# [SI-LIST] Re: Impulse vs. Step Response?

• From: David Banas <DBanas@xxxxxxxxxx>
• To: 'steve weir' <weirsi@xxxxxxxxxx>, "'si-list@xxxxxxxxxxxxx'" <si-list@xxxxxxxxxxxxx>
• Date: Fri, 2 Sep 2011 09:48:08 -0700

```"You are not driving your transient with a step"

Why do you say that?
-db

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of steve weir
Sent: Thursday, September 01, 2011 6:40 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Impulse vs. Step Response?

As long as the frequency / time domain conversions cover a wide enough
frequency range the FD response and the FFT of the unit impulse should
match.  You are not driving your transient with a step so there should
not be a need to consider

U(w) = H(w)/jw

Steve.
On 9/1/2011 5:40 PM, David Banas wrote:
> Hi all,
>
> I've got a puzzler. I'm using this HSpice deck:
>
> .TITLE AC Sweep vs. Transient Correlation
>
> .OPTION
> + POST
> + PROBE
> + RUNLVL = 5
>
> Rin   in   out   r=1K
> Cout  out  0     c=1pF
> Rout  out  0     10MEG
>
> Vin   in   0     DC 1 AC 1
>
> .IC V(out) = 0
>
> .AC DEC 10 1 1G
> .TRAN 0.05n 1u 0 0.05n UIC
>
> .PROBE AC V(in) V(out)
> .PROBE TRAN V(in) V(out)
>
> .END
>
> to get both the transfer function, H(w), (.AC command) and the unit step
> response, u(t), (.TRAN command) of a simple RC LPF.
>
> Then, I take the FFT of the .TRAN output and compare it to the .AC output.
> And they match!
>
> I wasn't expecting a match, since all my textbooks say there's a `jw' factor
> relating the impulse response and the step response. That is:
>
>      U(w) = H(w)/jw
>
> So, when I compared the 2 spectra, I was expecting the FFT of my .TRAN output
> to have an extra 6dB/octave roll-off, as compared to the .AC output, due to
> the `w' in the denominator, above.
>
> Can anyone shed some light on this?
>
> Thanks,
>
> David Banas
> Sr. Member Technical Staff
> Altera
> +1-408-544-7667 - desk
>
> Did you know Altera offers over 150 free online technical training courses?
> Take one today!
>
>
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--
Steve Weir
IPBLOX, LLC
150 N. Center St. #211
Reno, NV  89501
www.ipblox.com

(866) 675-4630 Toll-free
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