The practicing instrumentation engineer's guide to the DFT - Part 3: Other window types, averaging DFTs & more
Author's note: There are many books and articles on the Fourier Transform and its implementation available. A quick survey of these resources shows that they are not geared to the needs of the "Practicing Instrumentation Engineer" but to the needs of DSP engineers who work in many fields. This article explains some of the math required to get "Calibrated" Fourier Transforms.[Part 1 of this article looked at understanding DFT and FFT implementations. Part 2 examines spectral leakage and windowing, and discusses how windows actually work.] Other Window Types
You have probably heard many window names like, Hamming, Hanning, Blackman-Harris, Gaussian, Kaiser, etc, etc, etc... These windows are classics and are still in use today for many applications. They are not so useful for Instrumentation Engineers however. This is because they all have scalloping errors greater than 1 dB  and as instrumentation engineers we usually want to calibrate our systems to better than 1 dB. The other problem with these windows is that they generally don't have optimal sidelobes for our modern very high dynamic range A/D converters. Generally as instrumentation engineers we have three types of signals.
- Pure noise where we are looking at measuring a noise figure or some other spectral density of noise. Note that almost all digitally modulated signals look like band limited noise.
- Pure Sine wave tones or multiple tones where we are using pure Sine wave inputs to our digitizer and we are looking for magnitude response or distortion products to give us calibration constants or dynamic range tests of our instruments. The signal to noise ratio of these input signals is also assumed to be very large.
- A combination of both - we might be looking at a noise signal that is contaminated by some spurious signals in the passband. Or we might be measuring linearity of a system and have to use a Sine wave input that is close to the noise level. Lastly we might actually be measuring Signal to Noise level - in which case we have both Signals well out of the noise and noise itself to measure.