The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain.

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How do I interpret the result of a Fourier Transform?

For example, I entered the following "equation" into Wolfram|Alpha: FourierTransform[Piecewise[{{sin[t],t > 0 and t < 2*pi}}, 0], t, \[Omega]] So as to ...
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64 views

Does “keying on” a sine wave at a zero-crossing reduce its bandwidth?

I understand that a pure sine wave of infinite duration occupies no bandwidth, i.e. it is only the modulation of a carrier that gives it sidebands. Does the exact timing of a sudden modulation make ...
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26 views

How to calculate Long Term Average Spectrum of an audio file?

I'm working with audio files and I have to find their long term average spectrum. Although I had an option available in the software Praat but I don't understand the algorithm of finding the spectrum. ...
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57 views

DFT of a continuous quasi-periodic signal

If I have a continuous quasi-periodic signal and I want to do a DFT of signal then what could be appropriate length of continuous signal that I should consider for sampling? I want to do DFT of the ...
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46 views

Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)

My apologies for perhaps the stupidity of this question. Presume that one has the 'frequency response' $Y_{data}(k)$ of a system and also has an estimated model $Y_{syn}(k)$ that fits the data. How ...
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27 views

How would Fourier and Cosine Transforms responds to summation of cosines with same frequency but different phases?

For example, if I have two signals, $\cos(2\pi ft+\frac\pi4)+\cos(2\pi ft+\frac\pi3)$, what would be different in both transforms (Fourier and cosine) how would the spectrum changes? And What would ...
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56 views

How to detect decaying oscillations in a signal

I have a sampled signal which contains (among other things) some damped oscillations. From the underlying theory I have reasons to believe that it can be characterized by some specific frequencies of ...
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30 views

sinus generation and it's fft in radians

I'm trying to generate sine signal and display it's fft in radians, byt I meet several issues that I can't understand. Please find my script below: ...
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41 views

Compressing a time-domain signal in the frequency domain Matlab

I'm new to frequency domain analysis. Let's say I have a frequency domain representation from a time domain signal. What I want to do is taking frequencies with a low amplitude out of this frequency ...
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18 views

concerning the usable frequency band of signal

The spectrum amplitude of the response of instruments is generally trapezoid-shaped, with a flat portion in the middle and decaying at higher and lower frequencies. By deconvolving with the ...
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1answer
58 views

Large spike at the center frequency when using Ettus X310

I am using the Ettus X310 SDR and GNU radio. On the GNU radio schema I have a standard UHD USRP source block connected to a GUI FFT sink - basically I'm just displaying the spectrum of the raw signal ...
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35 views

Sampling rate vs sampling time of FFT

I am having some trouble understanding the sampling time and frequency used in the computing of the FFT, and I was wondering if someone could make it clear for me : The Sampling time: the time in ...
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1answer
65 views

Bandwidth expansion by computing missing harmonics in music?

In old recordings or highly compressed audio files (lossy), the higher frequencies are lost, and we hear a distinctive muffling effect. (Just like if the song was played through a wall) Is it ...
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1answer
37 views

Difference b/w Spectral Entropy and Flatness Measure

What is the difference between Spectral Entropy and Spectral Flatness? As far as I understand, both the terms can be calculated from the power (or amp) spectrum, and describe the flatness (whiteness) ...
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1answer
24 views

How to validate an estimated model in case of output-only data (in frequency domain)?

Before moving to the actual question, I would like to emphasize on the following points (maybe they are obvious to some of you, but I still would like to list them, since they make the difference): ...
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1answer
55 views

How to shift a signal to the center of the frequency domain?

Let's assume I have a 1024 x 1024 matrix that represents the spatial domain. After I perform a FFT and center the frequencies, I get the a signal that looks like the following in the frequency ...
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88 views

Explaining / Communicating spectra: Generating Visualizations

I'm very often in the situation that I need to explain / visualize spectrum of signals or frequency behaviour of systems (esp. filters). My favourite, very "textbook" styled way of communicating these ...
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55 views

What is the difference between a'mixer' and a ' multiplier' used in modulation process?

I am not sure if it is valid to conclude that a mixer produces a difference/sum of frequencies at output ,while multiplier produces multiples of frequency at its output. I am keen to know how far I ...
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84 views

Two-Sided Frequency Spectrum

I am trying to make FFT simulation in Matlab by generating noise added two sinus waves in 60Hz and 100Hz. After adding the noise into these signals then I have applied the FFT as I put my Matlab code ...
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138 views

Fourier transform of a Fourier transform

I generate a Gaussian noise and then I filter it with a passband FIR Kaiser window filter. When I perform the Fourier transform of the output of the filter and plot its magnitude spectrum, it is ...
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44 views

Multipath resistance of spread spectrum systems

I have been reading about various telecommunications technologies and one thing keeps being repeated many times without a clear explanation - that spread spectrum is not only resistant to multipath ...
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1answer
72 views

Reduce the number of frequencies after FFT

I have a long signal (1 day sampled at 500 Hz), which results in many frequencies if I calculate the amplitude spectrum (see e.g. here). However, I am only interested in the "big picture", let's say ...
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1answer
49 views

Calculating spectral coherence coefficient (scc) - implementation help

I am trying to calculate the SCC of a cyclostationary signal. I have estimated the Spectral Correlation Function (scf) of the signal using FFT Accumulation Method (FAM). I implemented the following ...
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42 views

Unable to generate and verify a sound wave of frequency 200 Hz

I am trying to generate a sound that contains low frequency in the range 100-500 Hz. I then record the sound using a microphone and generate a spectrum for the recorded signal using ...
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54 views

$\mathrm{FFT}$ generates non-linear noise

I followed the tutorial for generating the frequency spectrum of a signal here, and for testing I generated a sine signal with the frequency of $440 \textrm{ Hz}$. That resulted in the time domain in ...
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1answer
22 views

How to determine the central frequency from a vectorial spectrum analyzer?

I have taken measures of an antenna with a vectorial spectrum analyzer. I need to obtain the central frequency at which the antenna works. In order to do so, I have selected S11 (reflection) and I ...
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88 views

Band-pass filter doubles the frequency

I ran into a strange bug while implementing a complex band-pass filter. The filter design process is based on the windowing method and seems to be working well, but when i apply the coefs of the ...
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126 views

How to design an interpolated notch filter in Python to filter powerline harmonics

I have a a time domain data set that records the magnetic field vs time, which must be processed to reveal an embedded signal. This data also contains power line harmonics (i.e. multiples of 60 Hz) ...
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117 views

Relation between the DTFT and the spectrum of a sampled signal

In the $\rm DTFT$ (Discrete Time Fourier Transform) the spectrum is periodic with period of $2\pi$ . A continuous signal when sampled has a spectrum which is a repeated version of its original ...
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119 views

How to interpret spectrogram correctly?

I have a pressure transducer signal from a reacting mixture available here, which has a sampling frequency of 50kHZ. I have also obtained the spectrogram of the signal with NFFT=256, noverlap=4 as ...
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59 views

Order Analysis Signal Processing

I'm currently working on vibration detection machine used to detect unbalance from a rotating shaft, rotating from 300-2500 Hz. I have both the tacho signal ( 1 PPR ) and the vibration from ...
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1answer
44 views

Fourier Transform of triangle function $x(t)=\Delta\left(\frac{t-1}{2}\right)$

Can you please tell me if my working is right for the Fourier Transform of this function: $$x(t)=\Delta\left(\frac{t-1}{2}\right)$$ My workings are: I have used the fourier transform standard ...
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163 views

why is moving towards higher frequencies so important in frequency spectrum?

As we know, as frequencies becomes higher, bandwidth becomes higher.And, according to channel capacity theorem, channel capacity increases with higher bandwidth. Also, energy is directly ...
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81 views

Why Fourier Transform doesn't show obvious periodicity?

I have a clearly 4Hz periodic signal (see image below). However when I apply a fourier transform, there is no peak at 4Hz. Also, when I do a power spectrum density (using Matlab's pwelch algorithm), ...
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What is frequency warping in regards to vocal tract adjustments?

When we do spectrum smoothing using a filter-bank how can we adjust to different vocal tracts? We do vocal tract length normalization: frequency warping. Can you explain what is frequency warping?
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13 views

Digital filtering - Just set values to 0? [duplicate]

Let's say we want to digitally filter a signal to preserve only relevant frequencies. We calculate the frequency response $F(\omega)$ of the time series data $x(t)$ using the FFT. Imagine that we ...
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1answer
80 views

Recovering phase from spectrogram

In this answer, an iterative algorithm is given for recovering a signal from its spectrogram, assuming overlapping windows: $$ x_{n+1} = \operatorname{istft}(S \cdot \exp(i \cdot ...
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60 views

FSK audio spectrum for demodulation

I am working on Python script to demodulate FSK audio signals. The audio signal contains GPS NMEA strings. I am a beginner in DSP, but trying to work my way through this problem. I think this is a ...
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32 views

Error in summation of spectral components

The error associated with a given estimated spectral component $f(w)$ ($w$ is the frequency) of a Gaussian signal follows a Chi-squared distribution with $\nu=2$ degrees of freedom. For instance the ...
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1answer
90 views

Relationship between the Real and Imaginary parts of a LTI causal system

Prelude I am writing an elaborate text on the relationship between the real and imaginary parts of a LTI causal system and how stability, causality and analyticity imposes various constraints on its ...
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72 views

Matlab fast fourier transform (FFT) function and time in hours frequency : hertz or millihertz?

I have a function of type $$C(t)=0.31 \left(e^{-0.267t}-e^{-1.72t}\right)$$ Where $t$ is in hours The function represents the evolution in a window of 24 hours of a drug blood concentration, after ...
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53 views

Single/ Double sided spectrum plot

After performing the fft transform there are 2 options to plot the spectrum the complex (Real and imaginair) spectrum and the ...
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118 views

Minimum Sampling Rate of Bandpass signal

Consider a DSBSC signal s(t) = m(t).cos(2.pi.20k.t) where say m(t) is multi-tone signal with frequencies less than 5 kHz. The ...
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17 views

SISO model? white noise excitation

I'm now trying to do this problem. I have data set including input and output for both 600 gal and 800 gal, and 3 white noise excitations. But i don't understand the model of this problem. 3 White ...
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274 views

Is R suitable for digital signal processing

While asking a question about representing large time series in R I was discouraged from using R for digital signal processing. I understand that R is geared towards statistics. However, a signal is ...
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62 views

Logaritmic amplitude squarewave

This morning i was experimenting with GNU Octave. I created several signals(Sine, Saw tooth, square wave and noise). After this i used the periodogram. in the periodogram the square wave weren't ...
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27 views

Shifting Signal Components of all Harmonics to a particular Harmonics

I have a Time-Domain signal. After performing the FFT, the signal component I'm interested in lies in 60Hz and it's Integer Multiple. The FFT of the signal is here: I want to shift the component of ...
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13 views

Wireless Resource Allocation Problem: How to acquire channel state information for different frequencies?

I am trying to understand frequency allocation in Dual Hop Relaying S-->R-->D. I have questions about Channel State Information. I am assuming the whole transmission occurs in two time slots and ...
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1answer
36 views

Phase spectrum: $\mathrm{arg}\mathcal{F}(\omega)$ or $\mathrm{-arg}\mathcal{F}(\omega)$?

Do we need minus or not? I need to extract phase spectrum from that thing $$f(x) = \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{i\omega x}d\omega\int_{-\infty}^{\infty}f(t)e^{-i\omega t}dt$$ I can do it ...
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Find unknown broadcast frequency

I'm very new to this stuff, so please excuse the dumb sounding terminology. I'm trying to capture the data from my elster smart hydro meter. How can I find its frequency (I know its between 902 and ...