Questions tagged [magnitude]
The magnitude tag has no usage guidance.
65
questions
0
votes
1answer
24 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 ...
-1
votes
0answers
18 views
Frequency response and corresponding magnitude response
I'm given this frequency response:
And I want to find the corresponding magnitude response.
My answer is $|H(e^{j\omega})|$ = 1 if $|\omega|$ is within $\frac{\pi}{2}$; 0 otherwise.
Is this correct?
0
votes
3answers
53 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
0answers
35 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 ...
0
votes
1answer
75 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 ...
0
votes
0answers
42 views
Magnitude attenuation by a filter
I have a filter, with coefficients given by W=sin((2*pi*2*Ff*k/Fs)/(2*pi*2*Ff*k/Fs))*h(k), where Ff is the filter reference frequency, k runs from -N/2 to N/2 (N is the order of the filter), Fs is the ...
1
vote
1answer
122 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
164 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.
...
0
votes
2answers
57 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
votes
2answers
220 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
2answers
74 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:
$$\begin{align}
|H(f)| &=\...
1
vote
1answer
75 views
Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$
I'm asked to sample the signal
$$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
14 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
44 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
353 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
50 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
130 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
148 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
88 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
704 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
3answers
845 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
211 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
127 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
185 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
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
vote
1answer
915 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
265 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
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: $500\textrm{ Hz}$
$$e = \tan\left(\frac{\pi \times f_c}{f_s}\right) = \tan\left(\frac{...
0
votes
1answer
85 views
Does a filter need to completely attenuate high frequencies to be considered low-pass?
I'm looking at a system with a frequency response that is: $$H(e^{j\omega})=\tfrac{1}{4}(2\cos(\omega)+\cos(2\omega)+2)$$
I think the magnitude of this system looks like this (not sure what is the ...
0
votes
1answer
819 views
When does the Amplitude Spectrum equal the Magnitude Spectrum?
I had the following question on edX:
I'm failing to understand why the second signal has $M(\omega)=A(\omega)$. First I find the DTFT of the signal:
$$\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
738 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
votes
3answers
6k 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
650 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
votes
2answers
24k 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
414 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:
$$
G^2(\omega)=\frac {1}{1+\left(\frac{\omega}{\omega_c}\right)^{2n}}
...
-1
votes
1answer
240 views
How to implement Cross Spectral Density [duplicate]
I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image.
Reading wiki1,wiki2,wiki3 from wikipedia, and ...
4
votes
1answer
11k views
Identifying the magnitude and impulse response from pole zero plot quickly
I have an exam next week and it's verty certain that a task of this kind will be there.
Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
0
votes
1answer
150 views
Converting magnitude to dBs
I have seen people using 10*log10 and/or 20*log10 while converting magnitude to dBs. What are the differences and which one is valid?
8
votes
2answers
47k views
Power spectral density vs. FFT bin magnitude
What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
0
votes
4answers
2k views
Coherence vs. Magnitude Squared Coherence
currently I am writing my masther thesis. The theory part is about the turbulent wind field generation, where the coherence (not magnitude squared) is used:
$$\text{coh}(f) = \frac{|P_{xy}|}{\sqrt{P_{...
0
votes
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
votes
2answers
408 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
2k 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
136 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
488 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 "...
2
votes
3answers
45k 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
21k 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
774 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})(...
