Questions tagged [phase]

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41
votes
5answers
50k views

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 ...
21
votes
1answer
5k views

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 ...
13
votes
1answer
10k 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 ...
10
votes
2answers
1k 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 ...
9
votes
4answers
5k 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 ...
8
votes
3answers
8k 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 ...
8
votes
2answers
7k 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 (...
8
votes
4answers
8k views

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 ...
8
votes
2answers
2k 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 ...
8
votes
2answers
7k 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 ...
7
votes
2answers
534 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 ...
7
votes
3answers
7k 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 ...
7
votes
1answer
986 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 ...
6
votes
1answer
203 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 ...
5
votes
3answers
226 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 ...
5
votes
5answers
10k 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. ...
5
votes
2answers
2k 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 ...
5
votes
1answer
3k 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 ...
5
votes
1answer
721 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 ...
5
votes
2answers
3k 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 ...
5
votes
1answer
389 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 ...
5
votes
3answers
479 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 ...
4
votes
3answers
5k 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?
4
votes
1answer
2k views

Group Delay of a system

Say I have an LTI system whose impulse response h[n] is: $$ h[n] = \delta[n] + \delta[n-4] $$ I want to find the group delay of this system. I know the group delay ($grd$) is defined as: $$ ...
4
votes
2answers
5k views

Extracting accurate phase and amplitude information from FFT with an arbitrary number of samples

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 ...
4
votes
1answer
460 views

What is a Phase Delay filter?

I'm looking at a job spec, detailed below. I'm perplexed as to what is being asked for. Could someone offer a basic understanding of this material? I can imagine a solution may involve performing ...
4
votes
2answers
2k views

Minimum phase systems with pole at infinity

If a system is given by a transfer function in the $z$ domain that has all poles and zeros inside the unit circle except for a factor of $z^{-1}$ in the denominator (pole at infinity), can it still be ...
4
votes
1answer
2k views

Audio Steganography using Phase Encoding Technique

I referred the below papers to understand the working of Phase Encoding,but the explanation is not proper.Just a few steps have been given in brief. ijcsi.org www.ijarcce.com Can someone please ...
4
votes
2answers
4k 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 ...
4
votes
2answers
2k 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 ...
3
votes
2answers
605 views

Do DCT results contain phase spectrum?

I've been working much with numpy.fft lately where just like the documentation says: When the input a is a time-domain signal and ...
3
votes
3answers
9k views

Am I understanding the phase angle from FFT correctly?

Long story short, I have a sinusoidal wave with DC offset going in with a given frequency of say 100 Hz and $\phi = 0$ (which I'm guessing is really $\pi/2$ since it is a sine wave not cosine). I get ...
3
votes
1answer
340 views

Discrepancies between FFT-based Hilbert Transform and FIR filter results

I compared the results of Hilbert Transform as provided in scipy.signal.hilbert() (which is uses I/FFT as you can see in the source code) with its approximation implemented as FIR filter using coeffs ...
3
votes
3answers
161 views

Why make the phase of an FIR filter linear?

I am new to DSP and filter design. It is easy to design an FIR filter with linear phase by making the coefficient sequence symmetric. However, why make the phase linear?
3
votes
4answers
3k 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(\...
3
votes
1answer
4k 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 ...
3
votes
1answer
596 views

Spectral Leakage, Phase and other questions about FFT

I'm currently implementing a voice recognition algorithm using FFT and now some questions came up to me: Spectral Leakage: I know what it is, why it appears and how to solve it using a Windowing ...
3
votes
1answer
731 views

Why is there little emphasis on phase distortion?

I have a question regarding the frequency response of digital filters. Specifically the phase aspect of the frequency response. Why do we not seem to care about the nonlinear phase response in ...
3
votes
2answers
308 views

Should the phase coefficients of the DFT of a real, even input signal all be zero?

The phase coefficients of a real, even input signals should all apparently be $0$ or a multiple of $\pi$. That's a property of the DFT I've learned about in the Audio Signal processing course on ...
3
votes
1answer
599 views

proving that a log gabor filter has 0 DC offset

I have read somewhere online that the log gabor filter has an advantage over the gabor filter, in the sense that it has 0 DC component. How do you prove this property mathematically? Thanks in advance....
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(\...
3
votes
1answer
213 views

Phase spectrum of 2D real function

I am trying to calculate the phase spectrum of a 2D function, $f(x,y)$, where $x$, $y$, and $f(x,y)$ are real, using MATLAB's fft2. Thus my operation is $f(x,y)\rightarrow F(k_x,k_y)$. My function is ...
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 ...
3
votes
3answers
888 views

Phase measurement

I have a problem with phase measuring. I'm acquiring two signal with a USRP (complex signals) with a coherent generator and I want to measure the phase different between them.. One is at 150Mhz and ...
3
votes
2answers
1k views

Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
3
votes
2answers
936 views

Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
3
votes
1answer
169 views

Phase Modulation and Intermodulation Anomaly ? (Spectrum plots inside - **Updated**)

I have a MATLAB script for modelling a two tone signal (a sum of two sinusoids) going through a non linear transfer function (such as an amplifier). The amplitude of a signal is amplified non linearly,...
2
votes
5answers
16k 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 ...
2
votes
2answers
2k views

The need for phase wrapping?

I understand the need for phase unwrapping and the complexity behind it. But, I'm struggling to understand why the phase information gets wrapped between $-\pi$ to $\pi$ in the first place?
2
votes
2answers
302 views

Can the instantaneous frequency be always derived from an analytic signal?

Instantaneous frequency can be defined as a derivative of an instantaneous phase of an analytic signal which can be nicely seen in practice in this example from Scipy's documentation. But it seems ...