Questions tagged [fourier]

Anything related to Fourier series, Fourier transform and similar mathematical tools used to analyze the frequency content of a signal.

Filter by
Sorted by
Tagged with
-1
votes
1answer
172 views

LCR circuits with changing input frequencies

simulate this circuit – Schematic created using CircuitLab Ok, imagine an LCR circuit with a resonant frequency f connected to a signal generator inputting a sine wave. The signal generator ...
-2
votes
2answers
85 views

Fourier Transform Impulse

My friend and I are revising and we are confused on how to start the question below, and we're hoping someone could give us a hint. Sorry if it's a bit blurry. We have the following equation, but ...
0
votes
0answers
22 views

Analyzing discrete odd time signals (coefficients)

I'm having trouble proceeding with the following homework problem. I have the following clues about a discrete time signal, x[n]. The period of \$x[n]\$ is N = 6. \$a_k = -a_{N-k}\$ x[1] = 2 \$\...
0
votes
2answers
43 views

Obtaining P(w) expression from figure for zero ISI

I have a practice test which asks to find P(t) and verify that it have no ISI I know that zero ISI means that the function will have a value 1 at t = 0 and 0 at multiples of T (sampling intervals) ...
3
votes
4answers
285 views

On what condition does Harmonic components of power generated in 50/60 Hz Grid Generators depend on?

I have power-recording data from 11 countries (USA-60Hz mains frequency / other nation 50Hz). These data were collected using a audio recorder (in a computer) connected directly to the power mains via ...
1
vote
1answer
316 views

Verifying Impedance of Capacitors, Inductors, Resistors

I would like some tips on how to build a circuit that will let me verify the impedances of these basic components. I had tried just measuring the output voltage from the component, but that didn't ...
1
vote
2answers
219 views

Number of samples (n) and number of data points (N)

I have a question: I am doing some research on the FFT and had an inquiry. If I have a fixed number of samples per period, what is the effect of increasing my data points, say from 128 to 256? I know ...
0
votes
1answer
74 views

Analyzing discrete time signals

I am given a signal \$x[n]\$ that have the following properties: Real and odd Period of \$N=8\$ and Fourier coefficients \$a_k\$ \$a_9 = 6j\$ The sum of \$|x[n]|^2\$ from \$n=0\$ to \$n=7\$ is \$576\...
2
votes
2answers
2k views

Understanding harmonics of different Amplifier Circuits (A,AB,AB w/OP-Amp)

I have been test the circuits for amplifiers and got somewhat stuck in understanding the results for the FFT's harmonics. With a standard type B I was able to get this graph for the harmonics for ...
0
votes
1answer
1k views

Why is X(jw) real and even if x(t) is real and even

So I'm going through Oppenheim's (really excellent) textbook "Signals and Systems" (2nd ed.) and the associated MIT course and I'm having an issue with the properties of the Fourier transform. On page ...
0
votes
1answer
104 views

Does the sign matter on the frequency response?

I've been trying to calculate the frequency response of a series LR circuit with the output measured across the resistor. I solved it in two ways, one by taking the Fourier Transform of the impulse ...
0
votes
2answers
1k views

Fourier transform to understand filtering on PWM

Is it correct to analyse the impact of a low-pass by regarding at the Fourier transform of a PWM signal, even if this one is generated with a H-Bridge ? And deduce that the higher frequencies forming ...
1
vote
1answer
100 views

Laplace domain: poles on both sides of the jw and x plane

For a pole/zero plot, if a system has a pole on the left side only it is stable, and if the pole is on the right only it is not stable, but if the pole is on the right and left, would that be stable? ...
1
vote
0answers
107 views

Calculating real part of a square wave

i'm trying to understand how Bruno putzey in Globally Modulated Self-Oscillating Amplifier with Improved Linearity in section 4.2 Analysis comes to the equation in presented in (2), see snapshot below....
0
votes
1answer
157 views

Fourier serie coefficients of real function

Let's take a periodic wave function defined by f(t) = (1 - t) with a period of 1. The Fourier coefficients can be calculated: $$ \omega_0 = 2\pi/T=2\pi \\ F(n) = \int_{0}^{1}(1 - t)e^{-jn 2\pi t}dt=-\...
1
vote
0answers
72 views

Fourier series and Fourier transform of signals which can be generated in real world

Let first remind on Dirichlet conditions: In mathematics, the Dirichlet conditions are sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at ...
0
votes
3answers
753 views

Interpretation of Laplace transformed function and Laplace vs Fourier

I'm used to Fourier transform, i.e. I have a good unterstanding of how to interpret a Fourier transformed function. But I'm struggeling with the Laplace transform. What's the meaning of its complex ...
14
votes
4answers
11k views

Can I use the FFT to recognize musical notes on a piano?

I want to create a tool which recognizes a few musical notes (I know this is re-inventing the wheel). So I would play middle C, D, and E on a piano and it should be able to classify those notes. Here'...
1
vote
2answers
2k views

Signal representation in frequency domain

My teacher taught me that the frequency representation of time limited signal will be band unlimited. Also the frequency representation of time unlimited will be band limited. i.e frequency domain ...
0
votes
2answers
204 views

Magnitude of fourier transform of AM signal

I'm taking a basis course in DSP and in class we had an exercise on amplitude modulating signal. we were given a signal \$x(t)\$ with fourier transform \$X^F (f)\$ with magnitude which looks like this:...
5
votes
2answers
254 views

calculate FFT based on an oscillogram

Hi, I'd like to understand the context in between an oscillogramm and the resulting FFT. My example is a full-wave rectifier and I am try to calculate some harmonics. Because the function is ...
0
votes
1answer
126 views

Fourier Transform

one the problems from my book, states the following: Find the Fourier Transform of: a) $$\frac{1}{2\pi(a-jt)^2}$$ the solution for it is -> \$\omega e^{-a\omega} \mathrm{u}(\omega)\$ I know there ...
0
votes
1answer
739 views

Gaussian function power spectrum (Matlab)

I am trying to plot the power spectrum (\$|FT(f)|^2\$) of a Gaussian function, and overlap it with the theoretically expected spectrum calculated from the Fourier transform pair: \$e^{-\alpha t^2} \...
0
votes
1answer
769 views

Gaussian Function Fourier Transform (Matlab)

I am trying to write my own Matlab code to sample a Gaussian function and calculate its DFT, and make a plot of the temporal Gaussian waveform and its Fourier transform. According to the FT pair: \$ ...
0
votes
2answers
72 views

Fourier Series Coefficients Calculation

Could someone tell me where my calculation is going wrong? So I integrate $$\int_{-1}^1te^{-jn \pi\ t}\ dt$$ and get $$\frac{e^{-jn \pi\ }}{-jn \pi\ }\text{+}\frac{e^{-jn \pi\ }}{-(jn \pi\ )^2}\...
4
votes
2answers
5k views

Under what conditions does jw equal the laplace variable s in an electrical circuit?

Imagine I've got an electromagnetic actuator and solved the underlying differential equations. I got an solution for sinusodially excitation, as follows (just an example, no physical backround): $$G(\...
-2
votes
1answer
1k views

Application of fourier transform in circuits

I try to solve this question in the following way. First I take the Fourier transform of the input voltage, and I get $$ 4/j\omega $$ then I find the transfer function. $$H(\omega) = 4/(4+jw) = v_0/...
1
vote
2answers
140 views

Impulse Response of a circuit

The following periodic function, \$x(t)\$, is the input to a linear, time-invariant system The impulse response of this system is $$h(t) = \frac{\sin t}{t} $$ which I converted to $$H(\mathrm{i}\...
0
votes
2answers
126 views

Impulse Response of a LTI system

The input to a L.T.I. circuit is \$x(t) = 6\cos(t)\cos(3t)\$, and the impulse response of the circuit is $$h(t) = \frac{\sin(3t)}{3t}$$ Obtain an explicit expression for the output y(t) as a function ...
4
votes
4answers
3k views

Fourier Transform and the Delta Function

The Fourier transform of cosine is a pair of delta functions. The magnitude of both delta functions have infinite amplitude and infinitesimal width. What I thought this meant: The cosine function can ...
0
votes
2answers
1k views

Inverse Fourier Transform of transfer functions

I want to find the inverse fourier transform of the following transfer function : $$ H(iw) = \frac{10 + (iw)}{4 - w^2 + 4(iw)} $$ So my first idea was to replace \$iw\$ with \$s\$. Then convert this ...
0
votes
1answer
78 views

Order analysis, need help

Hi fellow electronics enthusiasts. I'm currently working on vibration detection machine used to detect unbalance from a rotating shaft, rotating from 300-2500 Hz. I have both the tacho signal ( 1 PPR )...
0
votes
2answers
549 views

Fourier transform of \$x(t) =t^2e^{-|t|}\$

I have to find the Fourier transform of this function. (- sign exists BEFORE modulus). I thought of using this standard result. If I split this fourier transform into this will it be correct to ...
0
votes
1answer
343 views

How to design the frequency response of an analog filter when I get the transfer function?

I am not trying to design a filter. I just want to understand the theory of laplace transform and s-domain.I read an example from the book The Scientist and Engineer's Guide to Digital Signal ...
0
votes
1answer
75 views

Can I find the Fourier series expression from given terms?

I found the fundamental frequency, and all the harmonic components (an, bn), but is it possible to find the fundamental expression of an ,bn or cn? -The last part of the question-
0
votes
1answer
112 views

The relation between a link speed and Fourier coefficients

I am reading Computer Networks by Tanenbaum and the the chapter about the physical link and there is an example that I don't understand. The author states that given a bit rate of b bits/sec the ...
3
votes
1answer
171 views

Understanding the DTFT

So I am taking a signal processing course in EE and my professor is an Engineer who really likes math however his book which we use for the class falls in the dreadful purgatory of math books in my ...
1
vote
1answer
307 views

Fast Fourier Transform (FFT) of power consumption signals

I want to compare two power consumption signals, i.e., how the power consumption varies throughout a day. Now I have two options: Take two raw power signals and compute the Euclidean distance between ...
1
vote
1answer
761 views

From DTFT to DFT, why do we take N samples in frequency domain

In this post: Why does frequency equal k/K where k=0,…, K-1 in Discrete Fourier Transform? And I have read several books, the authors take N samples with DTFT to get DFT. Why N? I think N is simply ...
0
votes
1answer
3k views

Fourier transform of a rectangular pulse

I'm interested in knowing: 1. Why the frequency content has a larger magnitude at low frequencies 2. Why the magnitude is zero at frequencies which are composed of multiples of the rectangular ...
-5
votes
1answer
81 views

Circuit for DFT transform? [closed]

In my recent project I need to apply DFT to signal and find it's coefficient values. Can you please suggest any circuit/chip which can perform DFT/FFT transform on analog signals?
1
vote
2answers
715 views

Power supply Harmonics calculation using FFT

I am trying to calculate harmonics of power supply with using a FFT. My sampling rate is 400 samples/sec. This means 8 samples per cycle. I am not getting sensible answers and think that I am making a ...
0
votes
1answer
63 views

Finding Filtered Output using Convolution property of Continuous Fourier Transform

why the derivative of u[t] is delta[t] ? also I don't understand why the sin term disappeared once the derivative is taken.
4
votes
1answer
338 views

256-point FFT, but only need 5-6 frequencies, is there a better way?

Due to the constraints of my system, I have a 256pt FFT. However, I only care about the energy at 5 or 6 of the 256 bins. 256pt FFT is still faster than 5 or 6 specific DFTs, but it seems wasteful ...
1
vote
2answers
600 views

Application to solve for Fourier series coefficients?

Does anyone know a way to solve for Fourier series coefficients using Matlab, WolframAlpha, random web app, etc.? For example if I wanted to solve for and plot the Fourier series coefficients for the ...
3
votes
1answer
814 views

Lowpass LC filter

Here is my task: Lowpass filter circuit is given: Input signal to this circuit is: (it's periodic signal) L=36.4mH, C=85.4nF. Calculate and draw output signal. My idea is to: 1) Represent input ...
4
votes
2answers
861 views

What is the meaning of my fourier transform results?

I've been experimenting with Fourier transforms, and I'd like to understand some of the results I'm seeing. I've written a simulator which generates a data stream of length 1/120 seconds, sampled at ...
0
votes
1answer
167 views

Impulse Train Fourier Transform

My textbook defines the periodic impulse train and its Fourier transform as: \begin{align*} s(t) &= \sum\limits_{n=-\infty}^{\infty} \delta(t - nT) \\ S(j\omega) &= \frac{2\pi}{T} \sum\...
1
vote
1answer
779 views

How do I replace a capacitor with a resistance?

I'm studying Fourier transformations, and their relationship with electrical circuits. In the example below the capacitor is replaced by a resistance, in that way we can use the voltage-divider ...
2
votes
2answers
626 views

Calculate Inverse Discrete Time Fourier Transform

Calculate Inverse Discrete Time Fourier Transform of the following where \$|a| < 1\$: $$ X(e^{j\omega}) = \frac{1-a^2}{(1-ae^{-j\omega})(1-ae^{j\omega})} $$ Plugging this directly into the ...