When I take a signal, stream->vector-->FFT-->IFFT-->vector->stream, I'd expect to get the original signal back. Instead, I'm getting something like the original signal, but following a very low frequency carrier. I thought this was due to the limits in vector size, but making this very high (many times the sample size and signal freq) and the problem continues, What's weirdest is that a low pass filter or band pass filter on the output don't seem to solve the problem! What is my mistake?

on 2013-11-18 03:40

on 2013-11-18 08:41

Hi Robert! This is strange -- but could be explained by the fact that numerical inaccuracy don't allow us to *exactly* recreate all values during fft-ifft operation. Also, make sure you use a rectangular window. How do you know there is this very low frequency carrier? how low is it? How much power does it have? Greetings Marcus

on 2013-11-18 14:23

On 11/18/13, Marcus Mller <marcus@hostalia.de> wrote: > Hi Robert! > > This is strange -- but could be explained by the fact that numerical > inaccuracy don't allow us to *exactly* recreate all values during fft-ifft > operation. > Also, make sure you use a rectangular window. Wow, switching to a rectangular window of fft_size solved it! I'm baffled: I know windows are a way of pretransforming the wave prior to FFT, to eliminate artifacts. I just used the default window. Why did I need a rectangular window here? In what other cases do I need it? Now, the only discrepancy I see is that the FFT->IFFT ended up *increasing* the amplitutde by a constant (not sure why or what the constant is). > > How do you know there is this very low frequency carrier? how low is it? How > much power does it have? On the osilloscope, I see the input signal as a constant wave, which it is, and I see the output signal a wave of the same signal, but with amplitude visually oscillating between very high and nothing. On the audio, I hear the signal coming in and out, in and out, or, depending on how I set it, I hear a ringing over it (which I assume is the beat freq). On the FFT display, I see the carrier as a peak, and a long thick band trailing off to the left. I don't know how to measure the power - according to the FFT display, it's not just at one freq, but trails off very far to the left.

on 2013-11-18 14:35

On Mon, Nov 18, 2013 at 8:22 AM, Robert James <srobertjames@gmail.com> wrote: > FFT, to eliminate artifacts. I just used the default window. Why did > I need a rectangular window here? In what other cases do I need it? Were both windows the same or different? I've often seen people trying this experiment using a window on the forward FFT but no window on the inverse FFT. That would obviously cause different output results. > Now, the only discrepancy I see is that the FFT->IFFT ended up > *increasing* the amplitutde by a constant (not sure why or what the > constant is). The constant is N for an N-point FFT. It's part of the common algorithms for computing FFTs to grow the value without scaling it back, since that's an added extra step and we want our FFTs to be fast. You can use a multiply_const_cc block with constant (1.0/fftlen) after the vector-to-stream block to rescale it yourself. Tom

on 2013-11-18 14:35

On Mon, Nov 18, 2013 at 08:22:08AM -0500, Robert James wrote: > Wow, switching to a rectangular window of fft_size solved it! I'm > baffled: I know windows are a way of pretransforming the wave prior to > FFT, to eliminate artifacts. I just used the default window. Why did > I need a rectangular window here? In what other cases do I need it? If you want to keep all the properties of the signal, you need a rect window. What you did was: apply a window, then do an FFT, apply the window again, do an IFFT. Obviously, you're distorting the signal every time you do the (I)FFT. A boxcar window won't change the signal. For spectral analysis or filter design, you typically use other windows. MB -- Karlsruhe Institute of Technology (KIT) Communications Engineering Lab (CEL) Dipl.-Ing. Martin Braun Research Associate Kaiserstraße 12 Building 05.01 76131 Karlsruhe Phone: +49 721 608-43790 Fax: +49 721 608-46071 www.cel.kit.edu KIT -- University of the State of Baden-Württemberg and National Laboratory of the Helmholtz Association

on 2013-11-18 14:40

On 11/18/13, Tom Rondeau <tom@trondeau.com> wrote: >> >> Wow, switching to a rectangular window of fft_size solved it! I'm >> baffled: I know windows are a way of pretransforming the wave prior to >> FFT, to eliminate artifacts. I just used the default window. Why did >> I need a rectangular window here? In what other cases do I need it? > > Were both windows the same or different? I've often seen people trying > this experiment using a window on the forward FFT but no window on the > inverse FFT. That would obviously cause different output results. Both were the same - the default blackmanharris, set to the ftt_len size

on 2013-11-18 17:52

The purpose of a window is to lower bin-to-bin leakage. It is only useful when the FFT is the final product, since it changes the signal. Think of it this way -- you are multiplying a signal in the time domain when you window. If you window, then FFT, then IFFT, you will get back the windowed signal, not the original signal. Matt

on 2013-11-18 18:48

As Martin said, a rect window makes sense, when you want to keep *all* the properties of the signal vector. You experience leakage, but in fact, leakage is just a concept that refers to the input vector as a representation of a signal. And one chooses to use a window to reduce leakage, because for many aspects, leakage distorts what you want the signal to be. However, from a mathematical perspective, the DFT (of which FFT is only a class of clever implementations) is only a mapping between two vector spaces (or even within the same vector space, if you want so). "Leakage" is no defect here; the transform of a vector is just the value that specific vector maps to. If you want to reverse that mapping, you apply the IDFT (IFFT) to the mapped vector; and it doesn't care about leakage etc, it just reproduces the original vector from the mapped one. I have a rule of thumb: If I consider the FFT as a bijective mapping between two vector spaces, and the IFFT as the inverse, then I don't want windowing. If I, however, look at the FFT as a means to get the spectrum of a signal that has temporal properties, then, of course, I choose a window to avoid leakage, because I look at the DFT as a means to get a good estimate of the spectrum of a signal from a limited time sequence of samples. In communications, you usually need to avoid leakage, thus you usually window the signal. That, however, might break reversibility of the transform. Greetings, Marcus

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