DSP problem

[Richello]

Dear Guys.
I have a causal system with the function:
y [n] = x[n] + 0.5 x[n-1]+ 0.9 y[n-1] for n>0;
Could you please tell me how to find the expression of the frequenc
response of the input X [(e^jw)] if: y[n]=S[n]+ S[n-1]; S; delta function,
Thnks,

[Rune Allnor]

On 26 Jan, 15:34, "Richello" <[email protected]> wrote:
> Dear Guys.
> I have a causal system with the function:
> y [n] = x[n] + 0.5 x[n-1]+ 0.9 y[n-1] *for n>0;
> Could you please tell me how to find the expression of the frequency
> response of the input X [(e^jw)] if: y[n]=S[n]+ S[n-1]; S; delta function,
> Thnks,

1) Compute the Z transform H(z) from the expression
2) Evaluate H(z) on the unit circle

Rune

[Tim Wescott]

On Tue, 26 Jan 2010 06:49:07 -0800, Rune Allnor wrote:

> On 26 Jan, 15:34, "Richello" <[email protected]> wrote:
>> Dear Guys.
>> I have a causal system with the function: y [n] = x[n] + 0.5 x[n-1]+
>> 0.9 y[n-1] Â*for n>0; Could you please tell me how to find the
>> expression of the frequency response of the input X [(e^jw)] if:
>> y[n]=S[n]+ S[n-1]; S; delta function, Thnks,
>
> 1) Compute the Z transform H(z) from the expression 2) Evaluate H(z) on
> the unit circle

0) If this is the homework that it sounds like, ask your prof.
If it isn't, or if he/she isn't helpful, mention the fact --
we get so many "do my homework for me, and make it snappy!"
posts that we sometimes don't always notice when someone is
being polite.
3) this page may help (it really needs updating):
<<http://www.wescottdesign.com/articles/zTransform/z-transforms.html>>
3-1/2) If you like that page, get my book!
<<http://www.wescottdesign.com/actfes/actfes.html>>

--
www.wescottdesign.com

[Vladimir Vassilevsky]

Tim Wescott wrote:
> On Tue, 26 Jan 2010 06:49:07 -0800, Rune Allnor wrote:
>
>
>>On 26 Jan, 15:34, "Richello" <[email protected]> wrote:
>>
>>>Dear Guys.
>>>I have a causal system with the function: y [n] = x[n] + 0.5 x[n-1]+
>>>0.9 y[n-1] for n>0; Could you please tell me how to find the
>>>expression of the frequency response of the input X [(e^jw)] if:
>>>y[n]=S[n]+ S[n-1]; S; delta function, Thnks,
>>
>>1) Compute the Z transform H(z) from the expression 2) Evaluate H(z) on
>>the unit circle
>
>
> 0) If this is the homework that it sounds like, ask your prof.

The classic AoE of Horowitz and Hill has a chapter about PLLs. It is a
very clear "how to" guide for beginners. Although they are looking from
analog perspective, same ideas can be applied to digital.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com