Should any error appear when different types of convolutions on same vectors compared?

Hi,

I've got an assignment where I needed to check four types of convolution methods: linear, circular, Overlap add and Overlap save. Convolution performed between low pass filter and audio mp3 file. My assumption was that it shouldn't be any difference between results. However, I've got an errors as following: 1. Between linear and circular convolutions:

Error1_LinConvVSCircConv =

   4.1745e-12

2. Between linear and Overlap save/add convolutions:

Error2_LinConvVSOverlapSave =

   45.8247

Error3_LinConvVSOverlapAdd =

   45.8247

3. Between Overlap Save and Overlap Add convolutions:

Error4_OverlapSaveVSOverlapAdd =

   3.6087e-12

Error estimation was performed by mean percentage absolute error method:

% Error Calculation

Error1_LinConvVSCircConv = abs(mean(abs(pxx1 - pxx2)./pxx1)*100)

Error2_LinConvVSOverlapSave = abs(mean(abs(pxx1 - pxx3)./pxx1)*100)

Error3_LinConvVSOverlapAdd = abs(mean(abs(pxx1 - pxx4)./pxx1)*100)

Error4_OverlapSaveVSOverlapAdd = abs(mean(abs(pxx3 - pxx4)./pxx3)*100)

Comparison was performed in frequency domain. As I mentioned, received error was expected to be 0, and instead I got or very small value or 45%. Was my assumption wrong, or did I make mistake in a code?

[Greg]

Not sure what your pxx# variables are, but it sounds like you're asking why the convolution methods give different results.

I'm not an expert in convolution, but usually the whole point of having different methods for an algorithm is because they give different results. The job of an analyst is to know which one makes the most sense given the situation/data.

[DenisK]

Pxx1 - linear convolution Pxx2 - circular convolution Pxx3 - overlap save Pxx4 - overlap add