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3
votes
0answers
31 views

Pruned FFT runtime

Pruned fast Fourier transforms compute only a specified subset of the result indices in faster time, although sometimes with a slower implementation constant (because FFT is generally so optimized). ...
2
votes
1answer
45 views

What is the reason that is FFT multiplication slower than other methods for small N?

I've seen plenty of statements in papers and on websites that Fast Fourier Transform-based multiplication algorithms are slower than other multiplication algorithms for relatively small input size N, ...
1
vote
1answer
43 views

How to evaluate all derivatives of a polynomial at a point with FFT? [closed]

I found this problem: Evaluating all derivatives of a polynomial at a point Given a polynomial A(x) of degree-bound n, its tth derivative is defined by From the coefficient ...
3
votes
1answer
115 views

An $O(n)$ algorithm to FFT-evaluate an FFT evaluation

This question is from a practice exam in my algorithms class. I'm posting the question and the answer listed in that practice exam: Let $W$ be an $n\times n$ matrix whose $(i,j)$-th entry is ...
1
vote
0answers
24 views

finding period using fourier transform [closed]

In the plot squared length of Fourier coefficients vs frequency, the peak gives the strongest frequency. does it give the accurate value of period?? Is it like a single frequency in frequency domain ...
1
vote
0answers
30 views

fastest way to compute scalar product of an ensemble of vectors

I have an ensemble of points in 3D space, represented by their coordinates $\mathbf{c_i}\equiv(x_i,y_i,z_i)^\top$ . I need to calculate the distance between all these points: $\quad\forall i,j\quad ...
14
votes
1answer
1k views

Show how to do FFT by hand

Say you have two polynomials: $3 + x$ and $2x^2 + 2$. I'm trying to understand how FFT helps us multiply these two polynomials. However, I can't find any worked out examples. Can someone show me how ...
0
votes
1answer
54 views

Snowball Question FFT

http://courses.csail.mit.edu/6.046/spring04/handouts/prac-quiz2-sol.pdf I'm confused as to the solution for the snowball question. To start with, I have two specific questions: (1) Each pair ...
0
votes
1answer
106 views

FFT for expanded form of equation multiplication

I know how to use the FFT for multiplying two equations in $O(n\,log\,n)$ time, but is there a way to use FFT to compute the expanded equation before simplifying? For example, if you are multiplying ...
5
votes
0answers
79 views

(Slightly) faster simulation of quantum Fourier transform

Suppose I want to write a classical software simulator of a quantum circuit with $N$ qubits. When it comes time to simulate the quantum Fourier transform I can evaluate all $2^N$ states to determine ...
1
vote
1answer
42 views

How can you see which points in the spectrum is from which pixel in the original image?

Take the image and spectrum below. If I look at the spectrum, it just look like noise.... How to make sense of it intuitively? Image: Frequency spectrum of image (using Fourier Transform):
2
votes
1answer
416 views

What the difference between the Fourier Transform of an image and an image histogram?

Consider this small picture of a sunflower, and its histogram: What would the Fourier transform of the first picture look like? Is there any relationship between the histogram and the Fourier ...
0
votes
1answer
85 views

Intuitive way to understand the triangle spectrum?

Image on the top is in the time domain, image on the bottom is in the frequency domain. Why do we see -2T and 2T on image of the time domain and why do we see -1/2T and 1/2T of the image in the ...
2
votes
1answer
129 views

How to distinguish between the different frequency domains?

Sometimes the terms 'Fourier domain', 'complex frequency domain', 'Frequency domain' and 's domain' are used interchangeably. Take these answers here for example. Can you really use them ...
11
votes
1answer
512 views

FFT-less $O(n\log n)$ algorithm for pairwise sums

Suppose we are given $n$ distinct integers $a_1, a_2, \dots, a_n$, such that $0 \le a_i \le kn$ for some constant $k \gt 0$, and for all $i$. We are interested in finding the counts of all the ...
4
votes
3answers
2k views

Explaining why FFT is faster than DFT for the general public?

How would you explain why the Fast Fourier Transform is faster than the Discrete Fourier Transform, if you had to give a presentation about it for the general (non-mathematical) public?
2
votes
1answer
42 views

Confusion related to time complexity of fast fourier transform

I have this confusion related to the time complexity of FFT. I was reading this book related to Design and Analysis of Algorithms and I came across FFT. It says that lets say I have a polynomial of ...