Questions tagged [magnitude]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
5
votes
3answers
868 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 ...
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
votes
2answers
152 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/...
0
votes
2answers
41 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
1answer
128 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 ...
2
votes
2answers
323 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 ...
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_{...
1
vote
1answer
47 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
votes
1answer
61 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
vote
1answer
140 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
2answers
58 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 ...
1
vote
3answers
149 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
0answers
30 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
votes
1answer
42 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 (...
0
votes
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 ...
5
votes
2answers
7k 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
23k 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
3answers
60 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
38 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 ...
2
votes
3answers
226 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. ...
1
vote
1answer
155 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,...
0
votes
2answers
65 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
80 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
2answers
526 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
85 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
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(...
1
vote
3answers
271 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
103 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
919 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}(\...
0
votes
1answer
235 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
137 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
199 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 =...
1
vote
1answer
807 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 ...
3
votes
3answers
49k 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 ...
0
votes
1answer
59 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
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 ...
3
votes
1answer
283 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
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 = \tan⁡\left(\frac{\pi \times f_c}{f_s}\right) = \tan\left(\frac{...
0
votes
1answer
97 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
877 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
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 ...
0
votes
1answer
755 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
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
451 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
259 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
13k 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 ...
2
votes
1answer
494 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 ...
0
votes
1answer
160 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
2answers
437 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 ...