continuous-fourier | 易学教程

why do we need time sampling to plot a stationary signal?

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问题 I am new to matlab and signal processing. I have wrote the below posted code. what i could not understand is, the time soecification section at the beginning of the code. I do not why do we need sampling when specifying an interval or time duration, i think it suffice to specify something like the following : t = (0: 0.2: 1.0) for an example, why do i need some thing like sampling to plot such as stationary signal. another question is, this code gives me an error saying paranthesis imbalance

Matlab not plotting the exact fourier signal

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问题 I'm trying to plot a simple signal in fourier domain using Matlab. It's not plotting the correct signal. Here is my code: clc; clear all; close all; x=1:0.001:10; f1=sin(2*pi*10*x); f2=sin(2*pi*15*x); f3=sin(2*pi*30*x); f=f1+f2+f3; plot(2*pi*x,fft(f1)); figure plot(x,fft(f1)); I've expected a peak at 10 since the frequency is 10. But it is giving a peak at some other point Here are the two plot images: This is the image for plot(x,fft(f1)) This is the image for plot(2*pi*x,fft(f1)) It is not

Returning 'traditional' notations of functions in the context of fourier interpolation

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问题 in numerical analysis we students are obligated to implement code in R that given a function f(x) finds its Fourier interpolation tN(x) and computes the interpolation error $||f(x)-t_{N}(x)||=\int_{0}^{2\pi}$ $|f(x)-t_{N}(x)|^2$ or a variety of different $N$ I first tried to compute the d-coefficients according to this formular: $d = \frac 1N M y$ with M denoting the DFT matrix and y denoting a series of equidistant function values with $y_j = f(x_j)$ and $x_j = e^{\frac{2*pi*i}N*j}$ for $j =

Discretized continuous Fourier transform with numpy

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Consider a function f(t), how do I compute the continuous Fouriertransform g(w) and plot it (using numpy and matplotlib)? This or the inverse problem (g(w) given, plot of f(t) unknown) occurs if there exists no analytical solution to the Fourier Integral. You can use the numpy FFT module for that, but have to do some extra work. First let's look at the Fourier integral and discretize it: Here k,m are integers and N the number of data points for f(t). Using this discretization we get The sum in the last expression is exactly the Discrete Fourier Transformation (DFT) numpy uses (see section

Discretized continuous Fourier transform with numpy

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问题 Consider a function f(t), how do I compute the continuous Fouriertransform g(w) and plot it (using numpy and matplotlib)? This or the inverse problem (g(w) given, plot of f(t) unknown) occurs if there exists no analytical solution to the Fourier Integral. 回答1: You can use the numpy FFT module for that, but have to do some extra work. First let's look at the Fourier integral and discretize it: Here k,m are integers and N the number of data points for f(t). Using this discretization we get The