# 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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### In the formula for the windowed Fourier transform, why is the complex-exponential term not time-shifted to the position of the window?

I have a question about the "windowed / short-time / short-term" Fourier transform that is somewhat perplexing me. I have now added an Addendum at the bottom, where the issue is presented more ...
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### 1/3 Octave Analysis

Good Morning! I am new in signal processing and I am trying to do a work in noise control of an electronic steering lock device (ESL). My aim is to calculate the loudness (Zwicker Method- ISO 532 B) ...
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I didn't find a suitable tag for this, but figured it would fit under "Frequency spectrum". Which of the Spread-spectrum systems listed here are most resistant to multipath fading? Please, briefly ...
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### Question on spatial sampling for non-linear and/or non-uniform arrays

I am a little confused as to how to compute the nyquist criterion for a sensor array that is not linear, and/or non-uniform. For the linear, uniformly spaced case, the spatial nyquist is delimited by ...
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### Linear Frequency Cepstral Coefficients, is Filter bank needed?

I am working on my master thesis on acoustic pattern recognition and have a question to the calculation of cepstral coefficients. I understand the step with a filter bank in MFCC calculation, it is ...
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### Sinc interpolation formula for signal reconstruction in frequency domain from bipolar samples

As per the title, I was wondering if there was a $\operatorname{sinc}$ based interoplation formula for reconstructing a signal in the frequency domain which has been sampled with respect the bipolar ...
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### What's spectral “tilt”?

I am looking at article Speech-in-noise intelligibility improvement based on spectral shaping and dynamic range compression. In paragraph 2.2 the article mentions "tilt" of the spectral envelope. The ...
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### 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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### Convolution of spectra to sensor response function?

I am really sorry if it is wrong place to ask this question but i couldn't not find any stackexchange website appropriate. i have some reflectance values of a material which are measured in 10.5 and ...
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### What is the proper way to select the time-bandwidth product when doing multi-taper spectral estimation?

Frequently programs for calculating the spectrum of a signal using the multi-taper method require the user to specify the time-bandwidth product. What considerations must be made when selecting the ...
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### Getting the right frequency (using FFT)

I am implementing the method from this paper: https://dspace.mit.edu/bitstream/handle/1721.1/66243/Picard_Noncontact%20Automated.pdf?sequence=1&isAllowed=y The main idea is cardiac pulse ...
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### Two versions of Constant Q Transform (CQT) doesn't match each other?

To my knowledge, there's two major CQT papers, the one by Brown in 1991, and the one by Schorkhuber in 2010. The 2010 paper claims to be a more computationally efficient implementation of the 1992 ...
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### Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?

Let $$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$ Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure what will the frequency domain for $Y(\nu)$ look like for a ...
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### Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
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### Is the Auditory Spectrogram the same as the Magnitude Spectrogram?

This is in the context of speech signals. The magnitude spectrogram is computed by framing the signal into short time windows, applying a hamming (or similar) window, computing the fft over each ...
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### What is the correct way to do Short term Fourier transform and extract the phase information from local sections of a signal?

I took a triangular voltage signal and taking it's time derivative I obtained the current through a pure capacitor. Then I took different portion of voltage and current signals, took their Fourier ...
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### NMR spectrum deconvolution on Matlab

I am doing an NMR experiment by applying an rf signal to a sample which is mounted near a magnet and in the end I get an FID (free induction decay) and do Fourier Transform to this FID . So we have a ...
344 views

### How to make sense of audio file's $\textrm{dBFS}$?

I'm trying to build a song visualizer using the FFT method. When I analyze the audio, I get the $\textrm{dBFS}$ value for each frequency range. From my understanding, $\textrm{dBFS}$ is in the range ...
248 views

### 1/f noise generation

Recently I was reading a paper about the pink noise generation. But I don't have any background of this field. I am confused with some part in the paper. First, the Voss's algorithm generated a ...
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### Spectrogram, time vs frequency localization, and length of signal

So I'm having some trouble conceptually and am hoping somebody can clear something up for me. This is long and I apologize for that but I want to provide as much information as possible so that the ...
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### I have a sequence which is made of complex exponentials with arbitrary amplitudes and initial phases. No noise

I have a sequence which is made of complex exponentials with arbitrary amplitudes and initial phases. No noise. That is it is a sum of the complex exponentials of the form $A_i e^{jnw_i+p_i}$. For ...
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### Determining the point in a temporal signal when a periodic behavior begins to occur

I'm a newcomer to digital signal processing, so I'm looking for some general advice and direction on this problem I have. I have a signal like that shown below. Starting around x=40000, you can see a ...
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### What is the best way of filtering EEG signal for the specific frequency band?

I have an EEG data with a sampling rate is 500 Hz. Actually, there are too many ways to filter EEG signals. However, the abundance of options is not valid for me. I have to use a causal, linear-phase ...
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### How do I set window length and shift length for computing STFT on Scipy?

Does nperseg=32, noverlap=16 mean the window length is 32mS with a shift of 16mS? Refer here for more details
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### What is the “Energy” equivalent of the Magnitude Spectrum

I have a semantic issue regarding the discrete spectrum $X[k]$ of a time domain signal with limited length $x[n]$, so we're talking about the FFT. Now, when I what to compare the bandwidth and ...
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### How to determine number of observations based on measurement frequency?

So I'm working on a problem where I'm measuring a signal with two different instruments -- one is a low frequency measurement system (1 Hz), and the other is a high frequency measurement system (200 ...
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### How to take the inverse FFT of Welch's power spectral density in Python?

I have calculated the power spectral density of a weakly-stationary signal using Welch's method (as implemented by scipy.signal.welch in Python), and am looking to take the inverse Fourier transform ...
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### Noise floor flatness in IQ FFT window

I am doing a simple $P_{in}$ - $P_{out}$ linearity test for my RF generator/receiver system. The generator provides an IQ modulated CW single tone with $P = - 80dBm$ at 1 GHz. If we look at the RF ...
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### How to create a wide-sense stationary time series with a frequency of 40 Hz?

I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
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### Definitions of PSD, ESD and Autocorrelation

This question is going to encompass multiple areas and may not have a single answer but here it goes. I'm trying to conceptualize 3 different concepts and how they relate to each other. These 3 ...
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### How to draw a smooth spectrum from a discrete array of measurements at selected frequencies?

I have a AS7265x triad spectroscopy sensor from SparkFun (link) which gives me measurements at 18 individual light wavelengths between 410nm and 940nm. The datasheet says that the FWHM of each sensor ...
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### SNR computation in frequency domain with scipy.fftpack.fft

I have a noisy time series (gaussian coloured noise) to which I add a signal. I call the sum of noise+signal a segment. In the picture you can see an instance: I want to compute the signal-to-noise ...
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### What is the Assumptions behind obtaining Better Frequency Resolution based on Transformation of the Random Variables?

If the sequence is short (N is small), we cannot resolves frequencies being closed together (even by some tricks like zero padding). One way to solve it is to create a pseudo-sequence from the ...
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### How transmission speed and bandwidth are linked?

I don't understand why if I have a larger bandwidth I can transmit data faster. Is this linked with this property of fourier transform? thanks.
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### Conversion between FFT & ASD

I have raw data in units of time (sec) vs acceleration (g). I can convert to to the frequency domain, but am unclear about conversion from an FFT to ASD. For a bandwidth f1 -> f2 is it the sum or ...
389 views

### Spectrum of WBFM signal for triangular message signal spectrum

We Know: Frequency Modulated signal is given by: $$s_{FM} (t)=A_{c} \sin \{ w_c t + 2 \pi k_f \int m(t) \, dt \}$$ Now, if $\quad m(t)= A_m \cos(w_m t)$ , i.e, its spectrum $M(f)$: then, s_{FM} (t)...
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### Why is noise a power signal?

1. I'm generating a power signal: ...
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### Determine 3 most dominant frequencies in a signal, PSD or just the absolute value of a Fourier transform?

I have a noisy ECG signal recorded for 5 minutes. My goal is to determine heart rate every 2 seconds. To find out 3 most dominant heart rates (Beats per minute) in a 2s-signal should I calculate its ...
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### Matching two signals with small time drift

I have two time-domain signals sampled at 100 Hz that were measured using two different oscillators and therefore have a time drift between them. I have two synchronization points, one at the start ...