Questions tagged [fourier]

Anything related to Fourier series, Fourier transform and similar mathematical tools used to analyze the frequency content of a signal.

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36 views

Instantaneous and active power in an ideal switch powered by real source and squared wave

This is a somewhat theoretical question, but one that has some impact on power theory. The circuit in the figure is composed of a real DC source (with non-negligible internal resistance) and feeds a ...
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1answer
76 views

What is the type and frequency of x(t)

This is a Fourier waveform question that I am struggling with. $$x(t) = \frac{8}{\pi}\left(\sin(8000\pi t)+ \frac{1}{3}\sin(24000\pi t) + \frac{1}{5}\sin(40000\pi t) + \frac{1}{7}\sin(56000\pi t) + \...
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61 views

Frequency Domain Analysis with Transistors

I have some doubts about how some circuits with transistors are described in electronics textbooks. Let's see an example (taken from Thomas H.Lee, The Design of CMOS Radio-Frequency Circuits). This ...
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1answer
83 views

How can I calculate the amplitudes of this signal's harmonics?

How can I calculate the amplitude's of the harmonics? This signal is the voltage of a capacitor bank. There is a few amperes of current on the capacitors in form of PWM. On the signal the 200mV Jumps ...
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1answer
123 views

Why convolution in time domain is multiplication in frequency domain? [closed]

I am trying to understand intuitively why convolution is multiplication in frequency domain. I started at the mathematical derivation of this, but didn't understand what is happening intuitively. This ...
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42 views

Software to detect certain sounds?

I’m trying to incorporate into an arduino, some programme to light up an LED when it hears certain sounds. Basically Shazam. This app uses the fourier transform to break down songs into frequencies ...
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24 views

Parabolic wave equation, electric and magnetic field definitions

The split step solution for Parabolic Wave Equation (PWE) applied to the tropospheric propagation problem is: $$u(x+\Delta x, z)=e^{ikM(z)10^{-6}\Delta x}\mathfrak{F}^{-1}[e^{\frac{-ip^2\Delta x}{2k}}...
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1answer
34 views

Electric Power in Frequency Domain

Let's consider an impedance Z inside a certain circuit. Let's suppose that we are working with a generic non periodic signal (so it is possible to analyze the circuit with the Fourier Transform). How ...
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38 views

Voltage Measurement through Spectrum Analyzer

I have done some measurements with a Spectrum Analyzer of a square wave of 100kHz and amplitude equal to 1V. The resulting power spectral density is here shown: The highest peaks represent the odd ...
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1answer
36 views

Fourier Series of Convolution of Periodic and and Aperiodic Signals?

The impulse response of an LTI system is aperiodic and I pass in a periodic signal. Now I need to find the Fourier series representation of the output. Since Convolution in time domain is ...
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15 views

Using symbolic expression to store and fplot summation (symsum) - truncated Fourier series

I need help to: Create a symbolic expression of a summation; Using fplot, plot this summation for the interval between -1<=t<1 In other words, create a symbolic expression for xN(t) for N= 1,3,...
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29 views

Harmonics in the electric machine

Obtain the fourier series of the waveform of the current i_ {a} (t), considering that its frequency is w_ {0} = 2pi / T. Consider only until the ninth harmonic (Hint: Take advantage of the wave ...
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1answer
58 views

Fourier Coefficients

I have no idea how to solve the following exercise, can you help me, please? Find the periodic function whose Fourier coefficients are $$C_{k} = \frac{sin^{2}(\pi k T)}{(\pi k T)^{2}}$$ I think ...
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74 views

Apparent lack of rigor in Phasor domain analysis of steady state AC circuits

so I have encountered a hitch in my understanding of analyzing steady state AC circuits. I have looked everywhere for the answer to my question and I can find nothing. Usually when we analyze ss AC ...
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1answer
69 views

Finding a Fourier series of a Burst Fired sine wave having consecutive 2 cycles on & 2 cycles off?

I have been trying to find the solution of the following problem but with no luck. I have a system that generates a waveform of sinusoidal type with the only difference being that this wave has 2 ...
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0answers
129 views

Vanishing of Gibbs Phenomenon in MatLab

I was trying to represent a square wave with its Fourier series in Matlab. But as I increased the number of terms in Fourier series expression, the Gibbs phenomenon vanished and the edges of the ...
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74 views

How to determine the transient response of a circuit to causal periodic inputs?

As you know, analyzing a circuit with phasors provides only the steady-state response, and is only useful for sinusoidal signals and DC signals. Fourier series allow us to analyse a circuit with ...
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1answer
84 views

If I look at a signal in its frequency domain, are there some guidelines by which I can tell how that signal looks in the time domain?

I was studying the Laplace transform and the Fourier transform, and I can't figure out if there is some intuitive way of finding out how a signal looks in the time domain if we know its frequency ...
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1answer
47 views

Spectral lines vs Envelope of PWM wave

On the wiki page of 'Duty Cycle' there is a nice animation that shows the frequency spectrum of PWM wave as its duty cycle is modulated from 0 to 100%. The animation shows the 'spectral lines' as ...
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1answer
50 views

Find the exponential Fourier coefficients

I am confused as to what the periodic function, Vin, is! I know the slope is 2/pi, but what about the vertical line? I am also unsure about its relation to Vo.
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64 views

Phase, Frequency and Laplace transform

I have a doubt on the relationship between phase and frequency. We know that the definition of angular frequency is: ω(t) = d(\$phi\$(t) / dt, where \$phi\$(t) is the istantaneous phase of our ...
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1answer
101 views

Filtering a Square Wave into a Sine Wave

I am trying to Filter a +-4V odd inverted square wave into a sine wave. How should I go about doing so? So far I have computed the Fourier series of my particular input signal to be: Which I ...
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1answer
59 views

Real time spectrum analyzer and Fourier Transform

I am studying spectrum analyzers and a doubt came to me about real time spectrum analyzers. Suppose you have a signal in the time domain: in order to calculate the Fourier Transform, you need to know ...
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1answer
181 views

Phasors and Fourier Transform

I have always been told that for a sinusoidal variable (for instance a voltage signal), the fourier transform coincides with the phasor definition, and this is the reason why the analysis of ...
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1answer
47 views

Understanding the Fourier transform

In a current lecture we had a quick visual introduction to the Fourier transform. It was explained that the Fourier transform turns a given wave into an approximative wave that consists out of cosine ...
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1answer
42 views

AC signal analysis: Voltage dip (amplitude dip) at time = 0

I'm working on a series RLC problem where the input voltage is a sinusoidal function for all time. The catch is, for t < 0, the sinusoidal function is of greater magnitude than t >= 0. There is no ...
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63 views

Bandwidth of triangular wave for desired linearity

I'm attempting to replicate the Wavetek Model 188 Function Generator with original circuitry. This function generator has a 'VCG (Voltage Controlled Generator)' input which allows the user to apply ...
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41 views

Confused on Fourier Transform. What is amplitude spectrum and phase?

I am learning fourier transform by myself and I am confused on the description below. I can't understand how can I get the second formula by using the Euler formula on the first equation. Why is ...
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3answers
4k views

Do square wave exist?

If we send a square waveform through an antenna, will we get square electromagnetic waves with electric and magnetic fields looking like squares? Also, since there is an abrupt/almost jump in ...
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1answer
200 views

Impedance calculation from voltage and current (exponential) waveforms

If we want to find the impedance across two terminals (a port) at a frequency \$\omega_0\$ using the voltage waveform across \$v(t)\$) and current through (\$i(t)\$) the terminal, general intuition is ...
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2answers
441 views

How does one measure the Fourier components of a signal?

I attended a lecture on ground penetrating radar (GPR). I am used to reflection seismic where the incoming pressure amplitude is measured as a function of time. In GPR, instead the Fourier components ...
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1answer
48 views

Using Matlab poctave function under 3 Hz

I would like to get the Fourier transform of my data from 0,5 to 80 Hz at every 1/3 octave. I tried using Matlab poctave function but that one is only working over 3 Hz. My question is there a way ...
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2answers
66 views

Frequency division and signal spectrum

I need a mathematical description of what happens to the spectrum of a signal when that signal is processed to divide its frequency. As an example, construct an input signal as the sum of two sine ...
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2answers
57 views

Effect of frequency division on a signal's spectrum? [duplicate]

I am constantly on the lookout for effective yet inexpensive means to generate SSB signals. Analog Devices' LTC5598 Direct Quadrature Modulator turns baseband analog I/Q signals into RF from 5MHz to 1....
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6answers
4k views

What kind of hardware implements Fourier transform?

I looked around online but I found nothing relevant. It is very difficult for an electronic device to decompose a signal in different frequencies. How this is done at the bare metal level? Any ...
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0answers
29 views

ADS harmonic balance discrepancies with sawtooth waveform

I am using ADS for a simulation where I am biasing a diode with a sawtooth waveform. The sawtooth source provided by ADS, and 3 harmonics are specified There are different phase delays across the ...
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1answer
83 views

Fourier transform does not produce the correct result

I am trying to calculate the absolute value of a certain sinusoid to see how MATLAB calculates the Fourier Transform by using the freqz() command. Here is my Matlab code ...
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56 views

What exactly does the frequency spectrum represent?

The signals in the image represent a low pass signal and its Hilbert Transform. I know that a plot for a signal's magnitude with reference to frequencies can be found by applying a Fourier Transform. ...
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56 views

Amplitude-Frequency spectrum

I am tasked to find the amplitude of the first harmonic of a square wave. I did a time domain fourier series and plot a frequency spectrum I also did a frequency domain fourier series and plot a ...
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2answers
97 views

Fourier series coefficient for sin(wt+theta)

Am trying to find the Fourier series coefficient ck for the following function \begin{equation} x\left(t\right)=\sin\left(wt+\theta \right) \end{equation} Here is my work \begin{equation} c_k=\frac{1}{...
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2answers
76 views

Frequency Response Function Estimate via FFT Question

I want to estimate the FRF of a dynamic LTI system given experimental input and output data. I know generally the approach is to use a chirp as an input to make sure enough frequency content is ...
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2answers
454 views

How to calculate the phase difference between current and voltage?

Using the next circuit and the components of simulate this circuit – Schematic created using CircuitLab \$R=20\Omega\$ \$L=25mH\$ \$V_{DC}=36\$ \$v_{s}(t)=50+\underset{n=1}{\overset{\infty}{\...
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1answer
49 views

Significant low frequency content from digital oscilloscope measurement

I have been using a digital oscilloscope to measure a fast transient signal and have then processed the data in MATLAB. Performing an FFT on the data I consistently see a significantly large low ...
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1answer
59 views

Can a system have constant phase response other than +/- 90 deg (and multiples)?

I have seen frequency responses where amplitude response is constant( pure delay) and where phase response is constant(pure integrator). In an integrator the constant phase is -90 deg. In a pure ...
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1answer
725 views

Fourier Transform vs. Laplace Transform?

The question arose to me earlier, and I never really understood it.. What is the difference between fourier transform and laplace transform in terms of analyzing an overall circuit? I don't quite ...
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1answer
43 views

Fourier transform of a sum of 2 delta function

i have a channel impulse response \$h(\tau,t)=\delta(\tau-1/4t)+b\delta(\tau-T)\$ if I would like to take Fourier transform, I can take FT for each delta function and then sum up a result. \$FT(h(\...
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2answers
78 views

Relation between the Fourier transform of Y and X

So, I watched a video from MIT Signals and Systems Open course on youtube, and there is a moment when he substitutes \$ x(t)e^{jw_ct} \$ for y(t), and then: Shouldn't it be just \$ X(w - w_c) \$ ? ...
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1answer
760 views

Fourier Series Expansion of the phase current of a three phase full wave bridge rectifier

I am really struggling with this homework problem where I am asked to calculate the harmonic components as a ratio of the first fundamental harmonic of the phase current of a three phase rectifier ...
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1answer
244 views

How do you visualize the frequency spectrum for a digital waveform? [closed]

How does the mathematics of a single or periodic rectangular pulse help us quickly visualize the frequency spectrum for a digital waveform? Develop the ideas behind this. My professor posed this ...
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1answer
64 views

Spectral analysis of spectrum analyzer

Using measures from a spectral analyzer, I am a bit confused on how to properly compare the power of each spectral line with the fourier coefficients (Parseval). Take this signal: Take it's spectrum:...