# Why only take 205 sample when using a sample rate of 10khz or 8khz?

I've often seen i my DSP book, that when they record a sound, they use a sample rate at 10khz or 8 khz, which makes sense since the fs is 2 times bigger than the sampling signals max freq.
What i don't understand is why they only take 205 samples, rather than 10000 samples or 8000 samples, wouldn't each sample be "unperiodic"??.. What is the magic behind the number 205 ???

EDIT: I know they aren't able to sample 8000 times here, but why not take 320 samples then?? than just 205??

Example:

Estimating DTMF Tones with the Goertzel Algorithm

The minimum duration of a DTMF signal defined by the ITU standard is 40 ms. Therefore, there are at most 0.04 x 8000 = 320 samples available for estimation and detection. The DTMF decoder needs to estimate the frequencies contained in these short signals.

One common approach to this estimation problem is to compute the Discrete-Time Fourier Transform (DFT) samples close to the seven fundamental tones. For a DFT-based solution, it has been shown that using 205 samples in the frequency domain minimizes the error between the original frequencies and the points at which the DFT is estimated.

Nt = 205; original_f = [lfg(:);hfg(:)] % Original frequencies original_f =

     697
770
852
941
1209
1336
1477


k = round(original_f/Fs*Nt); % Indices of the DFT estim_f = round(k*Fs/Nt) % Frequencies at which the DFT is estimated estim_f =

     702
780
859
937
1210
1327
1483


To minimize the error between the original frequencies and the points at which the DFT is estimated, we truncate the tones, keeping only 205 samples or 25.6 ms for further processing.

tones = tones(1:205,:);

• Reference please? Where did you see that people only use 205 samples ?? – Hilmar Nov 9 '13 at 23:02