Question

Consider a discrete-time, linear, time-invariant system with impulse response $h[n] = frac{sin(frac{pi}{3}n)}{pi n}$ (a) Determine the frequency response, $H(e^{jomega})$, of the system. (b) Sketch the magnitude response, $|H(e^{jomega})|$. Provide sufficient details in your sketch to convey the pattern. (c) What type of filter is this system—high-pass, low-pass, or band-pass? (d) Determine the output of the system in response to the signal $x[n] = frac{1}{2} + 3cos(frac{2pi}{7}n) - 5sin(frac{pi}{2}n)$

          Consider a discrete-time, linear, time-invariant system with impulse response
$h[n] = frac{sin(frac{pi}{3}n)}{pi n}$
(a) Determine the frequency response, $H(e^{jomega})$, of the system.
(b) Sketch the magnitude response, $|H(e^{jomega})|$. Provide sufficient details in your
sketch to convey the pattern.
(c) What type of filter is this system—high-pass, low-pass, or band-pass?
(d) Determine the output of the system in response to the signal
$x[n] = frac{1}{2} + 3cos(frac{2pi}{7}n) - 5sin(frac{pi}{2}n)$

$Consider a discrete-time, linear, time-invariant system with impulse response h[n] = fracsin(fracpi3n)pi n (a) Determine the frequency response, H(e^jomega), of the system. (b) Sketch the magnitude response, |H(e^jomega)|. Provide sufficient details in your sketch to convey the pattern. (c) What type of filter is this system—high-pass, low-pass, or band-pass? (d) Determine the output of the system in response to the signal x[n] = frac12 + 3cos(frac2pi7n) - 5sin(fracpi2n)$

Added by Inmaculada B.

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