# Envelope following using FFT bin power -> Low pass effect on the modulation transfer function

I am deriving the temporal envelope of a signal (in a particular frequency band) by summing some FFT bin powers and taking the average, I do the FFT frame by frame, windowing and some overlap.

Please help me understand the following: when the envelope of the signal changes slowly (say 5 Hz), I can track the envelope fine. However when the envelope is modulated at a higher frequency, say at 100 Hz, the dynamic range and amplitude of the detected envelope are very reduced.

So the Modulation Transfer Function (MTF) of this method has a low-pass look.

I am trying to understand the reasons for this low-pass roll-off effect and the maths behind it. I see what's happening but I can't clearly conceptualise the underlying cause . It should also be possible to come up with a number regarding the slope of the MTF.

GP,

Edit 1 : Thanks for your answer. I can't post images cause I'm a new user apparently.. so here is a link: Link . you see on the left the input signal is 4 kHz modulated by 5 Hz and I take some fft bin powers to track the 5 Hz envelope and it works fine. But at 75 Hz modulation (right), the amplitude and dynamic range of the envelope are reduced, and it gets worse as you increase the modulation freq (low pass effect). This is what I am trying to get my head around: where is this effect coming from ? Is it because I destroy phase information when I take the power of the bins ? I apply a hann window on the time domain input frames, before computing the FFT.

• Can you provide some pictures? When are you performing the windowing? The window is typically a low-pass filter. – geometrikal Oct 30 '12 at 5:03
• What are you actually doing? Post some code and a minimal example. (i.e. code that synthesizes a signal, and then the code that processes it). – Henry Gomersall Oct 30 '12 at 11:24