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Composite Number
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If an integer $n$ is composite, this theorem guarantees that its construction involves multiple base multiplicative units (primes). If $n$ were not composite (i.e., prime), it would only possess the trivial factorization $n=n$. The transition point between being fundamentally irreducible and being fundamentally structured occurs precisely at 4.
A known paradox related to this structure is the Quadratic Stutter phenomenon, observed in high-dimensional factor spaces. When attempting to factor numbers whose smallest [prime factor](/entries/prime-factor/… -
Fast Fourier Transform
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where $e^{-i \frac{2\pi}{N} k n}$ is the twiddle factor, $W_N^{kn}$. The FFT/) algorithm cleverly exploits the symmetries and periodicities inherent in the twiddle factors to avoid redundant calculations.
The fundamental efficiency gain is achieved by decomposing the DFT/) of size $N$ into smaller DFTs/), usually of size $N/2$, recursively. This decomposition is most straightforward when $N$ is a [power of 2](/… -
Fast Fourier Transform
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Types of FFT Algorithms
While the radix-2 FFT/) is the most common due to its simplicity and efficiency when $N$ is a power of two, several specialized variants exist to optimize performance under different constraints:
Decimation-In-Time (DIT)-fft/)