Questions tagged [magnitude]
The magnitude tag has no usage guidance.
69
questions
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1answer
38 views
Terminology for instantaneous phase of magnitude component of complex signal
In my field, we deal with data that are originally complex-valued. Typically, researchers convert their data from real + imaginary to magnitude + phase, and then discard the phase data (i.e., we ...
0
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2answers
55 views
Working with a sound's magnitude instead of amplitude
I'm working on a project, where we're recording sound with a piezo-disc which looks a little something like this:
Now, unless we're doing something horribly horribly wrong, I've discovered that we're ...
0
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1answer
53 views
Impulse response from frequency response in Matlab
I am trying to design equalization filter and therefore I want to define my own amplitude and phase response and then to obtain the impulse response of the filter. I thought that the output of the ...
1
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3answers
148 views
What does this paragraph mean?
I'm reading this paper about about an algorithm to measure image sharpness, and am confused by these sentences in the 6th paragraph:
It is well known that the attenuation of high-frequency content ...
1
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0answers
28 views
What is the “Energy” equivalent of the Magnitude Spectrum
I have a semantic issue regarding the discrete spectrum $X[k]$ of a time domain signal with limited length $x[n]$, so we're talking about the FFT. Now, when I what to compare the bandwidth and ...
0
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1answer
38 views
Why is there a negative in front of the phase response equation for this complex exponential?
first time on here!
I'm working through "Digital Signal Processing using MATLAB" by Vinay and Proakis. Good book.
I am stuck on this example tho.
Shouldn't the imaginary part in the denominator (...
5
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3answers
843 views
Understanding FFTs for simple Sin / Cos
this is my first question in this forum, and although I read several threads on this side and googled a lot I could not find the answer to my question (maybe it is too basic)?
For anyone reading this ...
0
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1answer
64 views
Calculating the magnitude spectrum and phase spectrum
From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$.
Then, I want to calculate its magnitude spectrum and phase spectrum.
The ...
0
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3answers
58 views
Relationship between DFT input sequence and magnitude
Assuming there is a sequence that could look like this:
$$ x[n] = \{1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,1, 1, 0, 0, 1, 1, 0, 0,1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0\} $$
Using this sequence, I want to ...
0
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0answers
36 views
FFT frequency-magnitude not correct when a positive gain EQ point is applied
I have a measurement system, which applies a log sine sweep as stimulus to a DUT and records the return signal.
I then extract the impulse response, and perform an FFT on this to examing phase and ...
1
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1answer
116 views
Correctly scaling FFT of different lengths
I have been looking at using two FFTs of different lengths and displaying the output magnitudes on the same graph (a shorter length window for the higher frequencies, and a longer one for lower ...
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0answers
47 views
Magnitude attenuation by a filter
I have a filter, with coefficients given by
$$
W=\sin((2*\pi*2*F_f*k/F_s)/(2*\pi*2*F_f*k/F_s))*h[k]
$$, where $F_f$ is the filter reference frequency, $k$ runs from $-N/2$ to $N/2$ ($N$ is the order ...
1
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1answer
145 views
Energy definition for Autocorrelation lag 0 and lag 1 for complex signals
I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix.
Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
2
votes
3answers
210 views
Matlab IIR cheby2 bandpass, problems with Magnitude
I am trying to implement an IIR bandpass in Matlab. There are two things I don't understand. But first of all, let me post the code.
...
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2answers
62 views
Is it valid to calculate the magnitude, power, and phase of a real time-domain signal without converting it to the frequency-domain?
I would assume you perform the calculations the same way, but since there would be no imaginary component because the signal is not complex it would be simpler:
...
2
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2answers
298 views
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 ...
2
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2answers
75 views
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:
$$\begin{align}
|H(f)| &=\...
1
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1answer
83 views
Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$
I'm asked to sample the signal
$$x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$$
with sampling frequency $F_s = 1000$ and plot the magnitude spectrum for the resulting sampled signal.
My thinking is ...
1
vote
2answers
457 views
Zero padding and 2D Fourier transforms: how does zero-padding affect phase?
It's pretty clear that zero-padding an image before performing Fourier transform simply enlarges the magnitude image (stretching it to the new, padded size).
What I can't understand is how it affects ...
1
vote
1answer
60 views
How would I find the function given the magnitude plot and the phase response?
I'm wondering how I'd find the Fourier Transform X(jw) given the following information:
My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
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2answers
140 views
How to graph magnitude plots for basic 4-pole filters?
I have developed magnitude plots for basic one-pole and two-pole filters derived from various Physics PDF's and tutorials I have found online and calculated from:
https://www.desmos.com/calculator/...
1
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3answers
203 views
$e^{j\omega}$ on unit circle
I am new to DSP, and I'm self studying. I am confused about the magnitude of $e^{j\omega}$ - where $\omega$ is the normalized angular frequency - when we are on the unit circle.
According to the ...
3
votes
1answer
94 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(\...
1
vote
1answer
862 views
Spectrogram with square or non-square magnitude of STFT: power vs. magnitude
As seen in this question and answer, to do a spectrogram, it's common to plot either:
the square magnitude $|\text{STFT}(\text{frame}, \text{bin})|^2$ ("power spectrum")
the magnitude $|\text{STFT}(\...
2
votes
4answers
1k views
How do I calculate peak amplitude of the signal components after zero padding and FFT?
I am learning about DFT and trying to apply it to some audio processing. I am new to DSP but experienced in programming and have some background in math and physics. The FFT algorithm I use (lomontFFT)...
0
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1answer
230 views
Summing magnitudes of individual frequency bins
I am working on signal analyser and have problem with understanding relationship between display resolution and frequency resolution (range).
My frequency range is $ 1-20000\quad [ H z ] $ so to ...
2
votes
1answer
134 views
Why harmonic components appear only after a certain level when a signal is clipped?
I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level.
The Python code to reproduce the effect is given below. The signal has 3 ...
0
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2answers
192 views
Phase information from product of complex conjugate transfer functions
For an input signal $x(t)$ and output signal $y(t)$ through an LTI system I $H(t)$ I have found and interesting property that concerns signals' power spectral densities:
$${\lvert H(\omega)\rvert}^2 =...
0
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1answer
58 views
Computing real signal with minimum absolute values from even magnitude spectrum
I want to derive a real audio signal from an arbitrary even magnitude spectrum.
The phase spectrum affects the values of the signal in the time domain; for example, a phase of 0 for all frequencies ...
1
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1answer
998 views
Magnitude response and DFT normalization
Suppose I have an FIR denoted h that represents the impulse response of a system. Using MATLAB syntax (for convenience and brevity),
What does ...
3
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1answer
280 views
Calculating phase response of maximum phase filter using Hilbert Transform
Given only a magnitude response $A(\omega)$ of a minimum phase filter, one can calculate the phase response using the Hilbert Transform:
$$Īø(Ļ) = -\mathcal{H}\{\ln(A(\omega)\}$$
This paper suggests ...
0
votes
2answers
6k views
Plotting the magnitude response of a filter?
I have designed a second order butterworth filter.
Sampling frequency: $4\textrm{ kHz}$, Cut-off frequency: $500\textrm{ Hz}$
$$e = \tanā”\left(\frac{\pi \times f_c}{f_s}\right) = \tan\left(\frac{...
0
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1answer
90 views
Does a filter need to completely attenuate high frequencies to be considered low-pass?
I'm looking at a system with a frequency response that is: $$H(e^{j\omega})=\tfrac{1}{4}(2\cos(\omega)+\cos(2\omega)+2)$$
I think the magnitude of this system looks like this (not sure what is the ...
0
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1answer
862 views
When does the Amplitude Spectrum equal the Magnitude Spectrum?
I had the following question on edX:
I'm failing to understand why the second signal has $M(\omega)=A(\omega)$. First I find the DTFT of the signal:
$$\mathcal{F}\{\delta [n]+\delta [n-1]\}\ =\ ...
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1answer
2k views
Magnitude of function in $z$ domain
I am newbie to $\mathcal Z$-transform, I searched to find the magnitude of a function in $z$-domain, but I couldn't find anything, for example when we have
$$
H(z) = \frac{z-3}{z-0.5}
$$
How do you ...
1
vote
1answer
787 views
How to reconstruct signal of its phase and magnitude functions?
I have two continuous periodic (a period of $2\pi$) functions which belong to the phase and magnitude of Fourier transform of a signal, how can I reconstruct the original signal? What kind of ...
5
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3answers
7k views
How does zero-padding affect the magnitude of the DFT?
Let's simulate sinusoids of two frequencies using the following Matlab code:
...
0
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1answer
727 views
Recovering signal from magnitude and phase of FFT
I'm trying to code the basics of an analysis-synthesis system on MATLAB, but I'm getting incorrect results. From the Wikipedia page:
$$
X_k=\lvert X_k\rvert e^{i\angle X_k}
$$
Here's a simple MATLAB ...
0
votes
1answer
2k views
Bode plot of discrete-time transfer function $H(z)$
$H(z)$ is the transfer function of a biquad filter as described here.
I would like to plot the Bode plot of the magnitude response of $H(z)$.
Scipy has a bode method (...
0
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2answers
26k views
How to plot magnitude and phase response by hand if I have the Transfer Function?
I have the transfer function of the system, which is:
$$H(z) = \frac{1-z^{-1}}{5(1+2z^{-1})}$$
How do I sketch the magnitude and phase response?
I'm sorry for the bad formatting, it's my first time ...
1
vote
1answer
437 views
How can resonance be added to a fractional order Butterworth low pass
I am interested in how to add resonance (Q) to the magnitude response of a Butterworth low pass when it is expressed in the form:
$$
G^2(\omega)=\frac {1}{1+\left(\frac{\omega}{\omega_c}\right)^{2n}}
...
-1
votes
1answer
255 views
How to implement Cross Spectral Density [duplicate]
I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image.
Reading wiki1,wiki2,wiki3 from wikipedia, and ...
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1answer
12k views
Identifying the magnitude and impulse response from pole zero plot quickly
I have an exam next week and it's verty certain that a task of this kind will be there.
Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
0
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1answer
157 views
Converting magnitude to dBs
I have seen people using 10*log10 and/or 20*log10 while converting magnitude to dBs. What are the differences and which one is valid?
12
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2answers
50k views
Power spectral density vs. FFT bin magnitude
What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
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4answers
2k views
Coherence vs. Magnitude Squared Coherence
currently I am writing my masther thesis. The theory part is about the turbulent wind field generation, where the coherence (not magnitude squared) is used:
$$\text{coh}(f) = \frac{|P_{xy}|}{\sqrt{P_{...
0
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1answer
78 views
zero-phasing frequency components while keeping the same magnitude, in Matlab
How is it possible?
I was thinking of taking just the real part of the DFT of my signal (isn't that zeroing out phases?) with
real(fft(X))
but the magnitudes ...
0
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2answers
429 views
phase, magnitude, audio file and information
I've been doing some thinking lately. I know that for image files a larger portion of information is contained in the phase of the signal. How does that go for the audio? Does the same hold or is the ...
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3answers
2k views
MATLAB frequency magnitude spectrum
I am using the following code to generate four sine waves using a sampling rate of 8000.
...
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1answer
140 views
Sketching Phase Spectra Using Group Delay and Magnitude Spectra Informations
I have only magnitude spectra and group delay information and I need to sketch phase spectra from this information. For example, group delay is given like this: $\tau_{g}(\omega) = c$ where c is a ...
