# 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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### Can I "reverse" spectral leakage by solving a linear system?

When I compute a spectrogram of (say) a piece of music, there is a lot of frequency "smearing." Often we can reasonably expect that the "true" generating process is much sparser in ...
14 views

### Probability of the rate of change of a filtered random process

I am given the following problem: I have a filter with impulse response $h(t) = e^{-10t}, t \leq 0$, and autocorrelation function of the input signal, which is WDS and Gaussian with median equal to 0, ...
29 views

### Why aren't I getting my expected FM channel when multiplying these two frequencies?

Hope y'all are doing well. Recently I've picked up a LimeSDR and interfacing it with GNURadio and been having a blast with it. I got my first FM receiever demo working using examples from LimeSDR FM ...
1 vote
36 views

### What is the best way to decide whether a periodic signal is present in a noisy environment with a limited number of samples?

Suppose I have few samples (e.g. 20) of a decaying sinusoidal function and I am heavily noise-dominated (SNR ~1, noise is Gaussian or Poissonian). Let's think of e.g. \begin{equation} y(t) = A \, \sin(...
39 views

### Multiplication in frequency domain for a signal containing a whole frequency spectrum

Imagine we have two signals in the frequncy domain X(f) and H(f), for one of the signal H(f) I have the complex pair and the frequncy at which that complex pair exists. The second could be any random ...
39 views

### Extract a signal from noise, so I can view noise spectrum only?

I have a perfect modulated signal. I have the same signal but with noise, this noise is from non linear amplification. Is it possible, to extract the clean signal so it's just leaving the noise? The ...
51 views

### Autocorrelation and the dot product of complex signals

I have a question for the signal processing community. When trying to calculate the autocorrelation of an array containing complex data, could the result be purely imaginary, and is there any ...
50 views

### Examples & Applications of Quadratic Phase Coupling

Quadratic phase coupling is defined as follows: Consider the signal $$x(t) = A_{1} \cos(\omega_{1}t+ \phi_{1}) + > A_{2}\cos(\omega_{2}t + \phi_{2})$$ which is passed through the quadratic ...
1 vote
83 views

### Why distance index between 2 frequencies in M-FSK has to be odd?

I'm learning about M-FSK modulation from A. Bruce Carlson book, Communication systems. I've seen that ak, an index to select the frequency of each symbol, has to take odd values, spaced by 2 fd (...
35 views

### Which type of noise can we see from the given image signal and its abs of 2D FFT?

1. Background: I get an 128*128 2D one-channel noisy image as follows: I get the shifted absolute values of 2D FFT result by the following Python code: ...
39 views

### Long-Term Spectral Average in Python - question on sound intensity side bar

I have tried this code to find the Long-Term Spectral Average of a given signal. However, I am not sure if the side bar is correct as I was expecting negative values for them. Here are the parameters ...
51 views

### Does LPF limit the maximum sampling frequency of the input signal? [closed]

Consider the system where the signal passes through analog LPF with cutoff frequency of 50 Hz, so the maximum sampling frequency of the input signal could be 100 Hz (according to the theorem). But can ...
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### gmsk: suppression of higher-frequency spectral components

I study gmsk modulation and worked with gmsk implementation, BT = 0.5. I have decided to test with BT = 0.25, which is used for near Earth communicaiton. Spectrum of output signal with BT = 0.5, ...
45 views

### What make sample rate affect QspectrumAnalyzer output?

Use QspectrumAnalyzer to analyze signal,set sample rate as 8M and 32M. I get different output as below,32M sample rate cause ...
66 views

### Spectrum of a baseband digital signal

I'm building a Continuous-Phase BFSK Transmitter using Python and PlutoSDR. Something that I don't understand is the spectrum of the up-sampled baseband signal - the digital 0's and 1's over-sampled ...
84 views

### Phase extraction from Fourier transform

Is it possible in principle to correctly extract the phase from Fourier transform? I just tried to do so using Python, here some attempts: ...
671 views

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### Order analysis on sample vibration data to detect unbalance in python

My main goal is to figure out how to do an order analysis in Python. For this I'm trying to do an order analysis in python to some sample vibration data I found here (with and without unbalance). I ...
128 views

### FFT with High Time and Frequency Resolution

Can anyone describe in a bit more detail or provide references to the techniques for simultaneous enhancements to time and frequency resolution described in a high level in this video? Can anyone ...
25 views

### Phase Spectrum 0 Phase

I am a beginner in signal processing. I am learning about the Fourier transform. I was working on the zero-phase Ricker wavelet. As I understand If I extract the phase spectrum I should get something ...
62 views

### Confusion understanding Fourier series line spectra?

I am reading book signals and systems Laboratory with MATLAB where I am studing chapter 5, Fourier series and i trying to understand magnitude spectrum and phase spectrum but i have certain confuisons ...
68 views

### Shift of the signal spectrum to the desired frequency

I have a task to select only the area I need from the signal and shift its spectrum. I am digitizing the signal at 48kHz. A useful signal for me is in the region of 5500-5995Hz and 6005-6500Hz. In ...
46 views

### (Dis-)connecting a stochastic signals spectrum from its pdf

How might one generate a sequence of N pseudo random numbers that simultaneously have an e.g. pink spectrum and are gaussian distributed? A hunch would be to first generate an uncorrelated white ...
1 vote
34 views

### How does under sampling modify the spectrum of a signal in nyquist zones and BW?

I have two conflicting concepts when looking at the spectrum of a analog to digital signal that has been sampled. The nyquist zones. So any sampling frequency fs will make the spectrum replicate at ...
149 views

### Plot Power Spectrum of Noisy Image in Python

I've been asked to plot the power spectrum of an image where I added Gaussian noise to it. However, I am very new to Image Processing so I don't know exactly how to approach my problem. I calculated ...
50 views

### Combining multiple signal acquisitions to produce one big FFT

I found myself in working with an FFT that does not have sufficient frequency resolution and I would like to increase this sensitivity. Since I have to perform this FFT on multiple noise acquisitions (...
28 views

### Inferring shape of information signal from its DFT?

I came across this question recently, and I am very confused by (b)(ii). b(i) gives $x_n$ = [0.5, 0, -0.5, 0]. My approach to (ii) was to recognise that $X_m$ represents the frequency content of the ...
41 views

### what the difference between spectral density and the power spectral density?

What is the difference between the spectral density and the power spectral density, Or they are the same thing? In fact, I find this term in the book of GODA 2000.
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### How to draw the PSD from a time series

I try to draw the spectral density of a time series in order to compare it with the theoretical one. Please can any one help me to do this. This is the time series of all the data. Thanks Dan Boschen ...
1 vote
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### How to detect and distinguish oscillations in a signal?

I would like to detect oscillations in a signal $s$ and determine the nature of the oscillations, i.e. whether they are high-frequency oscillations or not. Edit : An example of $s$ is given below : ...
1 vote
27 views

### magnitude spectrum

I have an ECQ signal of 360 Hz sampling frequency. I used an FFT to extract the frequency spectrum of my signal. Now I don't know exactly how to interpret this plot. How can I know the noise from ...
466 views

### Why do transients exist when we input a sine signal to an LTI system?

Let $x[n]=a\cos(\omega_{0}n)$, if we pass it towards an LTI system, we should get as an output: $$y[n]=a|X(e^{j\omega_{0}})|\cos(\omega_{0}n+\phi_{X}(\omega_{0}))+\operatorname{transients}$$ My ...
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### Power spectral density and auto correlation function: Frequency vs time representation

I have a time correlated periodic signal $a(t)$ with $t=0,1,...,T$ and $a(t+T) = a(t)$ that has been sampled at rate $\Delta t$ and I analyse the signal using the PSD via FFT and the ACF. As far as I ...
796 views

1 vote
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### How to restore time domain signal after multiply cosine signal when cosine signal has unknown initial phase?

I use AD9954 as cosine signal generator,then use ad835 to multiply this cosine signal with antenna signal. As ,the antenna signal frequency shifted after ad835,then ...
23 views

### Does different frequency signal cause different voltage from antenna?

When antenna received signal,antenna generate voltage,then SDR convert voltage to I=amplitude*cos(t)and I=amplitude*sin(t). When ...
1 vote
32 views

### Simulated Room Transfer Function

I need help obtaining a simulated transfer function in a simulated room. I have created image sources for first and second order reflections, and am assuming a point source for my source. I have the ...
1 vote
102 views

### Understanding $\mathsf{FFT}$ of $x(t):=\cos(2\pi f_{0}t)$

I have been buzzed about this issue for more than an hour. I have been tasked to execute a simple DTFT task using MATLAB for the signal $x(t):=\cos(2\pi f_{0}t)$. Assuming we are sampling at a rate of ...
69 views

### Signs of waveshaping polynomial coefficients

I'm playing with some basic functions for distortion purposes. Odd order polynomials generate odd harmonics, even order polynomials generate even harmonics. When I combine them, both types occur at ...
1 vote
23 views

### What metrics should I use to describe the difference between two magnitude responses in octave band

Suppose that I have two frequency responses $H_1(k)$ and $H_2(k)$, I want to describe the difference or MSE between them in each octave band. The background is that I have a target frequency response \$...
1 vote