The frequency response of an ideal low-pass filter is 1 -1/2 < w <1/2 0 otherwise in

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The frequency response of an ideal low-pass filter is

1 -1/2 < w <1/2 0 otherwise in (–x,7] H(

(a) Find the impulse response h[n] of this filter. Is this filter causal?

(b) Suppose that the input of this filter x[n] has a DTFT  X(ejω) = H(ejω), what is the output of the filter y[n].

(c) According to the above result, does that mean that (h ˆ— h) [n] = h[n]?  Explain.

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