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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220 views

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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3answers
5k views

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) ...
5
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0answers
656 views

Spread-spectrum systems and multipath fading

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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0answers
256 views

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 ...
3
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0answers
551 views

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 ...
3
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0answers
932 views

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 ...
3
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0answers
4k views

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 ...
3
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0answers
100 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 ...
3
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0answers
1k views

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 ...
3
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0answers
846 views

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 ...
2
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0answers
47 views

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 ...
2
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0answers
58 views

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 ...
2
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1answer
117 views

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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0answers
27 views

Proof that the Lomb-Scargle periodogram reduces to the classical periodogram when the sample is equally spaced

If we have a equally spaced sample, we can use the conventionally used periodogram: $$P_x(\omega) = \frac{1}{N_0}\left[\left(\sum_j X_j\cos \omega t_j\right)^2+\left(\sum_j X_j\sin \omega t_j\right)^...
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0answers
130 views

Frequency resolution - resolution BW relation for different window functions

I am working on FFT based spectrum analyser and I am not sure how to proceed calculating the RBW. According to the document (page 20) in the link, RBW described as $k \frac{f_s}N$ where $f_s$ ...
2
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0answers
103 views

How to calculate the Fourier Transform of a solvable chaos waveform?

Recently I am stucking in frequency estimation of a solvable chaos waveform. Its local analytic expression in time domain is $$ z(t)=s_m(u_m-s_m)e^{\beta(t-mT)}\cos(\omega_0 t+\varphi),mT\leq t<(m+...
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0answers
148 views

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 ...
2
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1answer
636 views

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 ...
2
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0answers
144 views

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 ...
2
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0answers
244 views

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 ...
2
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1answer
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 ...
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0answers
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 ...
2
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1answer
5k views

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 ...
2
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0answers
35 views

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 ...
2
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0answers
40 views

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 ...
2
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0answers
563 views

Doppler shift using PLL

I am trying to apply phase lock loop to calculate phase shift due to doppler effect and finally calculate the doppler frequency($\Delta f$). I am assuming that the received wave is of the form, $r(t) =...
2
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0answers
842 views

What are variance and bias in spectral estimation (specifically periodogram spectral estimation)?

So far, I have read that all the non-parametric estimation techniques decrease the frequency resolution in order to decrease the variance in the spectral estimate What is the general "overview" ...
2
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0answers
3k views

Spectral Correlation Function estimation using FAM method — implementation help

I am trying to estimate the Spectral Correlation Function by the FFT Accumulation Method (FAM) in Matlab. The way I understand the FAM method is as this link (see page 6 & 7 for FAM tutorial). ...
2
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0answers
613 views

why wavelet (CWT) doesn't show accurate results always?

hmm any one can help please? I have a signal that contains some modes in it. I've run a CWT transform but I haven't got my desired results. so I implement a test signal that contains freqs [0.1,0.3,0....
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0answers
2k views

Calculating a filter's attenuation at a certain frequency from the Q-factor

I'm using the Web Audio API to make a graphic EQ with four BiQuad filters; a highpass, two bandpass and a low pass: You can see each node representing each filter's frequency. It's working nicely but ...
2
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1answer
183 views

Most appropriate spectral analysis method for a recording of a saxophone note?

I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $...
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1answer
43 views

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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1answer
15 views

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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0answers
29 views

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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0answers
31 views

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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0answers
55 views

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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0answers
21 views

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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1answer
46 views

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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0answers
245 views

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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0answers
57 views

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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0answers
377 views

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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0answers
34 views

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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3answers
60 views

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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0answers
103 views

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 ...
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0answers
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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0answers
157 views

Why is noise a power signal?

1. I'm generating a power signal: ...
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0answers
45 views

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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0answers
141 views

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 ...
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0answers
64 views

Frequency bins too powerful at the start and at the end of each sample computed DFT data

I've taken the following link http://coding-geek.com/how-shazam-works/#comments as a project to start practising and learning signal processing and python programming for me to get started in speech ...
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0answers
70 views

Can I have some feedback on this research paper on vibration diagnostics?

I have submitted this paper "Detecting a Valve Spring Failure of a Piston Compressor with the Help of the Vibration Monitoring" to figshare.com. I would like to get some feedback on the methodology ...