Consider a filter with frequency response

or a sinc function in frequency.

(a) Find the impulse response h(t) of this filter. Plot it and indicate whether this filter is a causal system or not.

(b) Suppose you wish to obtain a band-pass filter G(jΩ) from H(jΩ). If the desired center frequency of |G(jΩ)| is 5, and its desired magnitude is 1 at the center frequency, how would you process h(t) to get the desired filter? Explain your procedure.

(c) Use symbolic MATLAB to find h(t), g(t) and G(jΩ). Plot |H(jΩ)|, h(t), g(t) and |G(jΩ)|. 

Compute the Fourier transform using the integration function.

Transcribed Image Text:

sin(r2) H(jN)