Why Fftw on Windows Is Faster Than on Linux

Result from audio FFT function makes it near impossible to inspect low/mid frequencies

What you are seeing is indeed the expected outcome of an FFT (Fourier Transform). The logarithmic f-axis that you're expecting is achieved by the Constant-Q transform.

Now, the implementation of the Constant-Q transform is non-trivial. The Fourier Transform has become popular precisely because there is a fast implementation (the FFT). In practice, the constant-Q transform is often implemented by using an FFT, and combining multiple high-frequency bins. This discards resolution in the higher bins; it doesn't give you more resolution in the lower bins.

To get more frequency resolution in the lower bins of the FFT, just use a longer window. But if you also want to keep the time resolution, you'll have to use a hop size that's smaller than the window size. In other words, your FFT windows will overlap.

Single Precision math slower than Double Precision in FFTW?

Assuming Intel CPUs - It all depends on the compiler. Compiling for 32 bit applications , you can use normal i87 floating point where single and double precision are the same speed. Or you can select SSE for SP and SSE2 for DP, where SSE (4 words in registers) is twice as fast as SSE2 (2 words per register). Compiling for 64 bits, i87 instructions are not available. Then floating point is always compiled to use SSE/SSE2. Either due to the compiler or the particular program, these can be compiled as SIMD (Single Instruction Multiple Data - 4/2 words at a time) or SISD (Single Data using one word per register). Then, I suppose, SP and DP will be of a similar speed and the code can be slower than 32 bit compilations.

Using data from RAM, and possibly cache, performance can be limited by bus speed, where SP will be faster than DP. If the code is like my FFT benchmarks, it depends on skipped sequential reading and writing. Then speed is affected by data being read in bursts of at least 64 bytes, where SP is likely to be a little faster.

Such as trig functions are often calculated in DP. Then SP is a bit slower due to DP to SP conversion.

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