Questions tagged [magnitude]

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2
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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
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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 ...
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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
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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
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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
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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(...
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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
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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
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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
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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
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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
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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
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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 ...
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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 =...
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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
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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
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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 ...
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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
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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
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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]\}\ =\ ...
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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
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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
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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: ...
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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
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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 (...
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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
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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}} ...
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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
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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 ...
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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
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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
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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?
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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_{...
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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
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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
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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
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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 ...
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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
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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 ...
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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 ...
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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})(...
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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
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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 ...
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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 ...
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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
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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
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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
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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
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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 ...
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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?