Serious doubt regarding Convolution !!!

[rag_perfect]

Hi Friends...
i got a serious doubt regarding convolution.
Plz refer to the 2nd paragraph, page no.4 of the following Technical paper ; Located at:



which illustrates that:

"Recall that in continuous-time, a convolution in time is equivalent to a multiplication in the frequency-domain but This property is true in discrete-time only if the signals are of infinite length or if at least one of the signals is periodic over the range of the convolution."
That means if we have two discrete-time signals which are non-periodic and finite length then convolution in time-domain is not equivalent to a multiplication in the frequency-domain???

In any DSP text-book,this concept has not explained!!!

Can anybody plz explain, why it happens so???[/b]

 

[zorro]

For finite length discrete-time sequences, the multiplication in the frequency-domain corresponds to circular convolution of the sequences, rather that linear (ordinary) convolution. Look for "circular convolution".
Regards
Z

 

[rag_perfect]

Thankx Zorro...
I got the your point but In continuous time we are not having this restriction.why it happens only for discrete time signals only. can u plz explain a bit more to me!!!

also in paper;he wrote that:
This property is true in discrete-time only if the signals are of infinite length.

i m also confused regarding this..... how can it reflects the time-frequency relationship of convolution???