Questions tagged [frequency-spectrum]
The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain.
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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 ...
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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
$$X_1(f)X_2(f)=0,\qquad\...
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Calculating k-space coverage from antenna positions
I work with radar and I want to understand which spatial frequencies I can measure, i.e. the k-space coverage, given a set of coordinates of transmitter-receiver combinations. The ideal coverage for a ...
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Amplitude and Phase spectrum from fourier transform of sawtooth [duplicate]
Let the following $T$-periodic signal :
then $$\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 \...
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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{\...
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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 ...
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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?
<...
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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
...
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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-...
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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 ...
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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. ...
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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: "...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 "...
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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)...
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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(...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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:
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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 ...
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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 ...
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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 ...
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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,...
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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-...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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FMCW Radar timing of transmission and reception
I have a question regarding the implementation of FMCW radars that seems rather basic to me, but for some reason I am a bit unclear about this.
So I understand that in FMCW radar, transmitter and ...
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Sampling frequencies calculated on paper and in MATLAB not matching
So, I've been working on a signal described by the equation $$y(t) = \cos(2\pi \ |sin(2\pi t)|).$$ On paper, I've calculated a sampling frequency of at least 2 cycles/sec, since the frequency of my ...
