# A Linear Systems

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1. Nov 20, 2016

### 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?

2. Nov 21, 2016

### 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

3. Nov 21, 2016

### 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.

4. Nov 21, 2016

### 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

Thanks again.
Boudy

5. Nov 21, 2016

### Simon Bridge

Excellent - perhaps you could summarize what you found?

6. Nov 21, 2016

### 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