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

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Mathematical justification for zero padding?

This question asks what's the point of zero padding. The accepted answer is certainly very insightful, but I don't understand a big chunk of it: Zero padding allows one to use a longer FFT, which ...
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24 views

Calculating Phase Response for 2 microphones given the input

I want to measure and compare the phase response of two identical microphones. To do this, I have a pressure chamber, which allows to apply the same pressure to both microphones. I apply a sweeped ...
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1answer
40 views

Elegant way of calculating minimal sampling frequency without aliasing for annoying signals

Given a symmetric Fourier transform with finite support as below, there's an algorithmic procedure to determine the minimal frequency for sampling without aliasing: Find an integer $L>1$ ...
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38 views

MATLAB center frequency shift

I am wondering how to shift the center frequency of the below complex data from 0, to say 20 MHz (10 MHz to 30 MHz- 20 MHz bandwidth). I tried to change the indexing of the bins but I could not get ...
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1answer
21 views

Difference between PSD estimate and variance of DFT

In Bartlett's PSD estimate one averages over L segments of the squared DFT coefficients. From wikipedia I found this formula $$ \textrm{PSD}(k) = \frac{1}{L}\sum_{l=1}^{L} \frac{1}{M} \lvert X^{[l]}(...
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51 views

Butterworth filtering behaving unexpectedly -MATLAB

I'm new to signal processing but I'm trying to understand how the Butterworth filter works. To do so, I did the following: I assumed a sampling frequency of 100Hz and wanted to attentuate everything ...
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2answers
44 views

What's the meaning of the continuity in spectrum analysis? [closed]

We all know that for any, suitable, kind of signal $f(t)$, there corresponds a Fourier transform function $F(j\omega)$ such that $$ f(t) = \frac{1}{2\pi} \int_{-\infty}^{+\infty} F(j\omega) e^{i\...
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1answer
34 views

Finding the maximum and minimum frequency of a 2D image

Suppose I transform the image into frequency domain and obtain a 2D array of complex numbers. How can I determine the minimum and maximum frequency from that array? By finding magnitude of each ...
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1answer
40 views

System identification/ Filter estimation to mimic frequency equalizer of audio with Scipy

At the current problem I'm working on, I have two signals: One "original" signal that contains audio (voice). The second signal is the same audio file but edited with a frequency equalizer, for ...
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1answer
42 views

midpoint smoothing spline

Suppose we have a time series which have peaks and troughs.(The red curve below) I would like to get an algorithm which is able to identify the peaks and troughs locations, then find the midpoint ...
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23 views

Spectrum of OFDM with raised cosine window(overlap and add)

I'm having trouble observing OFDM with a raised cosine (RC) window in Matlab. I know how to generate an OFDM signal with a raised cosine (RC) window, I just don't understand when the last W samples ...
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0answers
16 views

generate 1D periodogram from noise spectrum

I have computed the noise power spectrum $S$ from an input image. Basically, I get spatial frequencies i.e. F (lower range = 0 , high range = some high value) and the corresponding noise values for ...
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2answers
59 views

Frequency resolution of DFT

I know that the frequency resolution in a DFT is given by sampling rate upon the total number of samples. $$\Delta f = \frac{f_s}{N}$$ But, what I want to know is where does this relation comes from? ...
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1answer
39 views

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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2answers
75 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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1answer
32 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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0answers
61 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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2answers
48 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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1answer
28 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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2answers
64 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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1answer
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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2answers
45 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
95 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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2answers
52 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
67 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
48 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
27 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
59 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 domain....
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2answers
92 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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68 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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2answers
118 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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2answers
150 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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46 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
74 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
55 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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0answers
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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1answer
56 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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3answers
92 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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0answers
161 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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119 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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3answers
125 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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1answer
64 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 transducer....
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1answer
45 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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2answers
172 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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2answers
84 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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0answers
8 views

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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87 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 \operatorname{angle}(...