CmdrMoozy
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 May25 accepted Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples May25 comment Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples Indeed. I meant "efficient" just in terms of, if one naively computed all $N$ members of the DFT, one would be performing approximately twice as many computations as necessary. Anyway, thank you for the most clear explanation of how the DFT relates to real inputs I've yet seen online. :) Particularly the point of what "physical" values $|X_k|$ and $arg\{X_k\}$ represent. May25 comment Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples Or, rather, the first $N/2+1$ members of the DFT from $X_0$ to $X_{N/2}$. May25 comment Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples So, if I understand correctly, to efficiently compute the DFT of a real-valued sequence with $N$ members, one can simply represent each real valued input $x_n$ as a complex number $x_n+0i$, and then compute the first $N/2$ members of the DFT, at which point each member of the second half can be trivially computed as the complex conjugate of each member of the first half? May25 asked Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples Dec11 awarded Scholar Dec11 accepted Reducing radical congruence to polynomial congruence Dec11 comment Reducing radical congruence to polynomial congruence This is great. I'm not totally convinced working with modulo arithmetic couldn't work, but reducing this problem to Pell's equation is honestly a more elegant solution anyway. Thanks! Dec11 awarded Supporter Dec11 asked Reducing radical congruence to polynomial congruence May7 comment Sieve of Atkin - algorithm for enumerating lattice points. Is the fact that f and g are remainders modulo 15 and 30 respectively just arbitrary, or are the numbers 15 and 30 picked specifically? Algorithm 4.2 uses remainders modulo 10 and 30 instead of 15 and 30, for instance. May1 awarded Student May1 asked Sieve of Atkin - algorithm for enumerating lattice points.