# Questions tagged [fourier-series]

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76 views

### What happens to sidebands when they enter "negative" frequencies?

I am working with PWM signals. These signals are generated by comparing a modulating (at frequency $f_m$), and a carrier (at frequency $f_c$), as shown in the following image: In the resulting ...
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### Improving the intuition for the 2d fourier transform

As far as I understand, the 2d fourier transform is calculated as following: ...
1k views

### Fourier series representation of a full wave rectifier output

I am trying to compute the Fourier series representation of a full wave rectifier output. The equation of the signal is: $x_8(t) = | \cos (2 \pi f_o t)$ | I have tried to find the Fourier series ...
65 views

### Power contained in a signal

Given a signal $$x(t)=16\cos(20\pi t+\frac\pi 4)+6\cos(30\pi t+\frac\pi 6)+4\cos(40\pi t+\frac\pi 3)$$how can I calculate the power contained in a frequency interval, say 12Hz to 22Hz. The total power ...
398 views

### Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away? Suppose we are given the ... 1 vote
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### Finding $A_k$ coefficients

I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as: $x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
1 vote
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### Pitch successfully changes with Phase Vocoder, but there's an issue

I've been working on a phase vocoder program. The goal is to change the pitch of a recording of my voice. While doing research on how to change pitch, I came across this from a paper on phase vocoders ...
1 vote
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### What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?

$\DeclareMathOperator{\sinc}{sinc}$ I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem. Context When ...
1 vote
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1 vote
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### Efficient format for 2D signal?

I'm trying to solve the following problem. I got a "low frequency" input 2D signal over a square region. I'll collect a few samples, somewhere around 10-30 maybe, the exact sample count will be ...
1 vote
7k views

### The Fourier Series, Amplitude and Phase Plot of a Saw Tooth Waveform

I am trying to find the amplitude and phase plots of the saw tooth waveform pictured.I have already computed the Fourier series of the waveform but I don't know how to derive the amplitude and phase ...
1 vote
156 views

### A Laymans Fourier transform and harmonics explanation?

Please bear with me, I know some of you will scoff but I have looked on Wiki and in various literature (see below) and can't quite get a handle on a few things. I am a general business programmer, ...
1 vote
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### On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies

It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
25 views

### Advantages of the Karplus algorithm for sound synthesis

For a personal project I am trying to make a software to synthesize plucked and hammered string instruments. This is a whole research topic and there are already some models and algorithms such as the ...
43 views

### Creating infinite continuous time series out of a finite discrete spectrum

I have a power spectrum $S(\omega)$: a $1 \times N$ real vector that matches frequencies from 0 to 125Hz. I would like to create a time series $S(t)$ $[-\infty<t<\infty]$ that matches this ...
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### Finding the Fourier Coefficients

Up until now, I have dealt with finding Fourier Coefficients for functions: $f(t) > 0$ Which made it convenient calculating the Fourier Analysis Integral. However, I am now presented with ...
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### Energy of a sinc signal

My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me $$x(t)=\operatorname{sinc}(t)$$ and $$s(t)=x(t-T)$$ and I found that ...
181 views

### Range of function $\frac{1}{n\pi}(1-\cos(n\pi))\sin(\frac{n\pi}{2})$ and determination of Fourier coefficients

I am computing the Fourier series expansion of the given signal $x(t)$. In that I am having difficulties in calculating range of function $\frac{1}{n\pi}(1-\cos(n\pi))\sin(\frac{n\pi}{2})$ (or) I am ...
76 views

### the DFT of a periodic signal represented by a fourier series

If I have a signal represented by a Fourier series(like in the photo), which is sampled with $T_s$: $$x[n]=x(t=nT_s) = \sum_{m=-\infty}^{\infty}a[m]e^{j2\pi m(nT_s)/T_0}$$ How do I find its DFT? I ...
78 views

### Approximating the fourier coefficients from a discrete time signal

Suppose I have a discrete time signal $x_t$ sampled with a frequency $f_s$. I know that if I take the discrete fourier transform of the signal and compute the power, I can easily (by visual ...
96 views

### transform signal

Hello everyone I need help solving a Fourier transform for the given signal, I know it will be a frequency convolution for the first function it will be a window function and for the second function I ...
I would like to raise a mathematical question : Let's say we are been given : $$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\ 0 & \textrm{otherwise} ... -1 votes 1 answer 85 views ### Why do we scale bins in FFT in this code? Hi I am learning FFT I am confused about this bit of code: what is the reason for scaling the sampling frequency and what is bin scale and why and when do we use it? thank you ... -1 votes 1 answer 489 views ### Fourier Coefficients Consider the signal$$x(t)=\cos(2\pi t) Since $x(t)$ is periodic with a fundamental period of $1$, it is also periodic with a period of $N$, where $N$ is any positive integer. What are the ...
Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of $x(t)$ given as $x(t) = > \cos4t +\sin8t+3$?