OutputResponse and RecurrenceFilter failure in WM10 with increased precision datasets

Question

Suppose I import sound from file into data list, like this:

(Set file name and path)

    nFileName = "p:\\TrueOscill250HzLongNoHiss128kSps.wav";

(Importing available wave info from file header)

    nSampleRate = Import[nFileName, "SampleRate"]

(Import raw samples into 1-dimensional list)

    data = Import[nFileName, {"Data", 1}]

(And amplify it)

    For[i = 1, i <= Length[data], i++, data[[i]] = data[[i]]*2.74892];

data

I design then LowPassFilter as follows:

 LowPass = Rationalize[ToDiscreteTimeModel[BesselFilterModel[{2, 12566.307}],1/nSampleRate, 
Method->{"BilinearTransform","CriticalFrequency"->12566.307,"StateSpaceConversion"->Automatic}],0]

and apply it over the data like this:

filteredsound = RecurrenceFilter[LowPass, data]]

The code runs smoothly and pretty fast, giving me low-pass filtered sound of 200,000 samples long, sampled 16 bit:

 ListPlot[Take[filteredsound, 2000], Joined -> True, DataRange -> {0, 1.63}]

But, once I tried to increase precision of data from default to say 16 digits, it only processes tiny portion of(100 samples or so) , and then numbers drop to zero with 10th at some huge power shown in red boxes in the output, and that's all :(

(*NB: I change precision of data at the import point, with SetPrecision[data,16], while `16 descriptors are added to all further numeric constants in the text)

De-Rationalizing filter doesn't change a thing. Rationalizing data inside the filter rather pushes the cores into infinite loop, eating memory at gygabytes rate per minutes and eventually runs out of it - and this is not due to Rationalization procedure itself.

OutputResponse behaves exactly the same way. Converting the transfer function into StateSpaceModel also doesn't seem to change anything.

Question: why simply changing precision from default to any other (even lower) ruins the symphony?!! Is there anything I can do to help it?

Note: you can download datafile (410KB) from http://www.2shared.com/audio/WtXidega/TrueOscill250HzLongNoHiss128kS.html

Thank you!

UPDATE1:

Bill kindly tested my problem and found no problem (see comments). However so far, I wasn't able to be that lucky. The code Bill provided does the same red box hell for me, and I don't know the reason why.

If anyone would like to test my notebook with own Mathematica, this can be downloaded from:

http://www.2shared.com/file/wVTQaGE_/playing_with_filters.html

Thank you!

Answer 1

I'm afraid that I can't reproduce your problem. Here is what I did: load in the data from your .wav file, which i had downloaded to my desktop. If you look at data[[1,1]] and test[[1,1]] you will see that they are the same but for the extra zeroes on the end.

data = Import["Desktop/TrueOscill250HzLongNoHiss128kSps.wav"]
test = SetPrecision[data, 16];
RecurrenceFilter[lowPass,  test[[1, 1]]]

Compare this to

RecurrenceFilter[lowPass,  data[[1, 1]]]

and the answers are the same (but for the extra digits).

I suspect though that you may be laboring under a false impression (that by setting the precision to be higher, you will get more accurate filtering). This is not really true, since the internal calculations are not done in 16-bit, they are done in machine precision arithmetic.