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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159 views

How do you find Fourier series coefficients for some weird waveform?

The formulae for the Fourier series coefficients contain f(x), e.g. $$ b_n = \frac 1\pi \int_{-\pi}^\pi f(x)sin(nx)dx $$ But if I don't know what f(x) is, e.g. or then how can I get the ...
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4answers
605 views

Why does my rectangle function on a FPGA look like this?

I programmed my FPGA to create a simple 1 MHz rectangle function. But when I display the resulting function on my oscilloscope it shows some oscillation after the edges. At first I thought this might ...
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3answers
179 views

How can the FFT analyze a wave in which the components are changing?

Based on what I've read about Fourier Transforms, it seems that they are designed to work on waves whose components are constant. For example, a simple square wave is \$\sin(\theta) + 1/3sin(3\theta)...
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1answer
1k views

how to get wave formula using IFFT

I have a wave and i can't know its formula so i used Fast Fourier Transform (FFT) to make frequency spectrum for this wave to get all frequencies and amplitudes (in db) of this wave. [1] i need to ...
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1answer
65 views

Finding the DFT size in relation to an OFDM encoded signal

I am completely lost here. How do I go about determining the size of the DFT matrix used in conjunction with an OFDM encoded signal? I have researched this a lot but cannot find a solid answer? Is it ...
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2answers
2k views

Which is the loudest in terms of sound intensity - Sine, Square or Sawtooth waveform?

From this, (Square wave / Sine wave is more audible) I now understand that a Square soundwave will be louder than that of a Sine sound wave when played at the same frequency (for example 500 Hz). ...
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2answers
210 views

Is there any simple way or trick to express given signal using waveforms of sum of simple sinusoidal signals?

We know that Fourier series for periodic signal \$y(t)\$ is given by $$ y(t) = \sum\limits_{m=0}^{+\infty} a_m \cos(w_m t) + \sum\limits_{m=0}^{+\infty}b_m \sin(w_m t). \quad$$ y(t) is sinusoidal ...
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1answer
3k views

How tuning of particular FM signal is done?

I have a transistor radio which has facility to play FM radio channels between 88MHz to 108MHz frequencies. Now,consider a situation ,there are five FM stations which I can hear in my city 91.1MHz,93....
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2answers
721 views

What are values of fundamental frequency and the harmonics for the below signal g(t)?

We know that a Fourier series formula for any signal $s(t)$ is given as $$\frac {a_0} 2 + \sum \limits _{m=1} ^\infty (a_m \cos \frac {2 \pi m t} T + b_m \sin \frac {2 \pi m t} T)$$ Here,as we see ...
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1answer
74 views

Fourier Transform using pairs table

I'm trying to find the Fourier Transform of: $$t^2e^{-2t}u(t)$$ I know that from the FT pairs table, $$ FT(te^{-2t})= \frac{1}{(2+jw)^2}$$ So I assume that we can just use the multiplication property ...
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1answer
236 views

How to apply the Fourier Transform to this?

I have the equation \$5\cos(t)e^{-3t}u(t)\$ and the Fourier Transform of it is $$\frac{5(3+j\omega)}{(3+j\omega)^2 + 1}$$ I can't figure out how to arrive at this answer. Using the FT pairs table, I ...
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1answer
209 views

Determining Existence of Transfer Function H(s) and Fourier Transform H(w) for Non-LTI Systems?

Given that $$y(t) = \cos(2\pi t)x(t)$$ where \$x(t)\$ is a system input and \$y(t)\$ is the system's output, I need to determine whether an \$H(s)/H(w)\$ relation exists. Since this system is not LTI, ...
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2answers
782 views

Please explain FFT Frequency Spectrum and different filters

It seems that I am not able to find the right key-words in order to get the answers from google but how can I recognize different filters based on their FFT Frequency Spectrum and how do different ...
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2answers
388 views

Can anybody give proof about features of phase and magnitude spectrum?

I have read that from Fourier transform we obtain magnitude and phase spectrum. The magnitude spectrum tells you how strong are the harmonics in a image and the phase spectrum tells where this ...
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2answers
2k views

RL voltage across inductor differential equation

I have a simple RL circuit such as the one shown below and I want to derive the differential equation relating the input and output voltages. I want to take the output voltage as the one across the ...
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1answer
124 views

Have some queries about Fourier Transform?

I am fond of Fourier Transform. I have some queries about Fourier Transform In most of the cases,the Fourier transform of a signal is symmetric about positive and negative axis.I think the ...
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1answer
8k views

Why isn't the Fourier transform of a single sine wave cycle a single bar?

I have tried different Fourier transform codes out there on single sine waves, and all of them produce a distributed spectrum with a resonance at the signal frequency when they should theoretically ...
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1answer
54 views

Whether phase congruency and phase coherence terms are same or different?

I am studying the importance of phase in signal.Can anybody explain what is phase congruency ? Also,I am confused between terms i.e. phase congruency and phase coherence. Whether phase congruency and ...
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2answers
2k views

Does the conjugate symmetry property of the Fourier series coefficients only hold for purely real input signals?

I'm learning out the Fourier series and trying to price conjugate symmetry for a genetic input signal but I'm finding that this property only holds for a purely real signal signal. Is this right?
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1answer
49 views

Fourier series period?

This might seem basic to most of you but I'd like some help with a DT FS question if possible. From what I understand, the period of a DT signal N is defined as the value such that x[n] = x[n + N]. ...
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1answer
12k views

Enery and power when we have trigonometric functions (Fourier transform)

It is asked to evaluate the energy and power of the signal $$x(t)=10\cos(100t+30°)-5\sin(220t-50°)$$ Since it is periodic, I need to find $$\int _{-\infty}^\infty |x(t)|^2 dt \text{ and } \frac{1}{...
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1answer
1k views

Proof: A strictly bandlimited signal must also be a signal of infinite time duration [duplicate]

How can I show that a bandlimited signal is also of infinite time duration? I know it has to do with Fourier transforms and convolution but I'm not sure how to actually prove it. I also know that the ...
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2answers
6k views

Does FFT (fast fourier transform) give RMS or peak to peak amplitude vs frequency?

I am using periodic triangular wave (Vp-p=3V, freq= 2kHz), as an input to my oscilloscope to do FFT. My question is that does the magnitude(y axis) of in FFT plot represent the peak to peak ...
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1answer
2k views

Fourier transform and signal envelope

is there any relation Fourier transform and signal envelope(time domain)? I want to find standing wave envelope function.
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0answers
835 views

Application of Fourier Series in Circuit

I am trying to find \$v_o(t)\$ in the circuit below, where $$v_s(t) = 3 - \frac{6}{\pi}\sum_{n=1}^{\infty}\frac{1}{n}\sin2\pi n t$$ The correct answer is $$v_o(t) = \frac{3}{2} - \frac{3}{\pi}\sum_{n=...
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2answers
175 views

Find the power spectral density?

I don't understand how the graph of H(w) is used to find the equation for H(150) and H(200.)
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1answer
2k views

When is a system's frequency response symmetric?

When is the frequency response of an LTI system symmetric, i.e. which property does it need to satisfy? Does it have to do with the system being causal (I believe this means that h(n) = 0 for n < 0)...
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1answer
168 views

Why are functions for the frequency domain expressed in terms of a whole complex number rather than just omega?

I don't understand why some formulas used in electrical engineering, especially why using fourier analysis, include static numbers in function inputs, rather than just the changing variable. For ...
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5answers
4k views

Is probability theory useful in electrical engineering [closed]

I have a few days off after finishing this semester and I am hoping to study something. Ideally, I would like to be able to benefit from it in any upcoming courses I might take. I'm thinking of either ...
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2answers
82 views

Finding a DTFT of a signal

I'm trying to figure out what's the DTFT of \$ (-1)^nx[n]\$. (I'm given the DTFT of \$x[n]\$) So I tried this, but I can't figure out how to proceed from here, if this is even correct. Any help and ...
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3answers
220 views

Why are these Fourier transform values not as expected?

We are being taught Fourier Transform in our EE course this semester and I have several questions about it. The answers do not need to be rigorous and mathematical, all I need is an intuitive 'feel' ...
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1answer
96 views

Fourier series - frequency shift of function [closed]

Let's say I represented some function $$f(t)$$ in terms of complex Fourier series. Then if I want to calculate complex Fourier series of frequency shifted function $$f(t),$$ can I use result I got ...
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1answer
6k views

Amplitude and phase spectra of fourier series

If I have even and periodic signal \$x(t)\$ that has cosine fourier series $$ x(t)\sim\underbrace{\frac 12}_{a_0}+\sum_{n=1}^{\infty} \underbrace{\left(\frac{6\cos \left(\frac{n\pi }{3}\right)-6\cos \...
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5answers
12k views

Frequency of square wave

I have a hard time understanding the concept of frequency in square waves. With sine waves, it is straightforward. You increase the frequency and the signal appears more often in the same time ...
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1answer
193 views

Question related to fourier transform? [closed]

I just have a simple question Can someone prove the fourier transform of 1. it is 2*pi*delta(omega) but i am not able to prove it without using the properties just prove from scratch (fourier ...
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0answers
845 views

How to get fourier series of 8-bit character to be transmitted?

I have been reading this in a book, but can't understand how he used the 8-bit in fourier series equation to get the result below. The transmission of the ASCII character ‘‘b’’ encoded in an 8-bit ...
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1answer
1k views

Using a Kalman filter requires a truth value?

I have some accelerometer data that I need to filter and clean. However, based on the online examples that I see, the filter requires what's called a "Truth value". The code is based on this: http://...
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1answer
478 views

Fourier series of modified sine

I must do this task: Short translate: Picture presents modified sine signal. I must calculate F(k) using Fourier Series, next draw amplitude spectrum and phase spectrum. I have 2 problems: Is this ...
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1answer
359 views

Fourier Transform involving frequency differentiation property

Going through some past exams, I've came across this question; To get started, I've noticed that it resembles to the frequency differentiation property; Now, the differentiation was extremely messy, ...
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2answers
400 views

Fourier Transform help

I have this question here, which I am unsure of my final answer: Firstly, I times the numerator and denominator by the conjugate 1-jt - resulting me in the alternate form of the function Next, I've ...
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3answers
2k views

Fourier Transform of a half triangle

I have to derive the Fourier transform of a half triangle which is shown here: So far I got the equation of the line as 1-t/T, and now I think that I have to substitute into the Fourier transform ...
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4answers
9k views

Fourier transform of a ramp funtion?

What will be the Fourier transform of ramp function? Actually I got some results regarding this on the internet, but I was wondering how it could be possible because Fourier Transform (as I have read) ...
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2answers
3k views

fourier transform for non-stationary signal

I have read that for non-stationary signal we break the signal into smaller segments by applying a window function . My question is how this can help to make the signal has a fixed features or to ...
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2answers
422 views

Trying to Understand Spurious Sideband Interference (and some causality problems...)

Suppose I have a radio and I intend to transmit a 0.1 µs pulse on a 100 MHz carrier. Fourier theory tells me that this signal will produce some sideband interference resembling a Sinc function. ...
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3answers
1k views

Fourier Transform in real life

what is the frequency spectrum mean in real life ? , if we said x(t) , we mean that each time we have an output which is represented by x(t) , also it can represent decaying ,growing of an object , it ...
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1answer
98 views

Check me on this modulation question?

I need to check my answers for parts (a) and (c); a) I got q(t) = p(t)cos(5pit) c) i got y(t) as a rectangle with amplitude 1 from -pi to pi. So, y(t) = 1/8 f(t) Am I correct for both parts;
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1answer
204 views

Fourier Transform

Does anyone have a mechanism to understand intuitively ( and automatically ) why the fourier transform of certain functions have certain shapes ( at least for some functions, not necessarily for all )...
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1answer
146 views

How are phase values able to capture motion from video?

I know that the phase spectrum contains most of the structural information about the image. But I want to know more about importance of phase spectrum related to video signals. I have read that ...
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1answer
96 views

Regarding Phase Angle Of a Fourier Transform

Please tell me what would be the phase angle diagram of Fourier transform $$X(e^{jw})=\frac{1}{1-ae^{-jw}}$$ and how?
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1answer
200 views

Why does frequency equal k/K where k=0,..., K-1 in Discrete Fourier Transform?

I totally can't understand why f = k/K. What does k, K means, respectively?. I really want to know what they actually indicate in real world. Or, please give me an example. I spent 2 days night but ...