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Questions tagged [phase]

A quantity representing the fraction of cycle of a periodic signal, usually represented as an angle.

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What is the difference between phase delay and group delay?

I'm studying some DSP and I'm having trouble understanding the difference between phase delay and group delay. It seems to me that they both measure the delay time of sinusoids passed through a ...
dB''s user avatar
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26 votes
1 answer
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How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
endolith's user avatar
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16 votes
4 answers
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When concatenating sine waves, how do I phase shift in order to prevent "pops" caused by sudden jumps in amplitude?

I'm writing a synthesizer using numpy and python. I've run into a problem where concatenating sine waves causes 'pops' or 'clicks' when they are outputted to audio, say, via ...
Tim's user avatar
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16 votes
2 answers
3k views

How to build a phase shifter with arbitrary phase shift

Fred, a DSP engineer, goes to his favorite DSP store to do some shopping. Fred: Hi, I'd like to buy a phase shifter. Shop assistant: Hmm, what exactly do you mean? Fred: Well, you know, if you put ...
Matt L.'s user avatar
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13 votes
1 answer
12k views

How to perform carrier phase recovery in software?

What are the options for recovering the phase of a BPSK signal in software? The only resources I can find online contain circuit diagrams – there seems to be no one willing to explain this to people ...
Keith's user avatar
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12 votes
4 answers
4k views

Fastest way to compute Arctan2 on an FPGA

Rip Van Winkle here -- is the fastest and least-footprint way to compute an arctan on an FPGA still to use CORDIC? Or is there a way to leverage block RAM and DSP blocks to speed and/or reduce the ...
TimWescott's user avatar
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11 votes
4 answers
9k views

Can a causal filter without phase shifts exist?

When I was studying dispersion of refraction index in semiconductors and dielectrics, my professor tried to explain that if a filter (like a dielectric absorbing some light frequencies, or an electric ...
Ruslan's user avatar
  • 249
11 votes
4 answers
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Calculate and interpret the instantaneous frequency

I'm new to the principle of calculating the instantaneous frequency, and came up with a lot of questions on it. You find them all in a bullet-point list at the end of this text. The text might be a ...
muuh's user avatar
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11 votes
4 answers
11k views

How can a filter have zero group delay?

If you put a wave packet through the passband of a 1st-order low-pass filter, it will be delayed by the group delay of the filter, and remain the same amplitude, right? If you put the same wave ...
endolith's user avatar
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10 votes
3 answers
21k views

How important is it to use power of 2 when using FFT?

Here is the problem. I have a 2D array of data, first column represents the time data and the second column represents the sinusoidal response data, based on the time data. I apply fft and I get my ...
lamia's user avatar
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10 votes
2 answers
9k views

Phase Correlation - Poor Performance on Noisy/Blurred Images?

I have successfully tested 1D phase correlation algorithm to determine vertical shift between two synthetic images. When I moved to real images, however, it is not able to detect translation at all (...
Libor's user avatar
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10 votes
2 answers
3k views

Phase shift and phase spectrum terms in multidimensional signal

I know about phase of a 1D signal. But when I go into higher dimensions like 2D,3D etc, it becomes headache to grasp the concept. What are the terms phase shift and phase spectrum mean in case of ...
devraj's user avatar
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9 votes
3 answers
8k views

Extract Sine Phase and Amplitude - accurate and robust method

This is a followup question to one I asked earlier based on the chat after the answer given by @hotpaw2, and cross-posted from stackoverflow since it was suggested it is more relevant to DSP. I have a ...
KBriggs's user avatar
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8 votes
6 answers
14k views

Meaning of Phase response of a filter? In simple words?

What is meant by phase response of a filter? Often it is associated with restoration of signal shape,so if a filter has linear phase response, its output looks like input otherwise output is ...
DSP_CS's user avatar
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8 votes
3 answers
6k views

What is the difference between phase noise and frequency noise?

I'm reading Audoin and Guinot's The Measurement of Time: Time, Frequency and the Atomic Clock, and ran across a confusing an interesting passage (Section 5.2.5, pp 72-73): The physical origins of ...
mpdonadio's user avatar
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8 votes
3 answers
10k views

baffled by fft phase spectrum!

A very simple MATLAB experiment: f = 200; fs = 1000; t = 0: 1/fs : 1; x = cos(2*pi*f*t); plot(angle(fftshift(fft(x)))); And here's the output: Now, made ...
user4673's user avatar
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8 votes
2 answers
2k views

Negative group delay and envelope advance

I am having a doubt reading about delays in signal processing. Let there be an input to a LTI system with frequency response $H(f)$, given signal $x(t) = a(t)\cos(2\pi f_ot)$, where $a(t)$ is a ...
Dsp guy sam's user avatar
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8 votes
2 answers
978 views

QAM constellation slicer with unknown carrier phase

As shown in the image, I have a 16QAM constellation that is misaligned due to a phase rotation. In this case you can see that rotation amount is approximately $\theta = \pi/4$, but this won't be the ...
user827822's user avatar
8 votes
5 answers
30k views

What is an Intuitive Explanation of the Phase of a Signal

I understand that the meaning of the phase response of a system is simply how much the system delays a frequency component. However, I do not find an intuitive explanation for the phase of a signal. ...
hbak's user avatar
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8 votes
2 answers
4k views

Confirmation on how to calculate phase differences at every frequency point between two wideband signals?

I have a problem that I thought was going to be simple, but it has become surprisingly stubborn and I question my method... I have used the method (described below), but I wanted to confirm that ...
Spacey's user avatar
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7 votes
1 answer
226 views

Variant of discrete fourier transform that isolates phase delay?

I'm not quite sure of the mathematical terminology here but... Is there a variant (or post-processing) of a Discrete Fourier Transform that separates the shape of a signal from any phase shift ...
finnw's user avatar
  • 401
7 votes
1 answer
1k views

Removing a sinusoidal artifact from a set of movie frames

I am doing some post-hoc analysis of a dataset consisting of a series of movie frames that are contaminated by a strongly periodic artifact. I would like to remove this artifact from my frames. For ...
ali_m's user avatar
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6 votes
5 answers
24k views

Best method to extract phase shift between 2 sinosoids, from data provided

I have been asking around if the way I was extracting phase shift (lag) was correct, and I ran into some trouble. So in general, given 2 arrays of data of the same length, representing: the input ...
user3723's user avatar
  • 135
6 votes
3 answers
2k views

Understanding FFTs for simple Circular Function (sin/cos)

Background : 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 ...
Jonas Jo's user avatar
6 votes
1 answer
612 views

Getting phase response from magnitude. How to develop and solve this Hilbert transform?

I'm trying to generate phase data from magnitude data in a frequency function, assuming the system is minimum phase. Using Hilbert Transform. For instance, having this simple system: $G(s) = s$ $G(j\...
Leandro Alsina's user avatar
6 votes
2 answers
156 views

Best parameter to estimate image reconstruction quality?

Context: I am a PhD student in physics and right now I am studying phase retrieval with low illumination With two different parameters I obtain these two images: With hight illumination (less noise) ...
MementoMori's user avatar
6 votes
2 answers
6k views

Effect of Hanning Window on phase of FFT

I'm calculating the beat of song through the frequency domain. I have 60 seconds of audio sampled at 48000Hz, multiplied by a Hanning window in the time domain. This gives me a resolution in the ...
ablatner's user avatar
6 votes
2 answers
3k views

What is the right way to extract particular frequency phase information from FFT?

Signals acquisition: Two proximity sensors are positioned Orthogonal to each other. These would be measuring the vibrations of a rotating shaft. Problem: Each of these 2 signals has two dominant ...
Agni's user avatar
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5 votes
3 answers
597 views

Group delay of $H(\omega)= 1- re^{j \theta}e^{ - j \omega} $

I'm studying chapter 5 of Discrete-Time Signal Processing 3rd edition by Alan Oppenheim and I'm having serious difficulties understanding how he obtained equation 5.57. For those who don't have this ...
VMMF's user avatar
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5 votes
1 answer
8k views

Phase synchronization in BPSK

In BPSK for demodulation at the receiver end we do phase recovery between received wave and carrier wave. We can find the phase difference between the carrier and received waves using : PLL And ...
Sate's user avatar
  • 121
5 votes
2 answers
426 views

Group delay compensation for non coincident drivers

Suppose I have a two-way speakers system which can be modeled as a two-way Linkwitz-Riley crossovers network with impulse responses $h_{lp}(n)$ and $h_{hp}(n)$. I would like to equalize the group ...
Spark123's user avatar
5 votes
1 answer
1k views

Why can't realisable IIR filters have linear phase?

I am studying IIR Filter Design and came across this arbitrary statement in my textbook which says that 'physically realisable and stable IIR filters can not have linear phase'. Would really ...
Devesh Lohumi's user avatar
5 votes
2 answers
1k views

How can I experimentally find the bandwidth of my PLL?

I recently designed a phase-locked loop. I would like to quantify its bandwidth so that I can better understand it. However, I made this bandwidth in an informal manner due to my lack of formal ...
ExactPlace441's user avatar
5 votes
1 answer
6k views

How does time shift correspond to phase change in a discrete signal?

I was watching this video where the presenter remarks: For a discrete signal, time shift corresponds to phase change in a discrete signal but not vice versa. I was trying to figure out how this ...
curryage's user avatar
  • 419
5 votes
1 answer
31k 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 ...
thileepan's user avatar
  • 183
5 votes
1 answer
485 views

Group Delay for Hilbert Transformer and Resulting Dispersion

An ideal Hilbert Transformer shifts the phase for all positive frequencies by $-\pi/2$ and all negative frequencies by $+\pi/2$ while maintaining constant magnitude everywhere. Group Delay is the ...
Dan Boschen's user avatar
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5 votes
1 answer
1k views

Phase Locked Loop Basics

I am trying to better understand discrete-time PLLs. I drew a picture of a simple feedback system here: I want to be able to describe and understand the system at v(t) and y(t). I found a fairly good ...
Kyle Weller's user avatar
5 votes
1 answer
467 views

Filter design with a phase delay specification?

Given a desired filter magnitude response, plus acceptable linear phase and minimum phase FIR filter approximations, how can one design a filter with the given response and a delay specification of ...
hotpaw2's user avatar
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5 votes
3 answers
986 views

Continuous phase for phase delay calculus in FIR filters

I would like to estimate the phase delay accurately for any random FIR filter. The definition of the phase delay is the continuous phase divided by the angular frequency (with a sign change). That ...
IvanC's user avatar
  • 61
5 votes
2 answers
10k views

What effect does rotation in the spatial domain has on phase in Fourier transforms?

More precisely, let's say I apply a 45 degrees rotation to an image (in the spatial domain) say, in Matlab : Ir=imrotate(myImage,45,'crop'); FT_I=fft2(I); In the ...
SheppLogan's user avatar
5 votes
1 answer
128 views

Interpolation of STFT between time and frequency bins

I am trying to identify and remove airplanes in a time series obtained at a radio meteor receiver. Here we have a spectrogram which displays the power content of my signal as a function of frequency ...
Vakeras's user avatar
  • 51
4 votes
2 answers
2k views

Correcting phase response of a signal

I have a sensor that applies a frequency dependant phase alteration to my signals. I'm trying to find a way to correct these phase responses using an FIR filter. Essentially, I'm looking for methods ...
RTbecard's user avatar
  • 189
4 votes
2 answers
328 views

Accurate phase calculation in sinusoidal linear regression?

I've been trying to work out a way to minimize the error in phase calculation. The underlying model is the following $$s(t) = \sum_{i=1}^{M} A_i\sin\left(\frac{2\pi t}{T_i} + \phi_i\right) + \...
Cifer's user avatar
  • 41
4 votes
3 answers
1k views

Fast phase calculation

I need to detect the PSK modulation posted on my previous post (phase difference detection) with 8 to 16 phase constellations (depending on selected baud rate) over a max $60^\circ$ PSK phase range. ...
user49745's user avatar
4 votes
4 answers
5k views

Evaluation of phase difference between two acquired signals (expected to be sine waves) with the same frequency

I would like to calculate the phase difference between two signals $F(t)$ and $R(t)$ which are expected to be: \begin{align} F(t)&=A_F\cos\left(\omega t+\phi_F\right)\\ R(t)&=A_R\cos\left(\...
Francesco's user avatar
  • 143
4 votes
3 answers
8k views

Converting from a phase response to a group delay response and vice-versa

I'm trying to figure out how to convert any phase response to the corresponding group delay response. Is there a way to do that, and vice-versa if possible?
ion_one's user avatar
  • 195
4 votes
1 answer
214 views

FFT-based phase estimation better than CRLB in MATLAB simulation

I am trying to understand the concept of CRLB for a simple sinusoid in AWGN with a simulation in MATLAB. According to Kay (p. 57) the CRLB for phase estimation is: $var\{\phi\}=\frac{2(2N-1)}{SNR\cdot ...
HaLoe's user avatar
  • 43
4 votes
1 answer
912 views

Why is the phase of the FFT not exactly 0 degrees for a cosine and 90 degrees for sine wave?

Let's say I have two signals. The first is a cosine wave and the second is a sine wave. Each oscillates at 0.01 Hz. The sample rate is 1 Hz and the length of time series is 1000 seconds. Each has an ...
Darcy's user avatar
  • 296
4 votes
1 answer
849 views

Phase Difference Calculation in Frequency Domain

I am currently working on an application in which I have a Linear acoustic array, the audio of which is analyzed using FFT. Now I also want to perform phase difference calculation and have also learnt ...
Emerald_Waves's user avatar
4 votes
1 answer
3k views

How might I go about detecting phase changes in a sine wave of a certain frequency?

I want to detect occasional instantaneous changes in the phase of a sine wave. I have a signal that is a sine wave whose frequency is in the kHz range and experiences random changes in its phase. I ...
SomeRandomPhysicist's user avatar

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