February 7, 2017
Computationally inexpensive sound compression is always difficult, at least if you want some quality. One could think, for example, that taking the 8 most significant bits of 16 bits will give us 2:1 (lossy) compression but without too much loss. However, cutting the 8 least significant bits leads to noticeable hissing. However, we do not have to compress linearly, we can apply some transformation, say, vaguely exponential to reconstruct the sound.

That’s the idea behind μ-law encoding, or “logarithmic companding”. Instead of quantizing uniformly, we have large (original) values widely spaced but small (original) value, the assumption being that the signal variation is small when the amplitude is small and large when the amplitude is great. ITU standard G.711 proposes the following table:

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1 Comment | algorithms, bit twiddling, data compression, hacks | Tagged: alpha-law, companding, ISDN, mu-law, noise, sound, spectrogram, voice, white noise | Permalink

Posted by Steven Pigeon

January 31, 2017
So for an experiment I ended up needing conversions between 8 bits and 16 bits samples. To upscale an 8 bit sample to 16 bits, it is not enough to simply shift it by 8 bits (or multiply it by 256, same difference) because the largest value you get isn’t 65535 but merely 65280. Fortunately, stretching correctly from 8 bit to 16 bit isn’t too difficult, even quite straightforward.

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Leave a Comment » | algorithms, bit twiddling, hacks | Tagged: 16 bits, 24 bits, 65793, 8 bits, bits per samples, Samples, sound, WAV | Permalink

Posted by Steven Pigeon

January 24, 2017
While flipping the pages of a “Win this interview” book—just being curious, not looking for a new job—I saw this seemingly simple question: how would you compute the sum of a series of floats contained in a array? The book proceeded with the simple, obvious answer. But… is it that obvious?

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1 Comment | algorithms, C, C-plus-plus, C99, hacks | Tagged: float, IEEE 754, Interview, std::accumulate, std::sort | Permalink

Posted by Steven Pigeon

January 17, 2017
On a number of previous occasions, I have used the *pseudoinverse* of a matrix solve systems of equations, and do other things such as channel mixing. However, the demonstration I gave before isn’t entirely correct. Let’s see now why it’s important to make the difference between a left and a right pseudoinverse.

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Leave a Comment » | algorithms, Mathematics | Tagged: left pseudoinverse, Pseudoinverse, quadraphonic sound, quadraphony, right pseudoinverse | Permalink

Posted by Steven Pigeon

January 10, 2017
Something that used to bug me—used to, because I am so accustomed to work around it that I rarely notice the problem—is that in neither C nor C++ you can use strings (`const char *` or `std::string`) in switch/case statement. Indeed, the switch/case statement works only on integral values (an `enum`, an integral type such as `char` and `int`, or an object type with implicit cast to an integral type). But strings aren’t of integral types!

In pure C, we’re pretty much done for. The C preprocessor is too weak to help us built compile-time expression out of strings (or, more exactly, `const char *`), and there’sn’t much else in the language to help us. However, things are a bit different in C++.

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9 Comments | algorithms, bit twiddling, C, C-plus-plus, hacks | Tagged: C++11, compile-time, constexpr, hash, hash function, Switch/case | Permalink

Posted by Steven Pigeon

January 3, 2017
The traditional—but certainly not the best—way to compute the value of the logarithm of some number is to use a Taylor series, for example

but that expansion is only valid for , or so, because it is the Taylor expansion of "around 1", and the convergence radius of this particular expression isn't very large. Furthermore, it needs a great deal of terms before converging.

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Leave a Comment » | algorithms, bit twiddling, Mathematics | Tagged: Convergence radius, Logarithm, Numerical Approximation, Taylor Series | Permalink

Posted by Steven Pigeon

December 27, 2016
Sometime last week, a tweet from @nixCraft prompted the question, quite ironically, how do you get the maximum (largest positive) value for an integer?

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Leave a Comment » | C, C-plus-plus, C99, Portable Code, programming | Tagged: CHAR_BIT, intptr_t, INT_MAX, ptrdiff_t, size_t, stddef, stdint, uintptr_t | Permalink

Posted by Steven Pigeon