- #1

ace130

- 8

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- Homework Statement
- See System equation

- Relevant Equations
- N/A

Hello,

I am given an exercise in which I need to answer some questions, for this given system :

1/ find the impulse response h(n), then H(n)

2/ calculate the magnitude ||H(n)|| and tell the nature of the filter

3/ calculate Fc which is cutoff frequency when Fe=8Khz , and then calculate Fa at 10 dB of Attenuation

4/ find y(n) if the inpux x(n)=cos(2*pi*f*n)

My attempt was the following

- Applying a Dirac δ(n) as impulse I get

- Using Fourier transform for H(n)=FT[h(n)] I get

- Using trigonometry formula Cos(x)=1/2(e^jx+e^-jx) I found the magnitude

I am given an exercise in which I need to answer some questions, for this given system :

**y(n)=1/3[x(n)+x(n-1)]**1/ find the impulse response h(n), then H(n)

2/ calculate the magnitude ||H(n)|| and tell the nature of the filter

3/ calculate Fc which is cutoff frequency when Fe=8Khz , and then calculate Fa at 10 dB of Attenuation

4/ find y(n) if the inpux x(n)=cos(2*pi*f*n)

My attempt was the following

- Applying a Dirac δ(n) as impulse I get

**h(n)=1/3[δ(n)+δ(n-1)]**- Using Fourier transform for H(n)=FT[h(n)] I get

**H(n)=2/3[1+exp(2*pi*j*f)] ;**- Using trigonometry formula Cos(x)=1/2(e^jx+e^-jx) I found the magnitude

**||H(n)|| = |cos(pi*j*f)|**

BUT I still cannot understand what is cuttof frequency, or how to calculate it. And what is the meaning of 10 dB of Attenuation and How to calculate Fa.BUT I still cannot understand what is cuttof frequency, or how to calculate it. And what is the meaning of 10 dB of Attenuation and How to calculate Fa.