response of my windows and the low pass filter I made in MATLAB. Please can you help ... several hours just ...
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347 views

How to convert my transfer function to the frequency domain

I have the following transfer function in the time domain: $h\left(t\right) = B x\left(t\right) + a x^2\left(t\right) + b x^3\left(t\right)$. My simulation is in the frequency domain, so I would ...
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116 views

Why does this transfer function estimation not work? System identification

Goal: I have an unknow dynmical system $G(s)$ and I want to find it from measurement data, output $y(t)$ and input $u(t)$. The data is frequency responses. Method: I begun first with creating the ...
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How can I plot the frequency response on a bode diagram with Fast Fourier Transform?

Assume that we have an unknow dynamical system and we only want to estimate its parameters. The system can be discribed as: Continous time: $$G(s) = \frac{3s + 5} {5s^2 + 3s + 2}$$ Discrete time ...
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How can I find the transform function, amplitude and frequency response of a digital filter in python?

I have applied a laplace filter mask to an image and now I want to find the amplitude and freqency response of a laplacian filter: [[1,1,1], [1,-8,1], [1,1,1] ]. I know I need to first find the ...
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788 views

Calculating the Fourier transform of shifted scaled unit step function

I have $x_1(t)$ here. To get $x_2(t)$, I need to differentiate $x_1(t)$. Express $x_2(t)$ as $2u(t+2)-4u(t)+2u(t-2)$. From Fourier transform definition integral, I got $X_2(j\omega)=\frac{2e^{j\omega ...
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How to cancel this noise to find numbers of DTMF tones?

Touch-tone telephones use a dual tone multi frequency (DTMF) scheme to encode key-presses as audio tones: I have a signal containing 10 number tones. I used frequency response to show what ...
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656 views

Power Spectrum and Power Spectral Density

From signal theory we know that a very useful representation of some power signals is that of its power spectral density, whose curve represents how the total power of the signal is distributed at all ...
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246 views

How to match zero-pole diagrams to their frequency responses (Discrete Time)

I get confused when there are a lot of zeros/poles in the zero-pole diagram and I find difficulty understanding their frequency response. I know the following: 1. Complex conjugates cause double ...
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Time and Frequency Domain Relationship

Why do we say that a good time response means a bad frequency response?
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Assume frequency response of x(t) is X(f). Find frequency response of x(-2t+4)?

Frequency response of $x(t)$ is $X(f)$. Find frequency response of $x(-2t+4)?$ Here is my work using the fourier transform property:$ x(-2t+4) = x( -2(t-2) )$, + First, I apply the property, $x(at)$ ...
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Least square error channel estimation in the presence of AWGN noise

I want to implement Least Square (LS) channel estimation method in the presense of AWGN noise in MATLAB. $y(n) = x(n) * h(n)$ $Y(k) = X(k)H(K)$ Y(k) is the received signal in frequency ...
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Can someone explain me how to generatee a doppler spectrum? [duplicate]

I have a signal generated in matlab, with Rayleigh Fading, how can I add a given type of Doppler spectrum ( Gaussian for instance) to that signal ? Any help will be really appreciated
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Why if I place the zero of the lead compensator at lower frequencies, do I obtain a resonance peak?

I am studying control systems, and I am studying the lead and lag compensator. I have seen than if I use a lead compensator for the closed loop transfer function, $T(s)=\frac{s+2}{(s+1)(s+8)},$ with ...
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What does it mean that a zero is slow?

I am studying control systems, and have encountered the definition of a slow zero. I am searching on internet and in books, but I don't understand the meaning this. I know that if a zero is too slow, ...
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210 views

filterbank: understand the different responses at the center frequency of each filter

I'm computing filterbank by applying 26 triangular filters on a Mel-scale to the power spectrum of an audio frame to extract frequency bands, and I found that some references use filterbank with equal ...
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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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70 views

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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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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242 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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167 views

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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