# Frequency and temporal domain

Hi all,

I have a filter whose amplitude and phase response in terms of w(omega) is known to me which i calculated numerically. Hence, the value is known only for discrete values of w(omega).

Now, I want to know the output which this filter will produce on sending a temporal pulse(pulse in time domain) as my input.

I know i need to fourier transform my pulse( in the form summation(A(w)exp(iwt)) and then write the output as something like summation(A(w)*H(w)*exp(jwt)).

The question is how can i find the fourier transform (i.e find A(w) at those w where response of filter is known)

Hi all,

I have a filter whose amplitude and phase response in terms of w(omega) is known to me which i calculated numerically. Hence, the value is known only for discrete values of w(omega).

Now, I want to know the output which this filter will produce on sending a temporal pulse(pulse in time domain) as my input.

I know i need to fourier transform my pulse( in the form summation(A(w)exp(iwt)) and then write the output as something like summation(A(w)*H(w)*exp(jwt)).

The question is how can i find the fourier transform (i.e find A(w) at those w where response of filter is known)

Usually you model the transfer function as a polynomial of poles and zeros. You know the DC gain and you see that whenever the transferfunction slope changes +-20 dB/decade that you have a pole or zero at that place.

Edit: I think this is more commonly done in the laplace domain than in the fourier domain.

Hi all,

I have a filter whose amplitude and phase response in terms of w(omega) is known to me which i calculated numerically. Hence, the value is known only for discrete values of w(omega).

Now, I want to know the output which this filter will produce on sending a temporal pulse(pulse in time domain) as my input.

I know i need to fourier transform my pulse( in the form summation(A(w)exp(iwt)) and then write the output as something like summation(A(w)*H(w)*exp(jwt)).

The question is how can i find the fourier transform (i.e find A(w) at those w where response of filter is known)

Well, since you have a filter whose amplitude and phase response in terms of w(omega) is known you can use those discrete values to determine the increment in which they are increasing/decreasing at... although I am not exactly sure how you have these values/the manner in which you calculated them.

When you transform your pulse (you never directly mentioned what kind) yielding a 'continuous' waveform, simply plug that incrementing discrete values of frequency in it. Remember, convolution in the Time Domain is multiplication in the Frequency Domain.