b*****k
发帖数: 80 | 1 First,make a correction for 1):the input signal should be x(wt)
And the output is |H(jw)|x(wt+arg(H(jw))
The result 1) is the eigenfunction property of complex exponentials for
LTI systems. The input sinusoid wave starts from time -infinate,so there
is no Transient response.
When you make the comment like 2),you assume that the sinusoid wave starts from time zero,
i.e. input is x(t)u(t), it is a suddenly applied input,
so there is a transient response.
From the view point of 2),if u assume the i | m*****y
发帖数: 67 | 2 I agree with burdock's explaination. I think the result one is
viewing the system response in the frequency domain, so, it cares more
about the amplitude and phase of each frequency component. So, it is
a steady state analysis, which is like burdock said, consider the
system at time infinity.
The reslut 2, is dealling with the problem in time domain, here you
care about the response developed in a time series, which is from time
0- time infinite, so, you have to consider the effect of the syst
【在 b*****k 的大作中提到】
: First,make a correction for 1):the input signal should be x(wt)
: And the output is |H(jw)|x(wt+arg(H(jw))
: The result 1) is the eigenfunction property of complex exponentials for
: LTI systems. The input sinusoid wave starts from time -infinate,so there
: is no Transient response.
: When you make the comment like 2),you assume that the sinusoid wave starts from time zero,
: i.e. input is x(t)u(t), it is a suddenly applied input,
: so there is a transient response.
: From the view point of 2),if u assume the i
| m*****y
发帖数: 67 | 3 To periodic signals, you can always decompose the signal into
a sum of sine and cosin waves. So, the conclusion still hold.
time domain analysis done in frequency domain is just
superimpose the response of each hamonics in steady state.
(provide the system is stable!!!!)
For example, a signal of y=5sint+3sin2t+4sin3t is not a sine
signal, but:
you can find amplitude and phase shift for each of the sine, and
put them together to get the steady state response of the system.
if you are doing it in |
|
