Hi,
I have a problem on frequency response.
Suppose you have H(z)=B(z)/A(z), the transfer function of a digital
filter.
How do you calculate the ANALYTIC expression of the filter's impulse
response? Meaning, how do you get the analytic expressions for the
amplitude response and the phase response?
Fla.
Frequency response
Started by ●November 28, 2007
Reply by ●November 29, 20072007-11-29
rendoddi wrote:
> Suppose you have H(z)=B(z)/A(z), the transfer function of a digital
> filter.
> How do you calculate the ANALYTIC expression of the filter's impulse
> response?
Since your filter is IIR, the impluse response is defined by a
recurrence relationship and hence there is no analytic expression.
> Meaning, how do you get the analytic expressions for the
> amplitude response and the phase response?
There are however analytic expressions for these. They can be
obtained by substituting
-j omega
e
for z in H(z) and then taking the absolute value of H(e^-j w)
to get the magnitude response and arg of H(e^-j w) to get the
phase response.
Erik
--
-----------------------------
Erik de Castro Lopo
-----------------------------
"... a discussion of C++'s strengths and flaws always sounds
like an argument about whether one should face north or east
when one is sacrificing one's goat to the rain god."
-- Thant Tessman
> Suppose you have H(z)=B(z)/A(z), the transfer function of a digital
> filter.
> How do you calculate the ANALYTIC expression of the filter's impulse
> response?
Since your filter is IIR, the impluse response is defined by a
recurrence relationship and hence there is no analytic expression.
> Meaning, how do you get the analytic expressions for the
> amplitude response and the phase response?
There are however analytic expressions for these. They can be
obtained by substituting
-j omega
e
for z in H(z) and then taking the absolute value of H(e^-j w)
to get the magnitude response and arg of H(e^-j w) to get the
phase response.
Erik
--
-----------------------------
Erik de Castro Lopo
-----------------------------
"... a discussion of C++'s strengths and flaws always sounds
like an argument about whether one should face north or east
when one is sacrificing one's goat to the rain god."
-- Thant Tessman
