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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Order one FIR Filter with complex coefficient

I am trying to learn about the behavior of the FIR filter however with complex coefficients. The filter I am trying to analyze is the following: $$H(z)=a+jbz^{-1}\quad\text{where the variable}\quad j =...
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190 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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615 views

What does it mean for a function to have frequencies?

In a lecture, my professor mentioned that $\cos$ has two frequencies. I see that using the inverse Euler's formula we can express $\cos$ as a some linear combination of complex exponentials, each with ...
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What is the between spatial frequency of an image and pixel size of the sensor?

In my lecture notes about the sampling of an image I've written that: Since pixels have a finite dimension the spatial frequency response is attenuated before the "ideal" Nyquist frequency ...
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43 views

Recovering DTFT from Z-transform

The relationship between the Z-transform and DTFT can be expressed like: $$ H(e^{j \omega}) = H(z)|_{z = e^{j \omega}}$$ Graphically, evaluating the Z-transform on the unit circle is shown as sweeping ...
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The effect of time increment $\Delta t$, frequency resolution $\Delta f$ and Gibbs phenomenon on the amplitude of the signal in the frequency domain?

Experiment: Vibration analysis (i.e.: major concern is on transfer function or frequency response). The input is an impulse (imagine as a knocking effect or knocking force), defined as a half sine ...
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36 views

FIR Filter 3dB Frequency

I am new to signal processing and I want to calculate the 3 dB - cut off frequency of this FIR filter, which has the following transfer function: For the evaluation i need to replace the z with and ...
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58 views

Is it possible to specify number of taps and cutoff frequency independently?

When specifying the properties of a moving average filter, is it possible to specify the number of taps and the cutoff frequency? My guess is no since taps (the number of samples in a moving average ...
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208 views

Can we choose a sampling frequency to remove unwanted noise at a specific frequency?

I am studying for my exam in signal processing. In one of the old exam papers I am told to find a sampling frequency, which will remove 80 Hz noise. The filter the exam question is based around has an ...
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172 views

DC gain from an impulse response

I am studying for my exam in signal processing. For one of the old exam sets, a discrete impulse response of a filter is given as $h[n]$ \begin{bmatrix} -3&0&-3&0 \end{bmatrix} With a ...
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51 views

What is the frequency of the Gaussian white noise model in control systems?

The design of control systems, particularly for SISO systems, is made convenient by tools such as Bode plots and the corresponding Nyquist stability criterion. These concepts allow engineers to design ...
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Correcting phase response of a signal

I have a sensor that applies a frequency dependant phase alteration to my signals. I'm trying to find a way to correct these phase responses using an FIR filter. Essentially, I'm looking for methods ...
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73 views

What happens to the phase spectrum when I resample?

[An update is added at the end of the post after receiving first response] I have an algorithm which is very sensitive to phase shifts. It works with signal sampled at 40MHz (it's a neural network so ...
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92 views

Impulse response $h[n]$ from input and output signal using cross correlation on Matlab

I have two signals on Matlab, one being input and the other output. I want to know if taking the cross correlation of these signals would give me the impulse response?And if so, will taking the ...
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26 views

frequency response of a time domain subroutine in matlab

I implemented a sigal processing structure using very basic operation like multiply and add, I wonder is it possible to find a built-in function in matlab to treat this as a black box and obtain its ...
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128 views

Does converting an FIR filter from causal to non-causal remove phase delay?

Let's say I have a causal 3-tap FIR filter: $$y[n] = ax[n] + bx[n-1] + cx[n-2]$$ Assuming I have access to all the data prior to filtering and generate a similar non-causal filter: $$y[n] = ax[n+1] + ...
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Clarification on eigenfunction property from Oppenheim's Discrete-time signal processing, 3rd ed

Could anybody explain what is meant by the following statement on page 50 of Oppenheim and Schafer's book Discrete-Time Signal Processing (third edition)? The eigenfunction property of complex ...
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Scipy visualize Linear filter using numerator coefficients

Python scipy signal package has a function freqs to get the frequency response of a linear filter from [b, a] numerator and denominator. So, I should be able to get ...
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Transfer function model to frequency response

I have a problem, I wanted to filter the signal with a Butterworth filter built on the basis of a prototype. I have zeros and poles and an $H (s)$ answer, and I do not have the frequency response. How ...
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The impulse response of a LTI discrete system is $h[n]=\big(\frac{1}{3}\big)^n u[n]$. Find the response of this system to the input $x[n]= e^{jnπ/4}$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $1.2503 e^{jnπ/4 -0.2991}$, and is found by computing $H(Ω)$ and evaluating this at $Ω=π/4$. when I try ...
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194 views

Frequency response of a digital state variable (Chamberlin) filter

I recently implemented a digital state filter based on the recommendation here. I've tested this filter's performance as a very low cutoff low-pass filter with limited coefficient quantization ...
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112 views

Suitable signal processing techniques for frequency response functions?

Good day everyone I have recorded experimental frequency response functions (frfs) for a loose bolt monitoring project. Please see figure 1 below for an example of the frf. Figure 1 The purpose of my ...
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Output of IIR filter not matching the frequency response - Proximity to fs/4

After not having dealt with digital filters for a long time, I have now been playing around with filter design in octave and I am observing a behavior which I do not understand. After designing a low-...
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971 views

How to model transfer functions using Python (without using higher level packages) and plot the magnitude and phase response?

I'm trying to model a transfer function in Python and thought I could do it by simply plotting the transfer function at many frequencies. This seemed to work for a 2nd order LPF. See the below figure. ...
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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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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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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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247 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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572 views

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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105 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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68 views

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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122 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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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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515 views

Attempting to use the trapezoidal rule to form a difference equation representing a circuit

I have a differential equation that has been proven to be correct. The transfer function obtained by Laplace domain analysis and Matlab freqs match up and all is well. The problem is somewhere in ...
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148 views

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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150 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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865 views

Design a linear-phase FIR filter approximating the magnitude of a given IIR filter

I have a biquad IIR filter from which I want to get a linear-phase FIR. I saw that related question but the OP does not care much about phase. I have troubles getting the exact same magnitude curve ...
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219 views

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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40 views

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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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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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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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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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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137 views

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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528 views

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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95 views

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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