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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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1answer
76 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
33 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
73 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
82 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
80 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
49 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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0answers
40 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
543 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
64 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
52 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
218 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
48 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
55 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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51 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
89 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
143 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
81 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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0answers
89 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
151 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
378 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
233 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
197 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
199 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
343 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
57 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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321 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
373 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
1k 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
109 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
480 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
89 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
413 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
341 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
477 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
257 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
80 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 ...
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1answer
526 views

Using Fourier transform to solve current in a circuit with initial condition

I am trying to solve the inductor current for the circuit below by using Fourier transform instead of Laplace. The purpose is to see if Fourier transform also works for problems with initial ...
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3answers
661 views

How Fourier transform be able to deal with transients?

Below is what Matt L.said in the thread here. Could anyone clarify how Fourier transform be able to deal with transitents? Reading that thread many times but I couldn't figure it out. Note that ...
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2answers
3k views

Fourier transform - LTSpice

Is it possible to get the Fourier transform in LTSpice? For example I'd like to plot the Fourier transform of the following signal: $$s(t)=A \space sin(2\pi f_0t)$$ Can you attached a LTSpice ...
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1answer
77 views

What is a good way to shift a function by 90 degrees through hardware? [closed]

I want to shift a function by 90.
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672 views

the .FOUR command in LTSpice

As far as LTSpice is concerned, the .FOUR command written in a netlist prompts the error log to record the Fourier-coefficients... That is fine, until one wishes to plot a particular coefficient ...
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3answers
555 views

Why do we need the Fourier transforms of sin and cos? [closed]

As we know we perform Fourier transform in case of continuous and "non-periodic" functions, while sin and cosine both function is "periodic" function then why we perform Fourier transform of sin and ...
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0answers
73 views

Fourier coefficients of a double frequency signal

I have a doubt regarding the fourier coefficients of a signal. I have a signal generator of sin(wt). After a single phase bridge rectifier of 4 diodes, I obtain in the output a signal equal to abs(sin(...