What is the maximum (and minimum) 16-bit double value?

Question

I am working on audio data manipulation (from/to WAV files, 16 bits), representing samples with double values (64 bits).

Since I am working with a lot of amplitude-domain convolution, a lot of time my resulting samples have (positive or negative ) values that go "above" the "maximum data" that can be represented on 16 bits, and the result is they get truncated.

So I need to normalize my data before writing it on a WAV file.

But it isn't clear to me what are the max (and minimum) double values that can be represented on 16 bits.

notice: here I refer to minimum value as the maximum negative double number that can be represented in 16bits.

edit: with 16-bits double I refer to data read from a 16 bit WAV file, stored in my code as a double value . After amplitude convolution, this data occurs to become greater than 1 or less than -1.

Answer 1

What is the maximum (and minimum) 16-bit double value?

It's unclear what you mean by "16-bit double".

There is a numeric type double in C++. It is a floating point type. The C++ language doesn't define its maximum or minimum representable values (although it does define a minium range, which the implementations may exceed), but it is possible to inspect those limits using std::numeric_limits .

However, on most systems, double is a 64 bit type, namely the "double precision" floating point type as specified in IEEE-754 standard.

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A 16 bit type can represent at most 2 ¹⁶ different values.

If used to represent an unsigned integer, the range will be [0, 2 ¹⁶ ).

If used to represent a signed integer, the range will depend on how the sign is represented. In the most common, 2's complement representation, the range will be [-2 ^16-1 , 2 ^16-1 )

WAV files

In the Microsoft WAVE format, the 16 bit samples are 2's complement signed integers. See the previous paragraph for their value range.

Answer 2

The simple answer is that your denominator (for normalizing 16-bit data) is 2^15 assuming signed PCM.

Divide all your incoming 16-bit data by 32767 is my solution for normalizing. Maybe a case can be made for 32768, as the data ranges from -32768 to 32767. But I've always used 32767.