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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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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
164 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
414 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
26 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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55 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
53 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
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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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20 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
82 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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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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53 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
83 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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46 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
200 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
47 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
51 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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DTFT of sampled function vs FT of impulse sampling

Given the function $$x(t)=2\cos{2\pi4t}$$ and a sampling rate of 6Hz I'm asked to find the Fourier Transform of the sampled signal. I tried doing this in 2 ways which give me two slightly ...
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1answer
310 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
39 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
76 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
288 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
116 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
56 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:...
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Power of random signal in AM

I'm trying to wrap my head around this problem : I must admit I'm pretty much blocked from the start, at a). I don't understand how I could derive the power of \$s_{AM}\$ given the frequency of the ...
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3answers
549 views

Mathematically derived waveform vs. captured waveform from an analog synthesizer

I was thinking about how the individual parameters on an analog synthesizer could be controlled digitally. What I mean is, instead of using mechanical potentiometers to adjust some quality of the ...
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2answers
81 views

What is the meaning of the difference between the Fourier transforms of a single pulse in these two cases?

In texts the Fourier transform of a single pulse is explained as below: They always create the pulse from -T to T, and they always show the sinc function symmetric around the origin. But in reality ...
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1answer
69 views

Finding the fourier series coefficients of the signal $$1+\sin (\omega_0 t) + \cos (\omega_0 t) + \cos (2\omega_0 t + \pi / 4) $$

I have come across this question that asks to find Fourier series coefficients of the following signal. $$1+\sin (\omega_0 t) + \cos (\omega_0 t) + \cos (2\omega_0 t + \pi / 4) $$ In my intuition, ...
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2answers
259 views

Gibbs phenonemon in real life

If I feed a square wave into a first order, passive, low-pass filter (resistor and capacitor), I get the following results on an oscilloscope (sorry, I don't know how to scale and rotate images): Why ...
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1answer
51 views

Antenna Directivity

How to make an antenna more directive by changing its physical size/scalling? My current approach: I should make the antenna bigger. A directivity is a Fourier transform of illumination, distribution ...
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1answer
65 views

Conversion of Additive Noise to Phase Noise

RF Microelectronics by Razavi contains the following snippet in section 8.7.3 concerning the analysis of phase noise in oscillators: We write \$x(t)=A\cos(\omega_0t)+n(t)\$ where \$n(t)\$ denotes ...
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52 views

How to find the Fourier transform when it is in the form of \$\frac j\pi\$ [\$\frac{1}{(t-3)^2-1}+\frac{1}{(t+3)^2-1}\$]

So as the title suggests, I can compute Fourier transforms in basic forms using the known properties. But how would one attempt to do this? How do I compute the integral? Or is there a pattern/pair ...
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1answer
151 views

How do I calculate THD in proteus?

I know how to plot the Fourier transform, but is there a more precise way to measure the total harmonic distortion? I have this graph: As you see, there's only one distinguishable component at 1 kHz ...
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1answer
277 views

About RMS in a non-sinusoidal electrical circuit

I am trying to compute the root mean square current with the main definition $$ \sqrt{\frac{1}{T}\int_0^T i^2(t)dt}$$ where the fourier expansion is given as: $$i(t)=I_0+\sum_{n=1}^{\infty}\sqrt{2}...
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1answer
54 views

Fourier Series, Transfer Function, Unexpected output

I am working on a project where I am trying to graph the output of input various functions represented by fourier series, applied to a transfer function of a bandreject filter. I am getting my ...
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1answer
215 views

Average of Fourier Transforms

I'm working on some acceleration data, looking at vibrations and at what frequencies they're occuring. The recorded periods are fairly long (~1 minute) and I was wondering, what's the difference was ...
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1answer
38 views

Should I consider systems to be causal or non-causal by default in questions like these?

Could anyone explain to me when to consider one-sided Fourier transform and when to consider two-sided Fourier transform? Normally in a question, just an input signal is mentioned, without stating ...
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100 views

How to deal with low pass filter questions if Fourier transform of signal does not exist?

I found this question in a previous test paper: I'm having a few confusions: 1) Low pass filters are supposed to block signals below a certain frequency. Here that certain frequency is \$w_c=a\$. I'...
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2answers
201 views

MATLAB Code to calculate intermodulation and Third Order Intercept (of an Amplifier)

My well annotated MATLAB code and plot is attempting to calculate the third order intercept of an amplifier. I have raw data of a non linear transfer curve, Voltage in (array) and the amplified ...
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3answers
794 views

Coefficients and harmonics of a PWM signal

I have been doing some research into the fourier analysis of square wave signals for my project which involves filtering of PWM signals. Just a few things online that I have found which don't make ...
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1answer
292 views

Sawtooth Wave Fourier Series - General derivation and Matlab issue

I am working on one of my first Matlab projects. I am trying to graph a sawtooth wave with 10-V Pk-Pk, 0-V average value. 50% duty cycle, 2.5 khz. I first attempted to find a general equation for ...
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1answer
260 views

How to find the phase spectrum of a rectangular pulse? (Fourier Transform)

How to find the phase spectrum of a rectangular pulse? The Fourier transform of a rectangular pulse $$ x(t) = \begin{cases} 1, & \text{for $|t| \le \tau /2$ } \\ 0, & \text{otherwise} \end{...
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1answer
325 views

Fourier series of output voltage

I've been practicing some Fourier series questions and then verifying my answers by generating an equivalent graph on MATLAB and comparing it with the graph generated by PSpice in simulating the same ...
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2answers
493 views

Role of complex number in electronics [duplicate]

Complex numbers contain imaginary numbers as we all know but often it is used for solving real life practical problems such as taking the impedance of a capacitor, inductor etc. Even in Signals and ...
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1answer
27 views

DFT: Given input signals, is there a way to compute the real part of DFT output without writing out the summation?

If I am given the inputs $$u = [2,1,0,1,2,1,0,1]$$ and asked to compute the real parts of the DFT outputs U(m) I would need to apply the formula $$U(m) = \sum_{k = 0}^{N-1} u(k) e^{\frac{-j2 \pi mk}{N}...
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1answer
68 views

What is the difference between modulating with cosine and exponential function?

Say I have an information signal x(t) with frequency f0 and I want to shift it on the spectrum to a much higher f1. I would have 1) \$y(t)=x(t) \cos(\omega_1 t)\$ and by looking at the spectrum I'd ...
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1answer
107 views

Fourier transform of a signal

I have the following signal and need to derive its Fourier transform: I just started learning Fourier transform and don't know how to solve this kind of question. I know though how to derive the ...
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1answer
41 views

Why averaging in Spectral magnitude domain not in complex domain to estimate spectrum of a process

Consider we need the magnitude spectrum of the signal. Signal is recorded in \$N\$ trials to a certain stimuli. Signal varies from each trial because of noise. So, to estimate the actual magnitude ...
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397 views

Draw Amplitude and Phase Spectrum for given signal

The above problem was asked in my class test. I understand that this waveform has a hidden symmetry. x(t) = Square wave with p-p A + (A/10) So, I can write fourier series expansion for it. As square ...
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3answers
544 views

Time shifted unit impulse function in frequency domain

How can we represent a time shifted unit impulse function in frequency domain ? Fourier transform of unit impulse function is 1. So I think it will be an infinite parallel line in frequency domain. ...