Time scaing in discrete time variable?

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The discussion centers on the relationship between the Discrete-Time Fourier Transform (DTFT) of a scaled signal y(n) and the original signal x(n). It is established that for y(n) = x(a*n), where a is an integer, the DTFT Y(e^jω) can be defined in terms of X(e^jω) using a specific formula. However, there is confusion regarding the case where y(n) = x(n/a), as this introduces zeros into the signal, complicating the definition of Y(e^jω). The participants are seeking clarity on whether Y(e^jω) can still be defined under these conditions. The conversation highlights the challenges of time scaling in discrete time variables.
ratn_kumbh
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I wanted to know , if x(n) has DTFT X(e^jw)
then can we define Y(e^jw) in terms of X(e^jw)?
where Y(e^jw)is DTFT of y(n)=x(a*n)or y(n)=x(n/a)
. Because in these cases terms of x(n) are either missed or '0' is padded up, so i think it won't be possible to define Y(e^jw) in terms of X(e^jw). can anybody tell i m right or not?
 
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OK, i got the answer for y(n)=x(a*n), where a is an integer. Y(e^j\omega) can be defined.

it is (1/a)*\sumX(exp(j(\omega+2\pim)/a)) where m varies from 0 to a-1.

But can anybody please tell; is it possible for y(n)=x(n/a) to define Y(e^j\omega). i am getting confused becoz of 0's which come in y(n) in this case.
 
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