Questions tagged [magnitude]
The magnitude tag has no usage guidance.
80
questions
18
votes
3answers
8k views
Why are magnitudes normalised during synthesis (IDFT), not analysis (DFT)?
In most examples and FFT code that I've seen, the output (frequency magnitudes) of the forward DFT operation is scaled by N -- i.e. instead of giving you the magnitude of each frequency bin, it gives ...
15
votes
2answers
54k 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?
5
votes
3answers
925 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 ...
5
votes
2answers
9k views
How does zero-padding affect the magnitude of the DFT?
Let's simulate sinusoids of two frequencies using the following Matlab code:
...
4
votes
1answer
24k views
Energy calculation in frequency domain
I was just wondering... The formula I learned to calculate the energy of the signal is expressed in the time domain:
$$E_x^{\text{time}} = \sum_{n=-\infty}^{\infty} |x[n]|^2$$
Then, what does the ...
4
votes
1answer
14k 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 ...
3
votes
3answers
4k views
Adequate representation of frequency domain amplitude/magnitude of FFT of a signal
I'm quite new to the subject and am having fun playing around with the FFT. What I am currently doing is trying to sample an audio signal and display its frequency spectrum at the same time. This ...
3
votes
3answers
4k views
recover image by only magnitude of image fourier transform
I have a image and I want calculate fft2 of it, after it I want recover image only by magnitude of it. how can I achieve this work?
...
3
votes
3answers
52k views
How to compute magnitude and phase response from transfer function in Z-domain?
I have a transfer function $$H(z)=\frac{1+1.2z^{-1}+0.8z^{z^-2}}{1-0.9z^{-1}}$$ from which I'm supposed to sketch the magnitude and phase response. I know that you can transform $z=e^{j\omega}$ to get ...
3
votes
1answer
118 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(\...
3
votes
1answer
293 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 ...
2
votes
2answers
94 views
Non-zero DFT components where zero is expected?
I am implementing DFT in Octave. Here's my code:
...
2
votes
2answers
85 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)| &=\...
2
votes
1answer
5k views
retrieving original data from phase and magnitude of Fourier transform
I use this snippet of python code to transform data to Fourier phase and magnitude and then retrieving original data.
...
2
votes
3answers
253 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.
...
2
votes
1answer
140 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 ...
2
votes
2answers
664 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 ...
2
votes
1answer
516 views
Plot Magnitude from RBJ Biquad
Currently I'm working out plotting biquads in a VST/AU plugin and have problems with the graphics part. I posted in several forums but haven't got a really useful answer for this case.
First, tell ...
2
votes
2answers
384 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
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)...
1
vote
3answers
416 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 ...
1
vote
3answers
152 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
vote
3answers
2k views
Fill matlab “ellip” function through transfer function magnitude response
The matlab "ellip" function can be used to design the unquantised coefficient set.
From matlab website:
$ [b,a]=ellip(n,Rp,Rs,Wp) , $
n: order of filter
Wp: normalized passband edge ...
1
vote
3answers
69 views
How do the magnitude and phase spectrum of an imaginary function look like?
Say I have the function
$$x(t)=j \operatorname{rect}(t)$$
Is the phase spectrum even or odd?
I am confused whether the phase spectrum is an odd/even function of $\omega$ (angular frequency, Fourier ...
1
vote
1answer
49 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 ...
1
vote
1answer
1k 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}(\...
1
vote
2answers
229 views
how to make fft ignore phase shift when only interested in magnitude
I have a signal that consists of a sine wave, on which I apply a rectangular window and then an FFT. I'm only interested in the magnitude of the sine wave, and I want it to stay the same even if the ...
1
vote
1answer
172 views
Obtaining the magnitude of the frequency response by plugging $e^{jĻ}$ into the z-domain transform function?
I am reading a text on discrete signal processing, which states that the frequency response of a signal can be obtained by plugging the value $e^{jĻ}$ into the z-domain transfer function $H(z)$. In ...
1
vote
1answer
56 views
Why do the DTFT and FFT give me completely different results for magnitude at a specific frequency?
I am trying to write a program to compute the magnitude and phase of a specific, non-integer frequency component (i.e. given a sampled finite signal of length $N$, I want to know the magnitude and ...
1
vote
1answer
112 views
Calculate the magnitude and phase of a signal at a particular frequency in python
I have a signal for which I need to calculate the magnitude and phase at 200 Hz frequency only. I would like to use Fourier transform for it. I am very new to signal processing. And this is my first ...
1
vote
1answer
39 views
Magnitude response of mirrored (with respect to unit circle) poles and zeros
I just want to check that my understanding about the following paragraph from Optical Filter Design
and Analysis by Christi K. Madsen, Jian H. Zhao is correct:
A filterās magnitude response is equal ...
1
vote
1answer
54 views
Squared magnitude of the Z-transform
I am basically new to the $z$-transform and there are some points regarding its square magnitude that I do not understand.
Basically I do not understand how in slide 4 of PDF, they arrive at the ...
1
vote
1answer
95 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)$$
with sampling frequency $F_s = 1000$ and plot the magnitude spectrum for the resulting sampled signal.
My thinking is ...
1
vote
1answer
65 views
How would I find the function given the magnitude plot and the phase response?
I'm wondering how I'd find the Fourier Transform X(jw) given the following information:
My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
1
vote
1answer
3k views
Magnitude of function in $z$ domain
I am newbie to $\mathcal Z$-transform, I searched to find the magnitude of a function in $z$-domain, but I couldn't find anything, for example when we have
$$
H(z) = \frac{z-3}{z-0.5}
$$
How do you ...
1
vote
1answer
470 views
How can resonance be added to a fractional order Butterworth low pass
I am interested in how to add resonance (Q) to the magnitude response of a Butterworth low pass when it is expressed in the form:
$$
G^2(\omega)=\frac {1}{1+\left(\frac{\omega}{\omega_c}\right)^{2n}}
...
1
vote
2answers
578 views
Averaging Multiple Magnitude Spectra
I'm currently trying to implement some of the methods found in this paper on intelligent equalization - http://www.aes.org/e-lib/browse.cfm?elib=16792 -
The first part of the process is to build a "...
1
vote
0answers
51 views
Blackman window magnitude attenuation
I am trying to compute the fundamental phasor using sliding window DFT. I have employed a Blackman window in conjunction i.e
$$
\sum_{k=0}^{L_{DFT}-1}x(k) w(k) e^{-j2\pi k/N}
$$
where $x(k)$ is the ...
1
vote
0answers
53 views
Moving average filter output magnitude in simulink
I was using the Moving average filter provided by simulink. I set the window length equal to 31 samples and i was using a fixed step solver with a step size of
$\frac{1}{(50\times24)}$. I used a unit ...
1
vote
0answers
33 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 ...
1
vote
1answer
178 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 ...
1
vote
1answer
173 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,...
1
vote
1answer
1k 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 ...
1
vote
1answer
845 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 ...
0
votes
2answers
27k 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 ...
0
votes
2answers
7k views
Plotting the magnitude response of a filter?
I have designed a second order butterworth filter.
Sampling frequency: $4\textrm{ kHz}$, Cut-off frequency: $500\textrm{ Hz}$
$$e = \tanā”\left(\frac{\pi \times f_c}{f_s}\right) = \tan\left(\frac{...
0
votes
2answers
71 views
How to convert magnitude to dB in matlab
I exported a diagram from FDTD simulation, and now I want to change the magnitude to dB, here is the exported codes:
...
0
votes
2answers
61 views
Working with a sound's magnitude instead of amplitude
I'm working on a project, where we're recording sound with a piezo-disc which looks a little something like this:
Now, unless we're doing something horribly horribly wrong, I've discovered that we're ...
0
votes
3answers
65 views
Relationship between DFT input sequence and magnitude
Assuming there is a sequence that could look like this:
$$ 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\} $$
Using this sequence, I want to ...
0
votes
1answer
101 views
Does a filter need to completely attenuate high frequencies to be considered low-pass?
I'm looking at a system with a frequency response that is: $$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 ...
