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What you want is basically a delay $$x(t-\tau) \Rightarrow e^{-j\omega \tau}$$ If you can live with $k$ being quantized you can simply use a single tap delay FIR filter. If you need more granularity you need to implement a fractional dealy. I would cascade a shot fractional FIR filter with a long single tab bulk delay filter. If $k$ is positive the filter ...

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