if i have the transfer function of magnitude response is there a method that i could calculate the frequency response?

For example the transfer function of the magnitude response is:

$ 3db \pm 3.5db $ for $|ν|<0.1$

$ <-55db $ for $|ν|<0.2$

  • 2
    $\begingroup$ That's not a transfer function, it's more of a filter specification. $\endgroup$
    – endolith
    Feb 25 '13 at 19:15

The frequency response of a system can be represented in polar format, in which the magnitude and phase response are considered separately:

$$ H(\omega) = |H(\omega)| \angle H(\omega) $$

With this representation, it should be clear that the magnitude response alone is not sufficient to characterize the full frequency response of a system; you have to know (or assume) what its phase response is also.

  • $\begingroup$ So there is no way to design a linear-phase lowpass filter if someone give me only the magnitude response? The exercise says also that the filter operate at a sample rate of 10 megasamples per second. I am confused. This is the frequency? $\endgroup$
    – pep
    Feb 25 '13 at 18:18
  • 2
    $\begingroup$ If you know that the filter is linear phase, then you can assume that for the system's phase response. The slope of the phase is proportional to the filter order. The sample rate refers to the time spacing between samples at the input of the filter. 10 million samples are input per second, so the time spacing between samples is $\frac{1}{10000000} = 0.1 \mathrm{ \mu sec}$. $\endgroup$
    – Jason R
    Feb 25 '13 at 18:52

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