Obtaining Step Response for Linear Systems in Sinusoidal Frequency Domain

[Boudy]

The transfer function of a linear system is known in the sinusoidal frequency domain. It is given in its final form as a complex function of the angular frequency ω (not jω ). How to obtain the step response?
Thanks in advance.

 

[jasonRF]

In order to figure this out you need to know two things:

1. The relationship between the transfer function and the impulse response

2. The relationship between the impulse response and the step response

Hopefully this points you in the correct direction.

jason

 

[Simon Bridge]

How would you normally obtain the step response given the transfer function?
Note: If you have $s=j\omega$ - then $f(\omega) = f(-js)$ right?

If you prefer, you can Fourier transform back to time domain, then transfer to frequency domain like you are used to.

 

[Boudy]

Dear friends:
Thanks for your kind comments. In the meantime I could find a direct straightforward answer in the 1959 publication:

SIMPLIFED METHOD OF DETERMINING TRANSIENT RESPONSE
FROM FREQUENCY RESPONSE OF LINEAR NETWORKS AND SYSTEMS

By: Victor S . Levadi

Thanks again.
Boudy

 

[Simon Bridge]

Excellent - perhaps you could summarize what you found?

 

[Boudy]

In order to find the Impulse response , f(t), you need only the real part , R(ω),of the transfer function
F(j ω).
According to the mentioned paper:
f(t)= (2/π).∫R(ω).cos(tω) dω
The limits of integration are from zero to infinity.
Best regards