Questions tagged [magnitude]
The magnitude tag has no usage guidance.
56
questions
2
votes
2answers
59 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:
$$\begin{align}
|H(f)| &=\...
1
vote
1answer
37 views
Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$
I'm asked to sample the signal
$$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 ...
0
votes
0answers
8 views
Wavelet Analysis Magnitude Scale
I am trying to plot magnitude against frequency averaged over a time window.
To do this I make a morlet wavelet Filterbank. And multiply the dft of each kernel by the dft of my incoming data set.
...
0
votes
0answers
28 views
Remove constant noise from Goertzel output
I'm trying to analyze a signal recorded from an analogue phone line and do DTMF recognition using a Goertzel algorithm. However, due to a fault in the hardware, there is a constant 50Hz power line ...
1
vote
2answers
75 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
31 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(...
0
votes
2answers
100 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
vote
3answers
103 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
59 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
363 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
3answers
509 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
votes
1answer
155 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
111 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
votes
2answers
151 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
votes
1answer
55 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
vote
1answer
675 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
votes
1answer
239 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:
$$θ(ω) = -\mathcal{H}\{\ln(A(\omega)\}$$
This paper suggests ...
0
votes
2answers
5k views
Plotting the magnitude response of a filter?
I have designed a second order butterworth filter.
Sampling frequency: $4\textrm{ kHz}$, Cut-off frequency: $500\textrm{ Hz}$
$$e = \tan\left(\frac{\pi \times f_c}{f_s}\right) = \tan\left(\frac{...
0
votes
1answer
67 views
Does a filter need to completely attenuate high frequencies to be considered low-pass?
I'm looking at a system with a frequency response that is: $$H(e^{j\omega})=\tfrac{1}{4}(2\cos(\omega)+\cos(2\omega)+2)$$
I think the magnitude of this system looks like this (not sure what is the ...
0
votes
1answer
722 views
When does the Amplitude Spectrum equal the Magnitude Spectrum?
I had the following question on edX:
I'm failing to understand why the second signal has $M(\omega)=A(\omega)$. First I find the DTFT of the signal:
$$\mathcal{F}\{\delta [n]+\delta [n-1]\}\ =\ ...
1
vote
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
557 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 ...
4
votes
1answer
4k views
How does zero-padding affect the magnitude of the DFT?
Let's simulate sinusoids of two frequencies using the following Matlab code:
...
0
votes
1answer
473 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
1k 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
votes
2answers
20k 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
367 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:
$$
G^2(\omega)=\frac {1}{1+\left(\frac{\omega}{\omega_c}\right)^{2n}}
...
-1
votes
1answer
178 views
How to implement Cross Spectral Density [duplicate]
I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image.
Reading wiki1,wiki2,wiki3 from wikipedia, and ...
4
votes
1answer
9k views
Identifying the magnitude and impulse response from pole zero plot quickly
I have an exam next week and it's verty certain that a task of this kind will be there.
Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
0
votes
1answer
135 views
Converting magnitude to dBs
I have seen people using 10*log10 and/or 20*log10 while converting magnitude to dBs. What are the differences and which one is valid?
0
votes
1answer
273 views
Amplitude of an image
If I take a two dimensional image and conduct a fourier transform on it, I would get a two dimensional matrix of complex values. If I want to find the amplitude of each value, is that the same as ...
4
votes
2answers
36k views
Power spectral density vs. FFT bin magnitude
What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
0
votes
4answers
1k views
Coherence vs. Magnitude Squared Coherence
currently I am writing my masther thesis. The theory part is about the turbulent wind field generation, where the coherence (not magnitude squared) is used:
$$\text{coh}(f) = \frac{|P_{xy}|}{\sqrt{P_{...
0
votes
1answer
74 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
votes
2answers
367 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 ...
-1
votes
3answers
1k views
MATLAB frequency magnitude spectrum
I am using the following code to generate four sine waves using a sampling rate of 8000.
...
0
votes
1answer
123 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 ...
1
vote
2answers
394 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
3answers
39k 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 ...
2
votes
1answer
17k 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 ...
0
votes
1answer
681 views
sketching magnitude of frequency response of H(z)
I am trying to plot the magnitude of H(z), I got it to factore, and would like to sketch its plot of magnitude. But I am have trouble evaluating the function.
$$
H(z)= \frac{(1-2z^{-1})(1+0.5z^{-1})(...
0
votes
0answers
847 views
fft magnitude scaling
I use the following code to calculate the fft of 1024 samples of a 200 Hz windowed sinusoid (code taken from aurio touch apple example app):
...
0
votes
1answer
215 views
Interpreting magnitude of DFT results
I'm working on creating a simple program to render spectrograms like this one. In this plot, the X-axis is time, the Y-axis is frequency, and the color represents the magnitude of the DFT at that ...
0
votes
2answers
1k views
Magnitude Spectrum, different magnitudes same amplitude
When the following code is written,the resulting magnitude spectrum shows magnitude values represented by two peaks is different even though they have the same amplitude. why is that?
a fast reply ...
3
votes
3answers
3k 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 ...
0
votes
2answers
173 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 ...
0
votes
1answer
250 views
Change of bin magnitude when phase of signal changes when doing FFT?
I am working on an implementation in which I need to apply an FFT to determine which of 4 frequencies are present in a signal.
I am doing a 64 point FFT on a buffer which only is partly filled (the ...
1
vote
1answer
168 views
Obtaining the magnitude of the frequency response by plugging $e^{jω}$ 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 $e^{jω}$ into the z-domain transfer function $H(z)$. In ...
16
votes
3answers
6k 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 ...
0
votes
0answers
177 views
Constant phase for each frequency?
FFT of some signal $x$ has two parts: $|x|$, which is the magnitude spectrum and $arg(x)$, which is the phase spectrum. I want each frequency to have the same phase. Is there a way to accomplish this?
