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And the result of that modulation is then the sample sequence x of p of n.
And so it's, in effect, time compressing the sample sequence or the original sequence so that we throw out the sequence values which were equal to zero in the sample sequence.
And so the reconstructed signal is the convolution of the sample sequence and the filter impulse response.
And we know of course that the Fourier transform of the sample sequence is just simply this summation.
And then the sample sequence is simply a sequence which alternates, in this particular case, those sequence values was zero.
If the identity and order of objects in the test sequence matched that of the sample sequence, animals were rewarded for releasing a bar.
Consequently, the sample sequence is an impulse train whose values are samples of x of at integer multiples of capital N.
And recognizing that this decimated sequence is just simply related to the sample sequence this way, these two become equal under a substitution of variables.
Thus, we turned to multiple-electrode data from a previously published experiment with a unique design8, 9. Monkeys determined whether a test sequence of two objects matched a sample sequence presented seconds earlier.
And then we have the sampling impulse train, or sampling sequence, and it's the modulation or product of these two that gives us the sample sequence x of p of n.
In particular what we want to develop is how the Fourier transform of the decimated sequence is related to the Fourier transform of the original sequence or the sample sequence.
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CEO of Professional Science Editing for Scientists @ prosciediting.com