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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How to plot the periodic digital spectrum?

In a previous answer, Dan Boschen wrote (emphasis mine): First let me explain the "unfolded" digital spectrum: If you allow the frequency axis of the sampled signal to extend to $\pm \infty$, ...
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Getting different spectrum from velocity, and position data using Omega arithmetic

I am solving a very long problem and one part of it requires me solving an ODE and computing FFT of the resultant data. Essentially I have a differential equation$\frac{dz}{dt}$ for velocity, from ...
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Cut-off frequency in Fourier-Spectrum of a noise message

I have a problem involving cut-off frequency. I have a voice message in an audio file .mat which have an eletromagnetic noise. I am trying to recover the original message by applying digital ...
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52 views

Difference between Fourier-Transform and FFT of rectangular pulse

I'm trying to find a link between the Fourier-Transformation of aperiodic Signals and the FFT of them. So to start with a basic example, let's take a rectangular pulse with width 0.1s and amplitude of ...
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Using the traditional instruments for measuring high frequency signal

All we know that we can not use the probe for measuring the high-frequency signal (microwave signals). I still can not understand the reason. I have read that the reason because of the wavelength size ...
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107 views

instantaneous frequency for a sum

In the literature, the instantaneous frequency for a signal $s(t)=e^{-j \phi(t)}$ is given by: $$f(t)=\tfrac{1}{2\pi}\frac{d\phi(t)}{dt}$$ This my problem: I have a signal $$u(t)=e^{-j \alpha_1 \phi(...
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DFT frequency resolution exercise [closed]

I have a discrete signal that goes as follows: $$x[n]=[-1,4,-1,0]$$ I have already done the DFT for the signal, with the following result: $$X[0] = 2, X[1]=-4i,X[2]=-6,X[3]=4i$$ But for some reason, I ...
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Power spectral density of surface roughness

I am currently working on understanding how visually and intuitively the power spectral density is the fourier transform of the autocorrelation of a signal. I was wondering if anyone had a good ...
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1answer
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Clarification regarding discrete wavelet transform

One of the books on "Conceptual Wavelets" by Fugal explains some major differences between the undecimated discrete wavelet transform (UDWT) vs. discrete wavelet transform (DWT). In UDWT the scale of ...
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Transmitting image in certain spectrum without mirroring

I have a problem because I want to transmit string at certain frequency that is simple .png with 0 and 1. I simply take height and width of the image and scale it to the bandwidth and time. Then I ...
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3answers
51 views

Creating uneven sidebands with AM + PM modulation?

I am trying to modulate an optical signal such that I create a pair of sidebands with arbitrary phase and amplitude with respect to each other. For example I would be like to be able to modulate my ...
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2answers
415 views

The spectrum of the sum of two periodic signals

Considering the continue, periodic signals $s_1(t)$ and $s_2(t)$, with the period $P_1$ and $P_2$ respectively. Consider now a new signal $s$ the sum of the two pervious signals. I come to know ...
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1answer
59 views

Scaling Function in Wavelet Analysis

I was watching a YouTube tutorial on wavelets https://www.youtube.com/watch?v=wgRgodvU_Ms, where the presenter showed that if we multiply a Gaussian with a sine wave (and follow some other conditions),...
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1answer
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Advantages of the Rotation Translation Operation Before Doing FT Smoothing

I was reading a relatively old paper from the 1970s on smoothing by FT methods (chemistry applications), where the authors show that if we do rotation translation operation on the signal (y- values) ...
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1answer
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Direct Digital Synthesis - Super Sampling - Unknown Harmonics

I'm using a Xilinx FPGA (Virtex) with 4 DDS cores (each supplied a 250MHz clock) used in parallel to provide a samples to a DAC38J82IAAV from TI, 16 bit DAC running at 1 Gsps. The four cores super ...
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Which frequency bins give the best interpolation for the derivative of a function?

A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\...
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Values of angular frequency of discrete-time sinusoidal signal

Why are the values of angular frequency of discrete-time sinusoidal signals in between -pi and pi?
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What is the form of the spectral derivative in the all-positive-frequency notation in DFT?

The Discrete Fourier Transform (DFT) of a function $u:[0,2\pi] \to \mathbb R$ sampled over $N$ equidistant points $\theta_j = 2\pi j/N,\, j = 0, \dots, N-1,$ is defined by $$ \tilde U_k = \frac1N \...
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1answer
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Sampling of frequency response

Let's consider any physical quantity depending on the frequency. For example, the impedance of a certain electrical component: $Z(f)$. Now, imagine to measure it in a continuous interval of ...
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1answer
52 views

Why sine wave leakage in FFT spectrum

The input is three sine waves with different amplitudes and frequencies. After FFT the spectrum shows the correct characteristic of each wave without leakage error. Why does the other spectrum leakage ...
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61 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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2answers
53 views

Fourier transform of a periodic/aperiodic signal

Generally speaking, I know that periodic signals (continuous-time domain signals) with period 2pi/wo have a spectrum with equidistance Delta-impulses of distance w0. My question is that, if we have ...
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1answer
54 views

Square wave function in FFT spectrum

The input function is a 60Hz square wave. From Fourier Transform I know that the frequency on the spectrum is 60,180,300....(2k-1). But there's a series of 120,240,360...(2k) signals appear. I've ...
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3answers
99 views

Frequency response of numerical derivative

Analytical derivative of a function is equivalent to convolution of that function with $s$ in Laplace domain. Numerical derivatives are limited in bandwidth due to finite sampling rate, so they are ...
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1answer
34 views

Finding the phase and frequency of a tone with Doppler. What is wrong in the code?

I am trying to find the phase and frequency of a single tone having a small Doppler (10 Hz). I have the following code. The integration time for the operation (the length of the time vector) is ...
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106 views

Do negative frequencies count towards null-to-null bandwidth?

I am aware that negative frequencies do not normally count towards the bandwidth when transmitting in the baseband. However when specifically asked to look at the null-to-null or zero-crossing ...
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1answer
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How do I make sense of the cosine wave having Fourier Transform coefficients which have infinite magnitude?

To illustrate my question better, consider the Fourier Transform of an aperiodic (as a periodic cosine wave has a Fourier Transform not Fourier Series) cosine wave $$f(x) = \begin{cases} \cos(2\pi ...
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power systems database

I'm having a hard time searching for a power systems database. I need some samples of a real wave form from a power source, like a residential power plug or an industrial one.
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51 views

Calculating Occupied Bandwidth with Spectrum Analyzer Data

Given a spectral plot recorded in F vs dBm, is it possible to calculate or estimate the Occupied Bandwidth. I'm only given the trace reading off a spectrum analyzer, dBm printed out as a csv, and I'm ...
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1answer
37 views

Calculate Frequency/Period from Output of a Maximum Entropy Spectrum MATLAB function

When I plot said function output, "p," it looks like a typical spectrum with an easily identifiable peak at a given ix on the x axis. The help rubric from the function is ...
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2answers
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Matlab and R functions for fft(): N-point FFT and dimension issue [closed]

In MATLAB, Y = fft(X,n,dim) returns the Fourier transform along the dimension dim. For example, if ...
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1answer
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What is Imaginary in Fourier transform?

How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
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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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2answers
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How to reconstruct a sound from magnitude spectrogram?

I have an audio magnitude spectrogram but I don't have the phase, try to randomize the phases of each container and then make a reverse fourier, but only pure noise is heard How can I reconstruct the ...
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1answer
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Adaptive Band pass filter for extracting respiratory waveform from accelerometer data

I am recording data from an accelerometer attached to the chest (1000Hz). I need to extract the respiratory waveform. I tried an adaptive bandpass filter based on a dominant frequency in my signal ...
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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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1answer
106 views

fft function in R vs spec function from 'seewave' package? They don't give a similar frequency spectra

I understand that spec will give me the frequency and the corresponding amplitude of that component, whereas fft will compute the DFT of the signal and throw the complex numbers for each component ...
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3answers
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Characterization of transfer functions with no local peaks

Assume that you are giving an arbitrary amplitude frequency response $A(\omega)=|H(j\omega)|$ Is there a characterization that ensures that $A$ is monotone? i.e, $A$ has a global maximum at $\omega=0$...
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1answer
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Polyphase components Spectrum formula in Discrete time

I am trying to understand the meaning behind some of the components of the formula for polyphase components in discrete time. Note that $\Omega$ indicates discrete in this notation and the formula is ...
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1answer
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How to sketch this multirate system spectrum?

In the following system: The signal x(n) is upsampled by 2 and then filtered. The signal and the filter have the following spectrum: After upsampling the spectrum of X would look the same except ...
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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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How to remove sum and difference terms while computing frequency from fft?

I am currently operating in vhf band AND trying to detect frequencies using Fast Fourier transform thresholding method. While detection of multiple frequencies , i received spurs(May not appropriate ...
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1answer
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How should I remove obvious anomalies from spectral data?

I'm working with raman spectra and it seems that our spectrometer produces some anomalies at very specific wave numbers and I'm looking to remove them from the dataset. Here's a picture of 27 spectra ...
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Moving noise floor spectrum after decimation

Currently I am working in a spectrometer with a stage of decimation previous the fft. In particular I am decimating with a factor of 16 in two stages of 4 each one. I attach a diagram of the model (I'...
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3answers
56 views

Why bit rate is same in a lower frequency spectrum and higher spectrum?

If there is a spectrum between 0 Mhz - 1 Mhz, bandwidth would be 1 Mhz here and for example with baseband we can send 2000 bps. What I can't understand is if spectrum is 5-6 Mhz instead of 0 - 1 Mhz, ...
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1answer
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Why is a first/second derivative useful in spectroscopy?

I'm currently working on Raman spectroscopy and while reading some literature I came across the first and second derivative of a spectrum. It's not clear to me why they are useful to look at since ...
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How does spectral density of a power signal change when it is multiplied by $\cos(2\pi f_ct)$?

Suppose we have a power signal $n(t)$ whose power- auto-correlation function is: $R_{n}(\tau)$. Now we multiply the signal by a cosine as $$\cos(2\pi f_ct) \cdot n(t)$$ whose auto-correlation is $R_{...
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1answer
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Why does downsampling stretch a signals frequency response and upsampling shrink and create images of a signals frequency response?

I am learning some basic DSP and I have a pretty good intuition as to why sampling creates spectral images of the frequency response at intervals of the sampling frequency (convolution with pulse ...
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1answer
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What should be my sampling frequency?

I have an accelerometer that I am reading the x, y, z values for m/s^2. I've written up my code in Python as follows. ...
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55 views

How to find fundamental frequency of two signals?

I am facing difficulty with finding fundamental frequency of signals I mean by fundamental frequency=(1/Time period) Correct me if I am wrong consider two continuous time signals with Time period ...