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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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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
56 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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39 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
142 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
45 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
50 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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18 views

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
191 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
34 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
75 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
161 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
93 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
53 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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41 views

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
548 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
70 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
57 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
230 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
49 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
59 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
126 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
204 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
130 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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94 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
172 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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1answer
519 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
258 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
224 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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How to derive scaling factors quickly for convolution theorem?

In case I use the following convention for Fourier transform: $$\mathcal{F(g(t))}=G(\omega)=\int_{-\infty}^{\infty}g(t)e^{-j\omega t}dt$$ and $$\mathcal{F^{-1}}(G(\omega))=g(t)=\frac{1}{2\pi}\int_{-\...
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1answer
246 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
407 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
26 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
62 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
92 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
35 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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362 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
463 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. ...
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3answers
2k views

How to obtain 3db frequency from transfer function

How can I calculate the 3db Frequency of the following transfer function $$ H(w)=\frac{1}{1-j\frac{250}{w}} $$ I have thought of doing the inverse fourier of H(w) so I can find h(t) and from that ...
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3answers
112 views

Why fake harmonics appear when using weighting windows?

As far as my understanding goes, windows in the FFT can be used to reduce the leakage error. Suppose that I need to sample a continuous time sinusoidal signal s(t) with frequency \$F = 10 Hz\$. ...
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2answers
555 views

square and triangle wave as a sum of sine wave [closed]

So in a project that I am working , I am supposed to use some filters to transform a square wave (in the first case) to a sine wave and a triangle wave(second case) to a sine wave again. The filters I ...
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1answer
97 views

fast Fourier Transform difference with discrete Fourier Transform

I'm a french student in engineering and I'm given a kind of mandatory technical project to work out on until February. I must investigate the following article: Precise and fast spatial-frequency ...
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1answer
432 views

Lock-In Amplifier: Why multiplication with Cos and Sin?

I have two questions: I was wondering, why a Lock-In Amplifier does multiply the incoming signal s(t) with both a cosine and a sine reference and not just a single one? What problem may eventually ...
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1answer
348 views

How to determine the RLC values for a bandstop filter

I've been looking through the vague online documentation for designing a basic bandstop filter. I have the two frequencies which I want to attenuate but I cant seem to find how to calculate the values ...
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6answers
546 views

Understanding Fourier, signals and spectrum analyzer

I'm having a hard time grasping the relation of Fourier analysis to the nature of signals and spectrum analyzers. From what I understand, Fourier analysis gives us a mathematical representation of a ...
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7answers
3k views

Would a triangle wave have finite or infinite sinusoidal components?

A discontinuity causes a signal to have infinite sinusoidal components, but a triangle wave is continuous, I was taking a class in which an instructor said that since the triangle wave is continuous ...
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2answers
280 views

Gain factor in real Resistance and Reactance (AD5933)

I'm trying to develop a system for bioimpedance measurement with the IC AD5933. The AD5933 is a high precision impedance converter system that combines a frequency generator with a 12-bit, 1 MSPS, ...
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1answer
86 views

Fourier Transform - convolution theorem

I have been studying the Fourier Transform and the convolution theorem is not clear to me. Sometimes, I see this: But other times I see this: Which one is correct? Where is this constant factor ...