Question

For a LTI discrete-time system whose impulse response is h[n]=αδ[n]+βδ[n−2],

Write down its frequency response, H(eʲω), as a function of ω.

Answer 1

The frequency response, H(e^jω), of the given LTI discrete-time system is α + βe^-jω2, calculated using the Fourier Transform of its impulse response.

Step-by-step explanation:

The question pertains to finding the frequency response, H(ejω), for a Linear Time-Invariant (LTI) discrete-time system with impulse response given by h[n]=αδ[n]+βδ[n−2]. The frequency response can be calculated using the Fourier Transform of the impulse response. Using the property of the delta function in the frequency domain, the Fourier Transform of δ[n] is 1, and the Fourier Transform of δ[n-k] is e−jωk. Therefore, we can write the frequency response as:

H(ejω) = α + βe−jω2

This equation expresses the frequency response as a function of angular frequency ω.