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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The relation between Fourier Transform and Discrete Fourier Transform [on hold]

I wanted to know the relation between FT and DFT
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1answer
65 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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50 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
52 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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46 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
36 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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34 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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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
178 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
429 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
27 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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56 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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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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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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23 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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51 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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54 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
85 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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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
259 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
48 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
415 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
41 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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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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385 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
145 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
58 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
42 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
551 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
96 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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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
280 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
66 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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53 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
182 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
348 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
55 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
293 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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107 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
231 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
950 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
302 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
288 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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406 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 ...