Questions tagged [frequency-spectrum]
The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain.
1,309
questions
1
vote
0
answers
18
views
Power Spectral Density and Total Power Calculation for Signal
I am currently working on analyzing a signal with the autocorrelation function given by:
$$R(\tau) = 100 \cos( 10000\pi\tau) (Λ(2000\tau))^2$$
I need assistance in plotting the power spectral density ...
1
vote
0
answers
27
views
Spectrum and Fourier transform of a sine wave
Take for example: $x(t)=A\sin(2\pi f_0t)$. The Fourier transform of this signal is $\hat{s(f)}=\frac{A}{2i}(\delta(f-f_0)-\delta(f+f_0))$. If we want to represent the spectrum of the signal we would ...
- 11
0
votes
0
answers
17
views
Allan variance plot does not match with the true plot
I am trying to simulate an Inertial Measurement Unit (IMU) by generating sample noisy gyroscope and accelerometer data. Currently I am analyzing the simulated gyroscope( gyro)
data. Using the noise ...
- 163
1
vote
1
answer
77
views
Fourier transform magnitude of the sum of two signals
Let
$$\mathscr{F}\Big\{x_1(t)+x_2(t)\Big\}=X_1(f)+X_2(f)$$
I think that in general
$$\big|X_1(f)+X_2(f)\big|^2\leq\big|X_1(f)\big|^2+\big|X_2(f)\big|^2$$
but I was wondering if
$$X_1(f)X_2(f)=0,\qquad\...
- 31
1
vote
0
answers
27
views
Calculating k-space coverage from antenna positions
I work with radar and I want to understand which spatial frequencies I can measure, i.e. the k-space coverage, given a set of coordinates of transmitter-receiver combinations. The ideal coverage for a ...
- 33
-1
votes
0
answers
51
views
Amplitude and Phase spectrum from fourier transform of sawtooth [duplicate]
Let the following $T$-periodic signal :
then $$\begin{align}F(x(t))(\omega) =& \int_{-\infty}^\infty x(t) \exp(-i\omega t) \mathrm{d}t = \sum_{k=-\infty}^\infty \int_{kT}^{(k+1)T} x(t) \exp(-i \...
- 123
0
votes
1
answer
113
views
Magnitude and phase spectrum of a periodic signal
Let the following T-periodic signal :
I found that
$$ x(t) = \frac{A \cdot t}{T} \qquad 0 \le t < T $$
and its Fourier series is :
$$ x(t) = \frac{A}{2} - \frac{A}{\pi} \sum_{n=1}^\infty \frac{\...
- 123
3
votes
1
answer
134
views
Applying Lowpass filter on a signal in time domain gives ringing artifacts - how to get rid of them
EDITED AND UPDATED:
My signal is an impulse response. In the following figure:
The frequency spectrum of the impulse response (original signal) is shown by blue line.
The original signal is ...
0
votes
1
answer
54
views
jumps in spectrogram of frequency ramping
I create spectrogram of a sine wave that changes its frequency from 60 MHz to 70 MHz over a period of 1 millisecond.
can someone help me understand why I see those jumps? how can I make it smoother?
<...
- 13
1
vote
1
answer
65
views
Why is the FFT of an even real valued vector not real?
I am trying to find the PSD of a signal by taking the DFT of its auto-covariance sequence.
My code is as follows
...
- 25
1
vote
1
answer
46
views
Up-sampling images and the Periodicity of the copies
In the three figures below, $H(e^{j\omega})$, $H(e^{2j\omega})$, and $H(e^{4j\omega})$ are shown. I understand that up-sampling shrinks the spectrum. However, I need a few clarifications:
Why does up-...
- 13
0
votes
0
answers
32
views
Cross-quantilogram method
What is this method in general?
What is the main difference between the quantile cross-spectrum (QS) approach developed by Baruník and Kley (2019) and the cross-correlation function (QS) developed by ...
- 1
1
vote
0
answers
24
views
Noise color in multidimensional frequency space - is there an angular effect or dependence?
I understand that if there is a non-constant level of noise in one-dimensional frequency space, e.g. noise variance increasing linearly with frequency gives "blue noise" in the iFFT space. ...
- 111
1
vote
3
answers
168
views
Real part of signal
A little story. At the university, I did laboratory work on expanding functions into the Fourier series. I have this drawing. My teacher told me he is faithful. But he asked me this question: "...
0
votes
0
answers
18
views
Decomposing Gaussian Diffraction Pattern
I was recommended to post this question here from the physics stack exchange. I have the following diffraction pattern produced by a fabry-perot etalon.
The red represents the center of that pattern. ...
- 1
2
votes
1
answer
44
views
How to test for SNR for an ADC
I have a 24 bit ADC and I need to test for signal-to-noise ratio. I have a function generator which can generate different signals, so can I simply take 10*log10(power of signal/power of noise)?
When ...
- 21
0
votes
1
answer
28
views
How to find Gain when i have frequency of input and output signal
I need to find the bandwidth of an filter, for this im generating frequency of 1Hz to 200 hz in step of 1hz from a function generator Im expecting -3db point anywhere between 1 and 200
The output of ...
- 21
2
votes
1
answer
56
views
How do you average the power spectra across multiple samples to compare 2 conditions?
I have physiological signals from samples under 2 conditions and want to compare the difference in frequency content between the conditions. Specifically,I'd like to compare the average power spectrum ...
- 23
0
votes
0
answers
23
views
GNSS : How to analyze and correct the impact of Doppler rate on Acquisition CAF?
Taking GPS L1C/A cold(initial) acquisition as an example. If there is a doppler rate(Hz/sec) on the received signal and GNSS receiver has performed a mixture of coherent and non-coherent integration ...
- 2,591
0
votes
1
answer
88
views
How to determine the nature (real or complex valued) of a signal?
A signal X(t) is a real valued time domain signal and Y(t) is a signal that only contains the non-negative spectral components of X(t). How do I determine whether Y(t) is real-valued or complex?
I ...
4
votes
1
answer
779
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 ...
- 296
1
vote
1
answer
164
views
Does bandwidth include negative frequencies?
I've seen countless definitions of bandwidth that disregard negative frequencies.
Is that done due to the symmetrical nature of a certain signal eg. a cosine or due to the inherent lack of meaning ...
- 11
2
votes
2
answers
107
views
How can I convert a 1/3rd octave spectrum into a linear spectrum for use as a frequency response?
I have a one-third octave spectrum with 23 frequencies, and I want to use it as a frequency response to filter another spectrum, however that spectrum is specified linear with 2049 points.
I know I ...
- 133
1
vote
1
answer
52
views
What causes sharp peaks in the spectrum of continuous phase BFSK with Manchester coding
I'm currently exploring BFSK and I've stumbled upon a result that I didn't expect. I wonder whether there is an intuitive explanation for it.
The intuition I've had about BFSK so far is that it can be ...
- 123
0
votes
0
answers
15
views
Clarification on video about frequency deviation in phase modulation bandwidth
I am watching this video and at 7:12 he calculates the frequency deviation $\Delta f = f_{c}f_{m}A_{m} $ where the $c$ underscript is for "carrier" and the $m$ underscript is for "...
- 143
0
votes
0
answers
38
views
Combining two time series with different cadences (different Nyquist frequencies)...?
If it helps, I want to do perform the below computation in python.
Two time-series - 30-min cadence (Nyquist of 24 cycles / day) lasting 27 days, followed by 10-min cadence (Nyquist of 72 cycles / day)...
- 101
2
votes
0
answers
61
views
How to retune this mixture of 2 close-frequency sinusoids?
I have a signal which is a mixture of 2 close-frequency sinusoids, something like 1320 Hz and 1325 Hz, with an amplitude envelope which is typical for a musical instrument (ADSR).
$$s(t) = a_1(t) \sin(...
- 491
1
vote
0
answers
77
views
Detect digitally time stretched audio made back to tape
Can anyone tell me how I might detect and measure a digitally time stretched audio signal (Pro Tools) when subsequently made back onto tape?
Could quantization of the signal be detectable on tape and ...
- 11
3
votes
1
answer
529
views
removing spikes from spectrum
I am working on 50 samples obtained from time domain signal by FFT. It appears at certain frequencies which are -- according to our experimentalist -- due to some issues with their oscilloscope. What ...
- 91
0
votes
0
answers
40
views
Why does FFTPack 5.1 not give the same complex numbers as Matlab's FFT2 command does?
I'm doing FFT2 with FFTPack 5.1 and it's working great. But it does not give the same result as Matlab's FFT2 command.
Turning Time domain -> Frequency domain -> Time Domain give the same result ...
- 403
2
votes
1
answer
56
views
Comparing results for spectrum generating in matlab using STFT and Filterbank approach
To analyse data in the frequency domain I often use functions like stft() in Matlab. Inspired by this video and this article I have compared the results of ...
- 380
1
vote
2
answers
199
views
How to do FFT with complex numbers - Ansi C code
I have a small issue.
I'm going to do FFT2 onto a matrix $X$, and the only library I have is FFTPack. FFTPack is the oldest FFT library, but it's one of the fastest and 100% portable too.
The problem ...
- 403
1
vote
1
answer
107
views
Three dimensional Wiener-Khinchin formula for incompressible isotropic random field
When I am reading Uriel Frisch's book "Turbulence", on page 55 he claimed that the Wiener-Khinchin formula for an incompressible isotropic random field, such as the velocity field of ...
- 63
1
vote
2
answers
226
views
Overall spectrum computation from Short-Time-Fourier-Transform
I am trying to computing the overall spectrum of a given signal from its Short-Time-Fourier-Transform. I am using python to do this and I wrote my function to compute the STFT:
...
- 113
0
votes
1
answer
292
views
Why do we have negative sign dB in spectrum in audacity?
I am trying to understand the spectrum of the sound of a cuckoo. It is 13-second audio clip and its download link is
https://file.io/d4nqddrb1NNY
Actually, I have a confusion, I have attached a snap ...
- 1,850
1
vote
1
answer
60
views
Separate two images using a statistical approach
So I have a fundamental question (for which I can't find a good answer anywhere). Say we have two images (A and B) and their mixed image (C) as follows:
Now say that I've been given Image (A) and ...
2
votes
0
answers
25
views
Event-related EEG (epoch averaging) as a form of inter-harmonic bandstop filtering?
There is a matter that comes to my mind from time to time, now I describe it in detail.
Anyway I am a first year PhD student, doing research in the field of cognitive neuroscience, but yet I only have ...
1
vote
3
answers
134
views
FMCW Radar - What's wrong with the transmitted signal model?
I am new to FMCW radar and trying to plot the transmit signal over time.
As you know, the transmitted signal is modelled as:
$$s(t) = cos(2\pi f_c t + \pi S^2),$$
where $S = BW/T_{chirp}$ is the slope,...
- 13
1
vote
2
answers
196
views
How to use MUltiple SIgnal Classification (MUSIC) algorithm to detect the wavenumber of a received signal at array of sensors?
I am working on analyzing data obtained from Fiber Optic - Distributed Acoustic Sensor (DAS) to estimate the properties of acoustic waves that impinge FO cable, such as velocity of acoustic waves. FO-...
- 153
0
votes
1
answer
183
views
MUltiple SIgnal Classification (MUSIC) for Frequency Estimation
I am trying to use MUSIC algorithm to detect individual frequencies of an incident signal. I read the original paper and some interesting books that explain the algorithm. I used the following ...
- 153
2
votes
1
answer
94
views
Does subtracting a phase from the frequency components of a DFT output result in rotation?
I'm currently reading a paper (Page 23 of the PDF) about the application of the Fourier transform to standardize some climatic data to easily compare them.
I have the following text :
2.3 ...
- 53
2
votes
3
answers
771
views
Why does spectrum magnitude decay away from DC for positive signals?
I would like to understand why the second frequency component usually has the greater magnitude within the range [1, (N/2)], i.e why (I remove the DC component and ...
- 53
0
votes
1
answer
62
views
Decimation effect on the spectrum
If I have a sampled cosine wave signal with Fc = 80kHz and Fs = 200kHz (so the Nyquist region is between 100kHz and -100kHz) and I want to preform a decimation by the factor of 2.
Will my input signal ...
- 15
1
vote
1
answer
55
views
How to calculate energy of a signal whose frequency is varying with time (like chirp signal or any audio signal) using Fourier coefficients
If I have two audio signals, say $A_{1}$ (music) and $A_{2}$ (Speech), I want to calculate the energy of the two signals for their relative comparisons. One method I can use is by adding the square of ...
0
votes
2
answers
167
views
Is it possible to predict the peak value of a time-domain signal from its frequency-domain spectrum?
As the question states, is it possible to predict the peak value of a time-domain signal given its frequency-domain spectrum?
Since the time-domain signal is just the sum of the individual sinusoids ...
- 296
0
votes
1
answer
76
views
Demonstrating linear filters on daily weather data
I have daily temperature data from some place on Earth. Apparently, the sampling frequency f_s = 1/day.
I would like to use these data to demonstrate (visually) the use of low-pass, high-pass, and ...
- 233
0
votes
0
answers
42
views
How to represent nonuniform resampling of signal using math functions?
I am working on optical coherence tomography algorithm. In main pipeline I should use nonuniform resampling to eliminate transformation of optical signal in IR-spectrometer (that signal disperses by ...
2
votes
0
answers
167
views
MUSIC Algorithm for 2D Power Spectrum
I am trying to use Frequency-wavenumber analysis for estimating speed of sound using two-dimensional data obtained via channel of arrays. The traditional technique is to use FFT to transform the data ...
- 153
2
votes
2
answers
433
views
What is the explanation that filter EQ changes "Ah" to "O"?
I recorded myself saying "Ah" in the tone of the note C3 which is about 130Hz, this is what it looks like:
Then I ...
- 135
1
vote
2
answers
398
views
Can someone explain the phase spectrum of a sinc function?
The Fourier transform of a sinc function will result in a rect function. Suppose I have a discrete time-domain sinc function with a frequency of $\omega_0 = 0.1$ Hz and amplitude of $A = 10^{-3}$:
If ...
- 296