Simple Fourier transform problem

[asdf12312]

Homework Statement

Given x[n] with transform X(e^jw), find the Fourier transform in terms of X(e^jw).

x₁[n]=[0.9ⁿcos(0.6*pi*n)] * x[n-2]

Homework Equations

time shift: x[n-k] -> e^-jwkX(e^jw)
convolution: x[n] * h[n] -> X(w)H(w)
freq. shift: x[n]e^jw_cn -> X(e^w-w_c)

The Attempt at a Solution

I think that this problem has no solution because 0.9ⁿ has no Fourier transform (not summable). 0.9ⁿu[n] on the other hand does but not the same case here. am i doing this right?

 

[Svein]

I am at a loss to understand the problem. It seems to me as if the problem is to calculate the Fourier transform of a constant - or a sequence of constants. Is that correct?

 

[asdf12312]

yeah, I guess i didn't word it correctly. what it reads exactly is 'given a sequence x[n] with Fourier transform Xe^jw, determine the Fourier transform of the sequences in terms of Xe^jw.

 

[Svein]

'given a sequence x[n] with Fourier transform Xejw, determine the Fourier transform of the sequences in terms of Xejw.

Still does not make any sense to me...