[SI-LIST] Re: Causality Condition -why real and imaginary part of a Frequency response of causal system need to be even and odd respectively
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: <piyush.nithmr@xxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Sat, 18 May 2013 08:54:54 -0700
Piyush,
Time-domain response must be a real function of time. If it is computed with
the inversed Fourier transform of the complex frequency domain response, the
TD response is be always real if the imaginary part of FD response is odd
and real part is even. It is the TD response realness condition. We do not
use negative frequency in analysis of interconnects, but the condition at DC
is useful to control quality of S-parameters: imaginary part and derivative
of real part of FD response must be zero at DC.
Best regards,
Yuriy
Yuriy Shlepnev, Ph.D.
President, Simberian Inc.
3030 S Torrey Pines Dr. Las Vegas, NV 89146, USA
Office +1-702-876-2882; Fax +1-702-482-7903
Cell +1-206-409-2368
Skype: Shlepnev
www.simberian.com
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-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of piyush bhatt
Sent: Saturday, May 18, 2013 3:47 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Causality Condition -why real and imaginary part of a
Frequency response of causal system need to be even and odd respectively
Hi All
An LTI system is causal if and only if h(t)=0 for t<0.
As derivation goes h(t)=h(t)sgn(t).Taking Freq transform both side and doing
some manipulations.We get to point that H(jw) = Hilbert transform of itself.
Then they say we can divide H(jw) into real and imaginary part.And real part
will be even function and imaginary part will be odd function.
Can you tell me why real part will be even function and imaginary part will
be odd function?
regards
Piyush
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