What is Frequency domain: Definition and 55 Discussions

In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.
A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called transforms. An example is the Fourier transform, which converts a time function into a sum or integral of sine waves of different frequencies, each of which represents a frequency component. The "spectrum" of frequency components is the frequency-domain representation of the signal. The inverse Fourier transform converts the frequency-domain function back to the time-domain function. A spectrum analyzer is a tool commonly used to visualize electronic signals in the frequency domain.
Some specialized signal processing techniques use transforms that result in a joint time–frequency domain, with the instantaneous frequency being a key link between the time domain and the frequency domain.

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  1. EmmanKR

    Finding the Frequency Domain and Time Domain magnetic field

    I was wondering if anyone could walk me though a better explanation on how to get the given results for these two questions. The solutions posted by my professor aren't really clear to me so if anyone is able to better explain how to get the solution it would be much appreciated!
  2. P

    LTSpice functionalities regarding its Frequency Domain Analysis

    The time domain analysis is easier to plot compared to analyzing the frequency with respect to the phase. But, LTSpice makes it look really easy. So, for a small signal AC analysis, LTSpice does use a AC voltage source for its frequency domain analysis function. This must be a really convenient...
  3. Boltzman Oscillation

    Engineering Help finding the damping ratio formula for this circuit

    The circuit to be analyzed is shown below: Since initial conditions are zero (from the instructions) I will use laplace transforms for the cirucit and I will use the MAME method to solve this circuit. The laplace transforms that are required will give me: $$E_g(s) = \frac{10}{s}$$ $$ L_3 =...
  4. Behrouz

    A Finding a specific amplitude-frequency in the time domain

    Hello, I have a signal and got the FFT result of that. I have shown them both below along with the MATLAB code. May I ask if there is any method to find the time zone(s) in the signal that a specific frequency has(have) happened? The reason I'm asking this is that I want to specify the time...
  5. D

    Question regarding Fourier Transform duality

    Homework Statement Given the Fourier transformation pair ##f(t) \implies F(jw)## where ##f(t) = e^{-|t|}## and ##F(jw)=\frac{2}{w^2+1}## find and make a graph of the Fourier transform of the following functions: a) ##g(t)=\frac{2}{t^2+1}## b) ##h(t) = \frac{2}{t^2+1}\cos (w_ot)## Homework...
  6. R

    MATLAB Frequency domain filtering in Matlab

    I am trying to implement several filters in Matlab for Fourier domain filtering. They are the cosine, Shepp-Logan, and Hann/Hamming window filters. These filters are defined as multiplying the ramp filter by the cosine function, sinc function, and Hann/Hamming windows respectively. This is how...
  7. R

    A Converting Partial Differential Equations to Frequency Domain

    Hello All, I would like to convert a partial diff equation in time domain into frequency domain, however there is a term of the form: Re(∇(E1.E2*) exp(j[ω][/0]t)) where E1 and E2 are the magnitudes of the electric field and [ω][/0] is the angular frequency. Can someone please help me to...
  8. Cocoleia

    Frequency domain and mesh currents

    Homework Statement Homework EquationsThe Attempt at a Solution So far I was able to transform each element into the frequency domain: I am just unsure how to work with the dots to find the mesh currents. Can someone explain? Thanks.
  9. B

    Understanding N-Stages of FFT & DFT Formula for Frequency Domain

    1) How many stages are in N numbers for a FFT? I know N=8 has 3 stages and N=4 has 2 stages ? 2) The DFT formula converts a signal from the time domain into the frequency domain. Is this done by comparing x[n] against signals known as sinusoidal basis functions? are e-j2 pi kn/N sinusoidal...
  10. D

    Fatigue analysis in the frequency domain

    Assuming that a TLP platform is examined and the wave forces acting on the tendons of the mooring lines are presented in RAOs (as a function of wave frequency). Using Jonswap spectra for North sea (i.e peakness factor equal to 3.3) we can obtain Hs (significant wave height); Tp (peak period) and...
  11. MexChemE

    I Motivation for Fourier series/transform

    Hello, PF! I am currently learning Fourier series (and then we'll move on to the Fourier transform) in one of my courses, and I'm having a hard time finding motivation for its uses. Or, in other words, I can't seem to find its usefulness yet. I know one of its uses is to solve the heat...
  12. R

    Understanding Electromagnetic/X-Ray Pulse in Time and Frequency Domain

    Dear All, Suppose we have a electromagnetic/x-ray pulse with fixed energy with finite line width. I want to know the schematic of a plot how it looks in time- and frequency-domain? I think I understand in time domain: there will a straight vertical line on plotting intensity vs time in x-axis...
  13. Y

    Integration in Frequency Domain

    How to integrate $$\int_{-0.5}^{0.5} {\bigg({\frac{1}{4-2e^{-j2{\pi}f}}}\bigg)}^2 df$$
  14. K

    What is a frequency domain and s domain?

    What is a frequency domain and how can we understand the same in practical world? How is it related to complex plain sight domain?
  15. E

    Phase shift in frequency domain

    Hello, I'using Matlab to simulate phase shift in frequency domain (FD). I have got real and imaginary parts of the signal after FFT. I'd like to use phase shift in FD. This works: Y=fft(y); YY=Y.exp(-i*2*pi*nk/N*samples_delay); result=ifft(YY); But in my DSP I can't use the formula above and...
  16. R

    How frequency domain topic should be taught in the academic course?

    This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics,Physics,Digital Signal and image Processing etc. Some of concepts which are very difficult to analyse in spatial or time domain can be very easily understood in the frequency...
  17. B

    Fourier transform and the frequency domain

    I understand that the Fourier transform maps one function onto another. So it is a mapping from one function space onto another. My question is, why is it often referred to as a mapping from time domain to the frequency domain? I don't understand why the image of the Fourier transform...
  18. S

    How Can I Analyze the Frequency Response of an Electric Current Shell in Comsol?

    Hello people, i need help with frequency domain study in electric current shell modul. I have one IDC and i have electrodes from gold, and i don't know what should i do to see my frequency response on diagramm? Does anyone has any idea?
  19. N

    How do you find the zero-input response in the frequency domain?

    I'm working on a problem and one part of it is finding the zero-input response of a system in the frequency (or "s") domain. The zero-state response can be easily found in the frequency domain, it's just: Y_{zs} = X(S)H(S) But I can't for the life of me find the equation for calculating...
  20. K

    Natural frequency from time domain and frequency domain plot

    Anyone have an idea to find a first and second natural frequency from time domain and frequency domain plot resulting from an accelerometer measuring the vibration in cantilever beam ? Thanks very much :)
  21. P

    Understanding "S" in the Frequency Domain

    Can somebody tell me exactly what is 'S' in frequency domain? I know that s=σ+jw where σ is neper frequency and jw is complex frequency but i want the precise information on s you can suggest me a book in which it is clearly explained. Thank you.
  22. C

    Express current in time and frequency domain (capacitor)

    Homework Statement Calculate the current in the capacitor shown if the voltage input is a. v1(t) = 10cos(377t - 30°)V b. v2(t) = 12sin(377t + 60°)V Give answers in both time and frequency domain. Homework Equations I = dQ/dt = C * dV/dt The...
  23. C

    Relation between entropys of spatial and frequency domain

    Dears, I wish to measure the entropy of visual data such as image and video. I did transform these image and videos into frequency domain such as DCT, then measured the entropy with these pdfs for each AC components of image and videos. However, when I measured the entropy over spatial domain...
  24. T

    Definition issue frequency domain - Random Signal Processing

    Hello i have a question about Random Signal Processing and the frequency domain. If i understand correctly one cannot use the Fourier transform to represent a stochastic process in the frequency domain. What is therefore used is the Power Spectral Density: S_X(f)=F\{R_X(\tau)\} Were F...
  25. S

    Plot frquency resonse from transfer function in complex frequency domain

    I am going through a past paper for an upcoming exam and I want to check that I am approaching this question correctly. H(s) = 1/(s2 + 8485.28s + 36x10-6) Calculate and plot frequency response for 0 rad/s, 500 rad/s, 1000 rad/s and 10000 rad/s. I am under the impression that the 's'...
  26. F

    Convolution in Frequency Domain

    Homework Statement Find the Fourier transform of the following signal JUST by using the FT table and the FT properties x(t) = sin(t) -pi<=t<=pi 0 otherwise NOTE: I am using CONVOLVED WITH as a substitute for * (the real convolution operator) because I cannot express...
  27. T

    Magnitude in frequency domain of Fourier Transform

    Homework Statement Hi All, I'm just trying to practice graphing signals in frequency domain and I came across a stiuation I wasn't familiar with. If the exp() has a constant*t in it I'm not sure how to graph it, I remember that just cos it like a double sided exp(jwt) but with half the...
  28. T

    Magnitude in frequency domain of Fourier Transform situation

    Hi All, I'm just trying to practice graphing signals in frequency domain and I came across a stiuation I wasn't familiar with. If the exp() has a constant*t in it I'm not sure how to graph it, I remember that just cos it like a double sided exp(jwt) but with half the magnitude. I've attached a...
  29. X

    Understanding the Image output in Frequency Domain

    I need help understanding how frequencies are distributed when taking the FFT of an Image and how can i determine those frequencies, I really need a detailed and easy tutorial with practical example to understand it. When we take the FFT of a Sine/Cos wave we can easily see its frequencies in...
  30. J

    Time-domain to frequency domain

    How will the graph of a sine wave (plotted against time axis) of a particular frequency look like if the same is plotted against frequency?
  31. F

    AM waveform in frequency domain

    Hello, I need to sketch the frequency domain for the following AM waveform showing total bandwidth and frequency. 8sin(2pi500kt - 4cos(2pi530kt) + 4cos(2pi(470kt) I have attached an attempt I have made. Does anyone know if I have this correct or not ? Thanks kindly for any input.
  32. R

    Filter DC offset - apply High-pass filter (in time-domain or frequency domain?)

    Hello all, I want to filter DC offset for a signal by applying a high-pass filter to it (I've been told that to filter the DC offset this is what I should do - I'm not sure why exactly!) My question is; do I do that in the time-domain or frequency-domain after applying FFT? And I would...
  33. P

    Frequency Domain Analysis - the math

    I am studying Control Theory from Ogata. My math is a little rusty, so this is a math question about Frequency Domain Analysis. Check this page - http://www.flickr.com/photos/66943862@N06/6337116280/sizes/l/in/photostream/ I get everything upto Equation 8-4 However I don't get the line after...
  34. S

    Can two functions have the same frequency domain representation?

    Hi, I stumbled upon the following two functions which have the same freq domain representation, 1/(j.pi.f) 1.signum(t) = u(t) - u(-t) 2. 2u(t) what is the reasoning behind them having the same f domain representation?
  35. N

    Pspice Problem - How do I take Logarithm_10 in a frequency domain?

    Homework Statement I am simply simulation using a small circuit consisting of a square wave generator, a resistor and a GND. The Voltage varies from 0 to 0.5V and the frequency is 100kHz for the sig-gen. I can simulate and output the transient response, a square wave with the above...
  36. pairofstrings

    Meaning of continuous frequency domain

    Homework Statement Discrete-time transforms What does it mean when it says this : These transforms have a continuous frequency domain: Discrete-time Fourier transform Z-transform What is the meaning of continuous frequency domain..?
  37. A

    Convolution of two delta functions in frequency domain

    Apparently, when convolving, for example: [δ(ω-π) - δ(ω+π)] * (δ(ω+50π)-δ(ω-50π)) the result is δ(ω+49π)-δ(ω-51π)-δ(ω+51π)+δ(ω-49π) where δ() is the Dirac delta function, * the convolution operator and ω the frequency variable How do we get to this? Can you help me on the intuition in...
  38. S

    Averaging in tthe frequency domain

    Hi... I have several Power Spectrua that I want to average into a single representative power spectrum. Then, I have to analize the amplitude spectrum of the average (i.e. sqrt(power spectrum)) Doing that doesn't give the same result as averaging the amplitude spectrums. Supose I have tho...
  39. R

    How to convert time domaine signal into frequency domain signal

    Hi, I am new to signal theory and don't know what is time domaine signal and frequency domaine signal. Please some can explaine me clearly and how can we convert between those two domaines. I read the topic in wikipedia which makes me somepart clear but interested to know...
  40. D

    Windowing in Frequency Domain: Exploring Effects on Time Domain Data

    Hey @ all, when windowing in DSP in time domain one multiplies all recorded time samples with a weighting factor (hanning, hamming, etc.), followed by a Fourier transform (FFT) to reduce sidelobes in the spectral domain. But now when thinking about starting up in frequency domain where I...
  41. D

    Estimation of dominant peak in frequency domain

    Homework Statement I have to develop an algorithm that can predict dominant peaks in the frequency domain, given a set of data in the time domain. I used FFT to check the frequency domain but apparently there are packet losses and irregular sampling intervals so FFT won't work. 2. The...
  42. I

    Sketching Frequency domain repsonses

    Homework Statement Sketch the z-plane pole zero diagram for: G(z) = \frac{z^{2} + z + 1}{z^{3}} Also sketch the time and frequency domain repsonses, the latter in amplitude and phase. Homework Equations G(z) = \frac{Y(z)}{X(z)} Zeros when Y(z) = 0; Poles when X(z) = 0 For...
  43. L

    Advantage of frequency domain analysis?

    hello, i am new here and this is my first post so please bear with me for any mistakes or so.. now my question is about time domain analysis and frequency domain analysis . why should one convert from time domain into frequency domain by using Fourier transform ? and what are...
  44. H

    How would wavefrom change change in time domain, frequency domain and

    how would wavefrom change change in time domain, frequency domain and its rms value if a dc level of 1 volt was added.
  45. D

    Faraday's Law in the frequency domain

    I'm trying to figure out what faraday's law is in terms of frequency rather than time. I think the equation is V = -N*B*A*2f. Where N is the number of turns in the loop, B is the magnetic field, A is the area and f is the frequency. However I am not totally convinced that my derivation is correct.
  46. N

    (signal processing)Time domain vs Frequency domain, totally confused

    Hey guys, I am totally lost in the idea why we have to change function in time domain to frequency domain to ease with our calculations. Let me break my question into serveral smaller ones. 1)What is the physical implication of transferring a signal to frequency domain? (I know that in...
  47. L

    Finite Difference Frequency Domain

    Hello everybody! I am trying to construct the FDFD method for 3D structures. I have already constructed the general formulation and specifically I have set the complete matrix form. Due to the fact that the matrices are too sparse, and my system is out of memory, I am trying to set the problem...
  48. P

    Cramer's Rule in Complex Frequency Domain.

    Does Cramer's rule work in frequency domain? For example, if we have to solve two simeltaneous equations, as in nodel analysis or mesh-current method, can we use Cramer's rule to solve em? Would this be an efficient method?
  49. C

    How Do You Convert a Time Domain Waveform to Frequency Domain in MATLAB?

    Homework Statement Dear all , Am new to matalb and am having some couple of problems. i want to convert the following wave form from time to frequency domain . 1.E=ACos(ωt+φ).[0,T] I have made conversion by using integration by parts.Please find the MATLAB attached files...
  50. N

    Images in the frequency domain

    Hi, I've been trying to understand more on frequency plots of images. 1. Assuming a 1d example of just a strip of an image; in the frequency map there are 'same' no. of frequencies as there are pixels. What is the reason for this? Does this have something to do with the Nyquist theorom...