On Wed, 15 Sep 2004 13:07:06 -0700
davidrclark@xxxxxxxxxxxxx wrote:
> Erik,
>
> > Notice that step where you throw away the middle N/2 samples?
> > That is a low pass filter applied in the frequency domain.
>
> Not if the amplitudes are all already zero above N/2.
Sorry, the filter exists whether the frequencies are there or
not.
In addition, your frequency domain method has the same the pre
and post ringing effects that I get with an FIR filter. This
can be proved in about 15 seconds using Octave or Matlab. In
fact, lets do that (using Octave in my case):
x = [1 1 zeros(1,2046)]; # create a signal
f = fft (x);
f_mod = [f(1:512) f(3*512+1:2048)];
x_mod = real (ifft (f_mod));
plot (x_mod)
As you can see from the plot, the ringing is plainly visible.
Now I will admit that if the signal is already bandlimited
filter many not be necessary, but that is a different matter
all together.
> In that case, the
> input and output frequency spectra are absolutely identical. If nothing
> was removed or even altered, then no filtering has actually occurred.
Thats not correct. The presense or absense of filtering does not
depend on whether there is a signal there or not. In effect, what
you are saying is:
"If I take a signal consisting of a single sine wave of frequency
fs/1000 and pass it through a lowpass filter with a monotonicaly
decreasing frequency response and a -3dB point of fs/4, then no
filtering has taken place because because there are no signal
components anywhere near where the filter has an effect."
Unfortunately, its not correct.
> > Less accurate how? Is this measurable or is this just hand waving?
>
> I have already addressed this in previous postings where I described the
> fact that I had merely listened to the recordings repeatedly until I
> could distinguish the original from the sndfile-resample one and could
> not distinguish the FFT-overlap one from the original --- ergo less accurate.
In other words, handwaving.
> My intention was not to "measure" accuracy, but to listen for the alleged
> distortions. You had posted a sort of celebration of the fact that I
> thought the sinc-based resampler produced a better-sounding version of
> the recording than my FFT-overlap resampler, but apparently had also
> neglected the fact that I was also saying that it sounded better than
> the original --- ergo was inaccurate (albeit very, very slightly so).
Was this a double blind test?
> Now I could take time to measure my resampler's performance,
Have you measured the signal-to-noise ratio?
> but I think
> we both know the expected results, don't we? In terms of absolute
> accuracy, any FFT-overlap resampler which utilizes large windows (hundreds
> of thousands or millions of samples) and which is properly implemented
> should, in fixed-rate conversions, outperform a sinc-based resampler that
If you work out the mathematical expression for your frequency
domain converter, you will find that there is a time domain
expression that is mathematically identical and that the time
domain expression is in part a FIR lowpass filter very much
like my converter.
The difference between the two would be that my version uses
linear interpolation into a very large table to obtain the
filter coefficients while yours are more exact. However mine
provides a *measured* SNR of at least 97dB.
> P.S. I'll be "sans computer" for the next few days, heading towards Ivan
> so won't be able to correspond on this for a while....
Good luck.
Cheers,
Erik
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