how to see the frequency response of difference equation

Question

moonman 2011-12-15

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https://ww2.mathworks.cn/matlabcentral/answers/24055-how-to-see-the-frequency-response-of-difference-equation

评论： Mike Shane 2023-7-27

采纳的回答： Wayne King

Hi I am having the difference equation

y[n] = -0.9y[n-1] +x [n] -x [n-1]

I want to see its frequency response. What should i do

should i first convert it into Z-Form and then proceede Any ideas how to go abt it

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moonman 2011-12-15

can anybody guide me

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Answer 1

Wayne King 2011-12-15

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在 MATLAB Online 中打开

You can do the following:

   W = -pi:(2*pi)/8192:pi;
   [H,W] = freqz([1 -1],[1 0.9],W);
   plot(W,abs(H));

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Boom 2016-8-7

How did you get [1 0.9]? Why 1? and why 0.9? I see the equation has a negative 0.9, but not positive 0.9. Thanks

Mike Shane 2023-7-27

I hope by now you've figured it out, but for those who have the same question here is a simple explanation

y[n] = -0.9y[n-1] +x [n] -x [n-1] is the origianl expression

you have to put y terms on one side and x terms on one side, as below

y[n] + 0.9y[n-1] = x[n] -x[n-1]

now you can take the coefficients of y and x correctly, otherwise you are making a mistake while taking the coefficients

after that you'll get the below,

y has [1 0.9]

x has [1 -1]

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Answer 2

Wayne King 2011-12-15

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在 MATLAB Online 中打开

Hi, here you go. If you want to visualize the magnitude:

fvtool([1 -1],[1 0.9]);

If you want the complex-valued response:

   [H,W] = freqz([1 -1],[1 0.9]);
   plot(W,abs(H));

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moonman 2011-12-15

Hi king thanks

i have plotted it and changed the scale as well in fvtool but not getting the desired option

I have uploaded question here

can u kindly review it

http://www.4shared.com/photo/Y3A4z6qx/question.html

Thanks a lot

moonman 2011-12-15

plz guide me

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Answer 3

Wayne King 2011-12-15

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https://ww2.mathworks.cn/matlabcentral/answers/24055-how-to-see-the-frequency-response-of-difference-equation#answer_31556

在 MATLAB Online 中打开

Hi, that's because your graphs are showing the frequency response over [-pi,pi). You can use the 'whole' option in freqz()

    [H,W] = freqz([1 -1],[1 0.9],'whole');
    plot(W,abs(H));

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Answer 4

moonman 2011-12-15

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在 MATLAB Online 中打开

When i plot by this

 [H,W] = freqz([1 -1],[1 0.9],'whole');
    W = W-pi;
    plot(W,abs(H));

I sm getting the peak magnitude of 20 where as in all options peak is 20. why its so

Anyhow as per ur direction Option 'A' is correct am i right?

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Wayne King 2011-12-15

the book is wrong, the frequency response in magnitude should be 20 at pi radians/sample and -pi radians/sample

moonman 2011-12-15

Thanks king for explaining me

So the answer is 'A'. Am i right

but one of my frd has solved it and he is saying answer is D

and in email he wrote me

answer would be D as the value of H(0) = 0

Is he wrong.Plz tell me

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Answer 5

moonman 2011-12-15

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Thanks a lot King People on forum say that i only accept the answer of Wayne King U always explain in such a nice manner and move with me in question till the time i m not satisfied Thanks a lot and may God give u more knowledge so that u can enlighten more people