FFT Bin Size Calculator for Audio Analysis

When you look at a spectrum analyzer, you’ll see peaks of data, but perhaps not know they’re limited by the number of samples provided to the math. Even experienced engineer get tripped up by the power of the Fast Fourier Transform and its forced trade-off between time and frequency. If your window on the FFT is too short, then you don’t have sufficient cycles of your waveform to resolve closely spaced tones so your frequency resolution suffers. Conversely, if you make the window too long, then you lose temporal precision and actualy miss transients all together.

Calculating precisely what resolution your bin size will give you with your chosen sample rate and target pitch is key to finding right balance. There is the raw bin spacing, which is simply dividing the sample rate by the FFT length. Underneath that, there is some complexity. If you have a 2048-point FFT at a 48 kHz sample rate, you’ll find about 23 Hz between each bin center. That sounds precise enough, right? Well how about trying to tune a low E bass note at 41 Hz? Half a bin means a big ol’ pitch shift. The problem lies in understanding whether or not the settings you’ve selected is capable of handling the cents of error you’re concerned with.

Understanding the FFT Trade-off

Most folks think that zero padding the FFT will fix things, because it adds extra points to the graph so it looks smoother. But it doesn’t create any new information; it only fills in the gaps between existing data. So while the graph looks smoother, it won’t be able to separate two distinct frequency that fall on either side of its resolution limit.

And then there’s a further compromise via window functions. After all, if you have a perfect amplitude measurement, you won’t have good frequency resolution either. If you use a rectangular window, you’ll get very narrow frequency bins but terrible spectral leakage, as energy spills over into adjacent frequencies so much that your display becomes a mess of side lobes: If instead you choose a Hann or Blackman-Harris window, you can reduce the spectral leakage a lot. It will still be present, but not as extreme than before because these windows taper the edges of the signal slice you are looking at. But you also widen the main peak doing so. That means that the actual effective bandwidth you’ve got is wider than just the size of each bin indicates.

That is why the tool displays the equivalent noise bandwidth. This is frequently a better number to look at if you are trying to identify quieter artifacts around louder fundamental tones, for instance.

In real world audio work, pitch and timing go hand-in-hand. You double the FFT size to get greater frequency detail (smaller bin width). This doubles the amount of time being analyzed which decreases the accuracy of the timing information. At 48 kHz, a 32768- point window represent almost seven-hundred milliseconds of audio. For a snare snap or kick drum hit, that’s an eternity. Because the energy is averaged across too many frames, the attack becomes smeared into a muddy blob. You may end up with the perfect frequency data on something that has already happen.

The solution to this lies partially in the overlap setting. Instead of jumping the window forward its entire length, overlap shifts the window slightly. This provides more frequent updates without losing the detail you gain from a longer analysis duration. In practical mixing terms, this means picking a setting that hits the sweet spot between these competing requirements. When analyzing a mix bus for the most part, a 4096-point FFT is typically fine for revealing instrument harmonics and vocal formants. It also won’t freeze the display in time.

Where you’re digging into really low frequencies (sub bass) or resolving very slow waves like measuring room modes, something like 16384 points or larger is probably required to sort them out properly. But again, the reference tables on the page set this all out in clear detail for commonly used sample rates so you don’t have to guess.

You are basically making a decision about whether you want to know when a frequency began playing or where it sits in the spectrum. Understand that compromise, and your settings will no longer feel like a guess but more like an engineer’s choice. Stop trying to measure everything down to the nth degree all at once and the mountain of data begins to get manageable, you should of known that.