Señales z

1)

2)a)

Para calcular el 0 de este sistema multiplicamos por Z/Z y luego nos fijamos que Z cancelaria numerador:

Entonces, esa Z seria 0.

b.i) The closer the pole is to the origin thefaster the impulse response decays both in the case of positive or negative poles, this is true for as long as the poles value is underneath 1, point where the impulse response becomes unstable andinstead begins to increase. ii) Changin the position of the pole we find that the magnitud of the frequency response becomes higher the farther we are from the origin, but in this case the location ofpeak is different if the pole is positive or negative. In the case of the positive the peak is fount in the origin within the magnitud of the frequency response, on the other hand the a negative polecreates two separate peaks at pi and -pi. iii)When the pole is on the right hand side (pole is positive) the closes point of the unit circle is fount on the coordinates (1,0), the closer the pole is tothe unit circle the narrower the magnitud’s peak becomes and maintains it’s position on (0,0) in the frequency magnitud response graph. iv) On the other hand when the pole is on the left hand side ofthe real line the closest point on the unit circle is (-1,0) and this affects the magnitud of the frequency response by causing it’s peaks to form at pi and -pi and get narrower on these positions thecloser it get to (-1,0). c) We can see that h[n] becomes constant and the H(e^jw) becomes a single impulse at position (0,0)

d) Observing h[n] we come to see that when we positionate the poleoutside the unit circle the impulse response begins to decay mirrorring the original decay inside the unit circle, so the last impulse response is decays last instead of first. e) We should keep the poleinside the unit circle so as to avoid that the system ‘blows up’

seeing as the continuous frequency response becomes unstable outside the unit circle.

3. a) The propierty is established in the...