QUESTION 2 In communication system, the tuned Radio Frequency signal x[n] that you receive is not x[n] but normally is y[n] due to the surrounding effect, where the expression is shown in the following equation 2 1 x[n] → x[n] -지n- 1] + 지n-2] → yln] The goal is to compute the inverse filter g[n] that recovers x[n] from y[n], so that g[n] undoes the effect of h[n]. The flow is as stated: x[n] → h[n] → y[n] → g[n] → x[n] Find G[z] and g[n]. Hint: The overall impulse response of the systems in cascade is the convolution of their impulse responses. So we want h[n]* g[n]= 8[n], which implies H[z]G[z] = 1.

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QUESTION 2
In communication system, the tuned Radio Frequency signal x[n] that you receive is not x[n] but
normally is y[n] due to the surrounding effect, where the expression is shown in the following
equation
1
x[n] → x[n] –5x[n – 1] +
교지n - 2] →
- y[n]
-
-
The goal is to compute the inverse filter g[n] that recovers x[n] from y[n], so that g[n] undoes
the effect of h[n]. The flow is as stated:
x[n] → h[n] → y[n] → g[n] → x[n]
Find G[z] and g[n].
Hint:
The overall impulse response of the systems in cascade is the convolution of their impulse
responses. So we want h[n]* g[n] = 8[n], which implies H[z]G[z] = 1.
Transcribed Image Text:QUESTION 2 In communication system, the tuned Radio Frequency signal x[n] that you receive is not x[n] but normally is y[n] due to the surrounding effect, where the expression is shown in the following equation 1 x[n] → x[n] –5x[n – 1] + 교지n - 2] → - y[n] - - The goal is to compute the inverse filter g[n] that recovers x[n] from y[n], so that g[n] undoes the effect of h[n]. The flow is as stated: x[n] → h[n] → y[n] → g[n] → x[n] Find G[z] and g[n]. Hint: The overall impulse response of the systems in cascade is the convolution of their impulse responses. So we want h[n]* g[n] = 8[n], which implies H[z]G[z] = 1.
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