5.4.2 Greatest hits from previous weeks

5.4.2.1 Calculate the 2D Fourier transform of an Image

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=29203

I am new to Mathematica, and using version 8.0. 
 
I would like to calculate the 2D Fourier Transform of an Image with Mathematica and plot the magnitude and phase spectrum, as well as reconstruct the  ... 
[image-processing] [image] [fourier-analysis]
 

asked by user8727 https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=8727 6 votes

answered by Nasser https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=70 28 votes

5.4.2.2 Finding Limits in several variables

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=21544

Is there a way to find a limit of a multivariable function, like 
 
$$\lim_{(x,y)\to (0,0)} f(x,y)$$ 
with Mathematica? 
 
When $f$ is continuous, we can use 
$$\lim_{(x,y)\to (0,0)}  ... 
[functions] [calculus-and-analysis]
 

asked by Dominic Michaelis https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=5899 27 votes

answered by whuber https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=91 38 votes

5.4.2.3 Plotting the frequency spectrum of a data series using Fourier

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=18082

testData = Table[N@Sin[500 x], {x, 0, 100}]; 
ListLinePlot[Abs[Fourier[testData]], PlotRange -> Full] 
 
 
Gives me 
 
 
 
Which I do not expect because the Fourier Transform is FourierTransform[Sin[500  ... 
[fourier-analysis]
 

asked by C. E. https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=731 12 votes

answered by KennyColnago https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=3246 15 votes

5.4.2.4 Figuring when the minute and hour hand coincide on a clock

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=573

I would like to list all possible times in a 12-hour period, where the hour hand overlaps the minute hand completely.  This is really a question about three distinct things - to be done in Mathematica  ... 
[equation-solving]
 

asked by Steve D https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=191 15 votes

answered by Verbeia https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=8 21 votes

5.4.2.5 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows: 
 
$$ 
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot  ... 
[calculus-and-analysis] [series-expansion]
 

asked by matheorem https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=4742 38 votes

answered by Jens https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=245 44 votes

5.4.2.6 Conversion of Sine to Cosine

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=67521

I'm solving equations with many Cosines and Sines. 
And I want to convert all the Sines to Cosines using trigonometric formulas such as cos(x)=sin(x+pi/2). 
How can I do this? 
 
[trigonometry] [conversion]
 

asked by YongCheol Kwon https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=23041 2 votes

answered by Sjoerd C. de Vries https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=57 1 vote

5.4.2.7 Labeling individual curves in Mathematica

https://mathematica.stackexchange.com/landing/r/newsletter?cta=question&id=4444

I need to create a plot for export and inclusion in a report. Is there a better way to label curves than PlotLegends? From what I've read and my personal experience, PlotLegends is pretty bad. 
 
Is  ... 
[plotting] [legending]
 

asked by Tianxiang Xiong https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=1041 53 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/newsletter?cta=user&id=184 41 votes